dynamic modeling / control engineering dynamical systems and

Control Systems Engineering LaboratoryCSEL

BDE 598 Fundamentals of Biological DesignFall, 2011

Dynamic Modeling / Control Engineering

Daniel E. Rivera

Control Systems Engineering LaboratorySchool for the Engineering of Matter, Transport, and Energy (SEMTE)

Ira A. Fulton Schools of EngineeringArizona State University

http://[email protected]


BDE 598 Fundamentals of Biological DesignFall, 2011

Daniel E. Rivera

Control Systems Engineering LaboratorySchool for the Engineering of Matter, Transport, and Energy (SEMTE)

Ira A. Fulton Schools of EngineeringArizona State University

http://[email protected]

Dynamical Systems and Control Engineering: How Can These Impact Behavioral Interventions?


About Daniel E. Rivera

Education:

- B.S. ChE degree from the Univ. of Rochester (1982)- M.S. ChE degree from the Univ. of Wisconsin (1984)- Ph.D. from California Institute of Technology (1987)

Positions Held:

- Associate Research Engineer, Shell Development Co., (1987 - 1990)- Professor of Chemical Engineering, Arizona State University (1990 - present)

Other Professional Activities:

- Senior Member, AIChE and IEEE- Chair, IEEE-Control Systems Society, Technical Committee on System Identification and Adaptive Control (TC-SIAC)

3

Control Systems Engineering LaboratoryCSEL Our Logo (in detail)

4

http://csel.asu.edu/health

Control Systems Engineering LaboratoryCSEL Current Projects in Behavioral Health

• R21DA024266*, “Dynamical systems and related engineering approaches to improving behavioral interventions,” NIH Roadmap Initiative Award on Facilitating Interdisciplinary Research Via Methodological and Technological Innovation in the Behavioral and Social Sciences, with L.M. Collins, Penn State, co-PI.

• K25DA021173*, “Control engineering approaches to adaptive interventions for fighting drug abuse,” Mentors: L.M. Collins (Penn State) and S.A. Murphy (Michigan).

*Projects funded by the US National Institutes of Health: NIDA (National Institute on Drug Abuse) and OBSSR (Office of Behavioral and Social Sciences Research).

5


Control Systems Engineering LaboratoryCSEL Current Research Activities

6

• Dynamical systems modeling, system identification, and control engineering frameworks for delivering optimized time-varying adaptive interventions.

• Analysis of smoking activity and cessation as closed-loop dynamical systems (M. Piper, T. Baker, and M. Fiore, U of Wisconsin-Center for Tobacco Research and Intervention).

• Dynamic modeling and optimization of a preventive intervention for excessive weight gain during pregnancy (D. Downs and J. Savage, Penn State University; D. Thomas, Montclair State University).

• Dynamic modeling of diary data from a low-dose naltrexone intervention in fibromyalgia patients; feasibility of system identification modeling and Model Predictive Control for pain treatment interventions (J. Younger, Stanford University School of Medicine).

Control Systems Engineering LaboratoryCSEL About this lecture

• Goal is to discuss how dynamical systems and engineering control theory can improve the design and implementation of time-varying adaptive interventions, and illustrate this in various application settings.

• Talk will be focused on describing important concepts; it will not be a comprehensive survey.

• We will attempt to establish connections between behavioral health, quantitative methods in the behavioral and social sciences, and engineering, discussing the opportunities (and challenges) that these present to the behavioral scientist, the methodologist, and the engineer.

7

Control Systems Engineering LaboratoryCSEL Lecture Outline

• Fundamentals of adaptive interventions

• What is meant by control systems engineering, and how can these concepts improve behavioral interventions?

- Shower operation as a closed-loop dynamical system.

- Analysis and design of a hypothetical time-varying adaptive intervention inspired by the Fast Track program.

• Some additional illustrations

- Fibromyalgia intervention using low-dose naltrexone.

- Dynamic modeling of a weight loss intervention.

- Mediational modeling of smoking cessation.

8

Control Systems Engineering LaboratoryCSEL Behavioral Interventions

• Behavioral interventions aim to prevent and treat disease by reducing unhealthful behaviors and promoting healthful ones.

• These play an increasingly prominent role in a wide variety of areas of public health importance, among them drug and alcohol abuse, cancer, mental health, obesity, HIV/AIDS, and cardiovascular health.

• Interventions can include components that are either pharmacological (e.g., naltrexone, buproprion) or behavioral (e.g., motivational interviewing, cognitive behavioral therapy, relaxation exercises) in nature. Likewise, these interventions can be designed to address multiple outcomes (e.g., co-morbidities).

• Adaptive interventions (in contrast to fixed interventions) represent an important emerging paradigm for delivering behavioral interventions intended to address chronic, relapsing disorders (Collins, Murphy, and Bierman, Prevention Science, 5, No. 3, 2004).

9


Basic Components of Adaptive Interventions(Collins, Murphy, and Bierman, Prevention Science, 5, No. 3, 2004)

• The assignment of a particular dosage and/or type of treatment is based on the individual’s values on variables that are expected to moderate the effect of the treatment component; these are known as tailoring variables.

• In a time-varying adaptive intervention, the tailoring variable is assessed periodically, so the intervention is adjusted on an on-going basis.

• Decision rules translate current and previous values of tailoring variables into choice(s) of treatment and their appropriate dosage.

10


Adaptive Intervention Benefits (Collins, Murphy, and Bierman, Prevention Science, 5, No. 3, 2004)

• An effective adaptive intervention strategy may result in the following advantages over fixed interventions:

– Reduction of negative effects (i.e., stigma),– Reduction of inefficiency and waste,– Increased compliance,– Enhanced intervention potency.

• Adaptive interventions can serve as an aid for disseminating efficacious interventions in real-world settings.

11


Adaptive Intervention Simulation (inspired by the Fast Track Program, Conduct Problems Prevention Research Group)

• A multi-year program designed to prevent conduct disorder in at-risk children.

• Frequency of home-based counseling visits assigned quarterly to families over a three-year period, based on an assessed level of parental functioning.

• Parental function (the tailoring variable) is used to determine the frequency of home visits (the intervention dosage) according to the following decision rules:

- If parental function is “very poor” then the intervention dosage should correspond to weekly home visits,

- If parental function is “poor” then the intervention dosage should correspond to bi-weekly home visits,

- If parental function is “below threshold” then the intervention dosage should correspond to monthly home visits,

- If parental function is “at threshold” then the intervention dosage should correspond to no home visits.

12


• The assigned dosage (frequency of counseling visits) decreases as the value of the tailoring variable (parental function) increases, as prescribed by the decision rules.

Parental Function - Counselor Home Visits Adaptive Intervention Single Participant Family Illustration (Ideal)

13

6 0 6 12 18 24 30 360

50

100

Pare

ntal

func

tion

(%)

Parental functionParental function goal

6 0 6 12 18 24 30 36No Visit

Monthly

Bi Weekly

Weekly

Time (month)

Inte

rven

tion

dosa

ges


Parental Function - Counselor Home Visits Adaptive Intervention Single Participant Family Illustration (Less Ideal)

14

6 0 6 12 18 24 30 360

50

100

time (Month)

Pare

ntal

func

tion

(%)

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


} offset!

Single participant family scenario. Offset (where parental function fails to reach a desired goal at the end of the intervention) occurs in this case.


Control Systems Engineering

The field that relies on dynamical models to develop mechanisms for adjusting system variables so that their behavior over time is transformed from undesirable to desirable,

• Open-loop: refers to system behavior without a controller or decision rules (i.e., MANUAL operation).

• Closed-loop: refers to system behavior once a controller or decision rule is implemented (i.e., AUTOmatic operation).

A well-tuned control system will effectively transfer variability from an expensive system resource to a less expensive one.

15

Control Systems Engineering LaboratoryCSEL Control Systems Engineering

• The field that relies on dynamical models to develop algorithmsfor adjusting system variables so that their behavior over time is transformed from undesirable to desirable.

• Control engineering plays an important part in many everyday life activities. Some examples of control systems engineering :

- Cruise control and climate control in automobiles,

- The “sensor reheat” feature in microwave ovens,

- Home heating and cooling,

- The insulin pump for Type-I diabetics,

- “Fly-by-wire” systems in high-performance aircraft,

- Homeostasis

• A well-tuned control system will effectively transfer variability from the more “expensive” system resource to a less expensive one.

16

Control Systems Engineering LaboratoryCSEL Open-Loop (Manual) vs.

Closed-Loop (Automatic) Control

• Climate control in automobiles is one of many illustrations of closed-loop control that can be found in daily life.

Manual AUTOmatic

17

Control Systems Engineering LaboratoryCSEL The “Shower” Problem

Controlled variables (y): Temperature, water flow

Manipulated Variables (u): Hot and Cold Water Valve

Positions

Disturbances (d):Inlet Water Flows,

TemperaturesThe presence of

“transportation lag”adds delay to the response

of this system

Objective: Adjust hot and cold water flows in response to changes in shower temperature and outlet flow caused by external factors.

18

Control Systems Engineering LaboratoryCSEL Signal Definitions

Controlled Variables (y; outcomes): system variables that we wish to keep at a reference value (or goal), also known as the setpoint (r).

Manipulated Variables (u): system variables whose adjustment influences the response of the controlled variable; their value is determined by the controller/decision policy.

Disturbance Variables (d): system variables that influence the controlled variable response, but cannot be manipulated by the controller; disturbance changes are external to the system.

19

Both manipulated (u) and disturbance (d) variables can be viewed as independent (x) variables; disturbances are exogenous, while

manipulated variables can be adjusted by the user.


0 2 4 6 8 10 12 14 16 18 2028

29

30

31

32

33

34

Time (seconds)

Show

er T

empe

ratu

re (d

egre

es C

elsi

us)

Open LoopNo Disturbance

0 5 10 15 20 25 300.5

0

0.5

1

1.5

Time

Hot

Wat

er V

alve

(per

cent

ope

n)

The “Shower” ProblemOpen Loop Disturbance Response

Controlled variable (y): Temperature

Manipulated Variable (u): Hot Water Valve Position

Disturbance (d):Inlet Water Flow

Consider the change in shower temperature caused by a sudden drop in inlet water flowrate as a result of a disturbance (e.g., sprinklers being activated).

20

0 2 4 6 8 10 12 14 16 18 201

1.5

2

2.5

Time (seconds)

Inle

t Flo

wra

te (l

iters

/min

)

Control Systems Engineering LaboratoryCSEL Control System Components

Sensors (i.e., assessment instruments): devices needed to measure the controlled and (possibly) the disturbance variables.

Actuators: devices needed to achieve desired settings for the manipulated variables

Controllers (i.e., clinical decision rules). These relate current and prior controlled variable, manipulated variable, and disturbance measurements to a current value for the manipulated variable.

21

Control Systems Engineering LaboratoryCSEL Feedback Control Strategy

• In feedback control:

- the measured controlled variable (y) is compared to a goal (also known as a reference setpoint r),

- a control error e (= r - y), representing the discrepancy between y and r is calculated.

- a control algorithm determines a current value for the manipulated variable (u) based on current and previous values of e and u.

22


The “Magic” of Feedback(Adapted from K. J. Åström’s “Challenges in Control Education” plenary talk at the 7th IFAC

Symposium on Advances in Control Education, Madrid, Spain, June 21-23, 2006).

Feedback has some amazing properties:

• can create good systems from bad components,

• makes a system less sensitive to disturbances and component variations,

• can stabilize an unstable system,

• can create desired behavior, for example, linear behavior from nonlinear components.

Major drawback: it can cause instability if not properly tuned.

23


Hot

Controller

T

Temp. setpoint

Sensor

24

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (seconds)

Hot

Wat

er V

alve

(per

cent

ope

n)

Closed LoopNo Disturbance

0 2 4 6 8 10 12 14 16 18 201

1.5

2

2.5

Time (seconds)

Inle

t Flo

wra

te (l

iters

/min

)

Disturbance:Inlet Water Flow

Cold

0 2 4 6 8 10 12 14 16 18 2028

29

30

31

32

33

34

Time (seconds)

Show

er T

empe

ratu

re (d

egre

es C

elsi

us)

Closed LoopOpen LoopSetpoint

Manipulated:Hot Water ValvePosition

Controlled: Temperature

Actuator

Shower Problem: Closed-Loop Feedback Control(Good: Stable, Smooth Responses)


0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (seconds)

Hot

Wat

er V

alve

(per

cent

ope

n)

Closed LoopNo Disturbance

0 2 4 6 8 10 12 14 16 18 2028

29

30

31

32

33

34

Time (seconds)

Show

er T

empe

ratu

re (d

egre

es C

elsi

us)

Closed LoopOpen LoopSetpoint

Hot

Controller

T

Temp. setpoint

Sensor

Shower Problem: Closed-Loop Feedback Control(Bad: Unstable, Oscillatory Responses)

25

0 2 4 6 8 10 12 14 16 18 201

1.5

2

2.5

Time (seconds)

Inle

t Flo

wra

te (l

iters

/min

)

Disturbance:Inlet Water Flow

Cold

Manipulated: Hot Water ValvePosition

Controlled: Temperature

Actuator


Open-Loop(Before Control)

Closed-LoopControl

Temperature Deviation

(Measured Controlled Variable)

Hot Water Valve Adjustment

(Manipulated Variable)

From Open-Loop Operation to Closed-Loop Control (Stochastic Viewpoint)

The transfer of variance from an expensive resource to a cheaper one is one of the major benefits of control systems engineering

26


Adaptive Intervention Simulation (inspired by the Fast Track Program, Conduct Problems Prevention Research Group)

• A multi-year program designed to prevent conduct disorder in at-risk children.

• Frequency of home-based counseling visits assigned quarterly to families over a three-year period, based on an assessed level of parental functioning.

• Parental function (the tailoring variable) is used to determine the frequency of home visits (the intervention dosage) according to the following decision rules:

- If parental function is “very poor” then the intervention dosage should correspond to weekly home visits,

- If parental function is “poor” then the intervention dosage should correspond to bi-weekly home visits,

- If parental function is “below threshold” then the intervention dosage should correspond to monthly home visits,

- If parental function is “at threshold” then the intervention dosage should correspond to no home visits.

27


Parental Function Feedback Loop Block Diagram*(to decide on home visits for families with at-risk children)

28

From Rivera, D.E., M.D. Pew, and L.M. Collins, “Using engineering control principles to inform the design of adaptive interventions: a conceptual introduction,” Drug and Alcohol Dependence, Special Issue on

Adaptive Treatment Strategies, Vol. 88, Supplement 2, May 2007, Pages S31-S40.

(Open-Loop)

(Closed-LoopSystem)


Parental function PF(t) is built up by providing an intervention I(t) (frequency of home visits), that is potentially subject to delay, and is depleted by potentially multiple disturbances (adding up to D(t)).

Parental Function - Home Visits Adaptive Intervention as an Inventory Control Problem

29

PF (t + 1) = PF (t) + KI I(t− θ)−D(t)

Intervention

Dosage

(Manipulated

Variable)

( Delay Time)

Parental Function

(Controlled

Variable)

Exogenous

Depletion

Effects

(Disturbance

Variable)

!(Gain)

Outflow

Controller/

Decision

Rules

Measured Parental

Function

(Feedback Signal)

Parental Function Target

(Setpoint Signal)

Inflow

PFGoal

I(t)

PFmeas(t)

PF (t)D(t)

KI


Parental Function “Open Loop” Dynamics

PF(t+1) = PF(t) + KI I(t – θ) - D(t) t = time, expressed as an integer reflecting review instance

KI = intervention gain

D(t) = depletion

I(t) = intervention dosage

θ = delay time

Parental Function (End of Review Instance)

! = Parental Function (Start of Review Instance)

! + Parental Function Contributed by Intervention

! - Parental Function Depletion

30


6 0 6 12 18 24 30 36

0

20

40

60

80

100

Time (month)

PF (%

)

6 0 6 12 18 24 30 36

No Visits

Monthly

Bi Weekly

Weekly

Time (month)

Inte

rven

tion

Dos

age

MonthlyBi WeeklyWeekly

Parental Function Dynamics“Open Loop” Response

• Variations in intervention dose response for a single participant family

31


6 0 6 12 18 24 30 360

20

40

60

80

100

Time (month)

PF (%

)

Participant 1:( , KI ) = (0,0.15 )Participant 2:( , KI ) = (0,0.1815 )Participant 3:( , KI ) = (0,0.1275 )Participant 4:( , KI ) = (1,0.15 )Participant 5:( , KI ) = (1,0.1275 )

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

Time (month)

Inte

rven

tion

Dos

age

• Between-participant variability as a result of individual dynamic characteristics

32

Parental Function Dynamics“Open Loop” Response (Continued)


6 0 6 12 18 24 30 36100

50

0

Time (month)

PF (%

)

6 0 6 12 18 24 30 360135

10

Time (month)

Dep

letio

n (D

(t))

D(t)=1D(t)=3D(t)=5D(t)=10

• Parental function change as a result of step changes in outflow (the disturbance variable) of varying magnitudes.

33

Parental Function Dynamics“Open Loop” (Continued)


High Depletion (D(t) = 5)No Depletion (D(t) = 0)

Single participant family scenario. The goal is for the family to attain a 50% proficiency (dashed line) on a parental function scale at the conclusion of the three year intervention. Offset (where parental function fails to meet goal) is more pronounced when high depletion is present.

Adaptive Intervention Using “IF-THEN” Rules

34

6 0 6 12 18 24 30 360

50

100

time (Month)

Pare

ntal

func

tion

(%)

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


6 0 6 12 18 24 30 360

50

100

time (Month)

Pare

ntal

func

tion

(%)

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


} offset!


Multiple participant family simulation. The goal is for each family to attain a 50% proficiency (dashed line) on a parental function scale at the conclusion of the three year intervention. Offset is observed in all participant families.

Adaptive Intervention Using “IF-THEN” Rules

35

6 0 6 12 18 24 30 36

123450

50

100

time (Month)Participant Index

PF (%

)

6 0 6 12 18 24 30 36

12345No VisitsMonthly

Bi WeeklyWeekly


Inte

rven

tion

Control Systems Engineering LaboratoryCSEL Engineering Control Design

• Based on a knowledge of the open-loop model, an optimized feedback decision algorithm (i.e., the “controller”) can be designed for this system.

• In general, the sophistication of the controller will be a function of the complexity of the model and the desired performance requirements.

• We consider a tuning rule for a Proportional-Integral Derivative (PID) feedback controller for an “integrating” system which relies on the concept of Internal Model Control (IMC; Morari and Zafiriou, 1987).

• User supplies the intervention gain (KI) and delay (θ) and a setting for an adjustable parameter (λ) that defines the speed of response and robustness of the control system.

36

Control Systems Engineering LaboratoryCSEL Control Design Requirements

• Stability. Many different notions exist, but “BIBO” stability (bounded inputs resulting in bounded outputs) is usually sufficient.

• No offset. Control error e = r - y should go to zero (meaning that the controlled variable should reach the goal) at a finite time.

• Minimal effect of disturbances on controlled variables.

• Rapid, smooth (i.e., non-oscillatory) responses of controlled variables to setpoint changes.

• Large variations (“moves”) in the manipulated variables should be avoided.

• Robustness, that is, performance should display little sensitivity to changes in operating conditions and model parameters.

37


Proportional-Integral-Derivative (PID) with FilterController Summary

Current Dosage = Previous Dosage + Scaled Corrections using Current and Prior Control Errors + Scaled Previous Dosage Change

• K1, K2, K3, and K4 are tuning constants in the controller;

• e(t) = (PF(t) - PFGoal), where PFGoal is the setpoint (“goal”) and e(t) is the control error.

• The dosage decision I(t) is a continuous value between 0 and 100%, but for purposes of this example it is quantized into the nearest of the four dosage levels (I weekly , I biweekly , I monthly, 0).

I(t) = I(t-1) + K1e(t) + K2 e(t-1) + K3 e(t-2) + K4 (I(t-1)-I(t-2))

38


K1 = TKcτF +T

�1 + T

τI+ τD

T

�K2 = − TKc

τF +T

�1 + 2τD

T

�K3 = KcτD

τF +T K4 = τFτF +T

Kc = 2(β+λ)+τKI(2β2+4βλ+λ2) τI = 2(β + λ) + τ τD = 2τ(β+λ)

2(β+λ)+τ τF = βλ22β2+4βλ+λ2

β = τ = θ2

Internal Model Control-Proportional Integral Derivative (IMC-PID) Controller Tuning Rules (Rivera et al., 1986)

User supplies open-loop model gain (KI), delay (θ) and the adjustable parameter (λ); T is the review period

I(t) = I(t− T ) + K1e(t) + K2e(t− T ) + K3e(t− 2 T ) + K4(I(t− T )− I(t− 2T ))

39


IMC-PID control (λ = 3; moderate speed)“IF-THEN” rules

36 month intervention reviewed at quarterly intervals. Offset problem is eliminated by more judicious assignment of intervention dosages during the course of the intervention.

Controller/Decision Rule Comparison, High Depletion Rate (D(t) = 5)

40

6 0 6 12 18 24 30 360

50

100

time (Month)

Pare

ntal

func

tion

(%)

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


6 0 6 12 18 24 30 360

50

100

time (Month)

Par

enta

l fun

ctio

n (%

)

Lambda=3

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges



6 0 6 12 18 24 30 360

50

100

time (Month)

Pare

ntal

func

tion

(%)

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


IMC-PID Controller, High Depletion Rate,Various Controller Speeds (determined by λ)

Fast (λ = 1)

Moderate (λ = 3)

Slow (λ = 5)

41

6 0 6 12 18 24 30 360

50

100

time (Month)

Par

enta

l fun

ctio

n (%

)

Lambda=3

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


6 0 6 12 18 24 30 360

50

100

time (Month)

Par

enta

l fun

ctio

n (%

)

Lambda=5

6 0 6 12 18 24 30 36No Visits

Monthly

Bi Weekly

Weekly

time (Month)

Inte

rven

tion

dosa

ges


Control Systems Engineering LaboratoryCSEL IF-THEN vs. IMC-PID Comparison

42

• The closed-loop response of five participant families is evaluated using a controller model based on an average (“nominal”) effect. The “transfer of variance” concept is illustrated here.

The intervention dosage is adapted at quarterly intervals over a 36-month time period. The goal is for each family to attain a 50% proficiency (dashed line) on a parental function scale at the conclusion of the three year intervention.

“IF-THEN” Decision Rules IMC-PID control (λ = 3)

6 0 6 12 18 24 30 36

123450

50

100


PF (%

)

6 0 6 12 18 24 30 36


Bi WeeklyWeekly


Inte

rven

tion

6 0 6 12 18 24 30 36

123450

50

100


PF (%

)

6 0 6 12 18 24 30 36


Bi WeeklyWeekly


Inte

rven

tion

Control Systems Engineering LaboratoryCSEL IF-THEN vs. IMC-PID Comparison

(Continued)

43

• The closed-loop response of five participant families is evaluated using a controller model based on an average (“nominal”) effect. The “transfer of variance” concept is illustrated here.

The intervention dosage is adapted at quarterly intervals over a 36-month time period. The goal is for each family to attain a 50% proficiency (dashed line) on a parental function scale at the conclusion of the three year intervention.

IMC-PID control (λ =5)IMC-PID control (λ = 1)

6 0 6 12 18 24 30 36

123450

50

100


PF (%

)

6 0 6 12 18 24 30 36


Bi WeeklyWeekly


Inte

rven

tion

6 0 6 12 18 24 30 36

123450

50

100


PF (%

)

6 0 6 12 18 24 30 36


Bi WeeklyWeekly


Inte

rven

tion


Additional Topics

• Feedforward control action: if disturbance variables can be measured, these can be incorporated as tailoring variables in the controller in a feedforward (i.e., anticipative) manner.

• Model predictive control: control design paradigm that features advanced adaptive functionality such as constraint handling, decision-making involving multiple outcomes, and formal assignment of intervention dosages to discrete-valued categories.

• System identification: examines how to empirically obtain dynamical models from data; also enables simplifying other model types (e.g., system dynamics, agent-based models) into forms amenable for control.

44

Control Systems Engineering LaboratoryCSEL Fibromyalgia Intervention Study

• Fibromyalgia (FM) is a condition characterized by chronic pain; its etiology is not well understood. Daily report data for a representative participant in a pilot study using low-dose naltrexone (LDN) as treatment for fibromyalgia is shown above.

• Deshpande, S., N. Nandola, D.E. Rivera, and J. Younger, “A control engineering approach for designing an optimized treatment plan for fibromyalgia,” 2011 American Control Conf., San Francisco, CA, June 29 - July 1, 2011.

45

0 10 20 30 40 50 60 70 800

50

100

Res

pons

e

0 10 20 30 40 50 60 70 800

20

40

Res

pons

e

0 10 20 30 40 50 60 70 8060

80

100

Time (Days)

Res

pons

e

Stress

Anxiety

Mood

0 10 20 30 40 50 60 70 800

50

100

Resp

onse

Daily Diary Variables

0 10 20 30 40 50 60 70 800

50

100

Resp

onse

Overall Sleep

FM Symptoms

0 10 20 30 40 50 60 70 800

5

Stre

ngth

(mg)

0 10 20 30 40 50 60 70 800

0.5

1

Time (days)

Plac

ebo

DrugPlacebo

J. Younger and S. Mackey (Stanford School of Medicine) “Fibromyalgia symptoms are reduced by low-dose naltrexone: a pilot study, Pain Medicine, 10(4):665-672, 2009.

Control Systems Engineering LaboratoryCSEL Dynamic Modeling Challenges

• Limited a priori knowledge regarding the dynamics of the system.

• Secondary data analysis on fixed protocol that was not designed for dynamical system analysis.

• No convenient means to generate a cross-validation dataset.

• Determinations of system input, outputs, and disturbances somewhat arbitrary

- Outputs (y): Typical symptom indicators such as FM symptoms, overall sleep, highest pain

- Inputs (u,d): LDN and placebo as primary inputs (u); exogeneous effects such as anxiety or stress as disturbances (d).

46


• Data Preprocessing: The data is preprocessed for missing data entries and is smoothened using a three day moving average.

• Discrete-time parametric modeling: The filtered data is fitted to a AutoRegressive with eXternal input (ARX-[na nb nk]) parametric model:

• Simplification to a continuous time model: The step responses from the ARX model are individually fit to a parsimonious continuous-time dynamical model of the form:

System Identification Procedure

47

τ2 d2y

dt2+ 2ζτ

dy

dt+ y(t) = Kp

�u(t) + τa

du

dt

�

y(t) + ... + anay(t− na) = b11u1(t− nk) + ... + bnb1u1(t− nk − nb + 1)...

+ b1iui(t− nk) + ... + bnbiui(t− nk − nb + 1)...

+ b1nuunu(t− nk) + ... + bnbnuunu(t− nk − nb + 1) + e(t)

Control Systems Engineering LaboratoryCSEL Multi Input Model Construction

• The multi-input ARX-[2 2 1] models (with respective input(s)) are:

- Model 1 (Drug)

- Model 2 (Drug, Placebo)

- Model 3 (Drug, Placebo, Anxiety)

- Model 4 (Drug, Placebo, Anxiety, Stress)

- Model 5 (Drug, Placebo, Anxiety, Stress, Mood)

48

10 20 30 40 50 60 70 80

10

20

30

40

50

60

70

80

90y1. (sim)

y1

model5%73.9943

10 20 30 40 50 60 70 80

10

20

30

40

50

60

70

80

90y1. (sim)

y1

model4%71.8943

10 20 30 40 50 60 70 80

10

20

30

40

50

60

70

80

90y1. (sim)

y1

model2%59.261

10 20 30 40 50 60 70 80

0

20

40

60

80

100y1. (sim)

y1

model1%46.5726

Model 1(46.57%)

Model 2(59.26%)

Model 4(71.89%)

Model 5(73.99%)

Control Systems Engineering LaboratoryCSEL Dynamic Modeling, Fibromyalgia

Intervention, Sample Participant

• Deshpande, S., N. Nandola, D.E. Rivera, and J. Younger, “A control engineering approach for designing an optimized treatment plan for fibromyalgia,” Proc. of the 2011 American Control Conf., San Francisco, CA, June 29 - July 1, 2011.

49

τ2 d2y

dt2+ 2ζτ

dy

dt+ y(t) = Kp

�u(t) + τa

du

dt

�

Model (Input-Output) Kp, τ, ζ, τa T98%(days)

Drug-FM symptoms -2.47, 1.57, 1.26, 1.96 11.49

Placebo-FM symptoms 45.81, 1.57, 1.26, 1.15 13.06

Anxiety-FM symptoms 0.86, 1.57, 1.26, 0.24 14.24

Stress-FM symptoms 2.29,1.57, 1.26, 0.49 13.94

Mood-FM symptoms -0.091, 1.57, 1.26, 4.67 11.93

Drug-Overall Sleep 4.98, 2.13, 1.04, -3.35 15.83


• Rise time, settling time, overshoot, oscillation, and inverse response are important characteristics of this model response.

Second-Order System with Zero

50

0 10 20 2510

0

10

20

30

Out

put

< 1, a < 0

= 1, a = 0

> 1, a > 0

0 10 20 25

0

0.5

1

Time

Inpu

t

τ2 d2y

dt2+ 2ζτ

dy

dt+ y(t) = Kp

�u(t) + τa

du

dt

�


Model Predictive Control (MPC)

• Control engineering technology widely used in many industrial applications (from chemical mfg to automotive and aerospace).

• As an optimization technology, MPC can minimize (or maximize) an objective function that represents a suitable metric of intervention performance.

• As a control system, MPC accomplishes feedback (and feedforward action) in the presence of model error, measurement unreliability, and disturbances that may affect the intervention.

• Three major steps in MPC:

– Prediction of intervention outcomes at time instants in the future (i.e., the prediction horizon) based on a model,

– Optimization of a sequence of future dosage decisions through minimizing (or maximizing) an objective function,

– Receding horizon strategy.

51


Prediction Horizon

Forecasted Anxiety Report dF(t+i) (if available)

PredictedFM symptoms y

(t+i)

Prior FM symptoms Report (Measured

Outcome)

Future Drug Dosages u(t+i)

Prior Anxiety Report (Measured

Disturbance)

Prior Drug Dosages

t t+1 t+m t+p

Move Horizon

Umax

Umin

Desired FM symptoms (Setpoint) yr(t+i)

Dist

urb.

Varia

ble

Cont

rolle

d Va

riabl

eM

anip

ulat

ed

Varia

ble

Past Future

Time (days)

Model Predictive ControlConceptual Representation

52

min{[u(k+i)]m−1

i=0 , [δ(k+i)]p−1i=0 , [z(k+i)]p−1

i=0 }J

�=

p�

i=1

�(y(k + i)− yr)�2Qy

Control Systems Engineering LaboratoryCSEL Model Predictive Control

Optimization Problem

53

Take controlled variables (primary outcomes) to goal, subject to restrictions on:

• manipulated variable range limits (i.e., intervention dosage limits)

• the rate of change of manipulated variables (i.e., dosage changes)

• controlled variables (i.e., primary outcome variables),

• associated variables (i.e., secondary outcomes)

min{[u(k+i)]m−1

i=0 , [δ(k+i)]p−1i=0 , [z(k+i)]p−1

i=0 }J

�=

p�

i=1

�(y(k + i)− yr)�2Qy

ymin ≤ y(k + i) ≤ ymax, 1 ≤ i ≤ p

umin ≤ u(k + i) ≤ umax, 0 ≤ i ≤ m− 1

∆umin ≤ ∆u(k + i) ≤ ∆umax, 0 ≤ i ≤ m− 1


0 10 20 30 40 50 60

40

50

Res

pons

e

FM sym

0 10 20 30 40 50 600

4.59

13.5

Time (day)Dru

g St

reng

th (m

g) Input drug

0 10 20 30 40 50 6005

1015

Time (day)

d(k)

Measured Disturbance (Anxiety)

Hybrid MPCContinuous MPCReference

Closed-Loop Control, Naltrexone Intervention for Fibromyalgia

• Simulation result showing MPC system response to goal change (stpt. tracking), increase in anxiety report (measured disturbance rejection) and unpredicted change in pain report (unmeasured disturbance rejection).

54

Deshpande, S., N. Nandola, D.E. Rivera, and J. Younger, “A control engineering approach for designing an optimized treatment plan for fibromyalgia,” Proc. of the 2011 American Control Conf., San Francisco, CA, June 29 - July 1, 2011.

Control Systems Engineering LaboratoryCSEL Conceptual Model for

Weight Change Interventions

The dynamical model consists of a system of integrated differential equations describing:

• Physiology (energy balance),

• Behavior change (Theory of Planned Behavior).

55

Energy

Balance

Model

Behavioral

Model

Diet

Physical Activity

Inte

rve

ntio

n a

cts

up

on

Attitude toward

the behavior

Subjective norm

Perceived

behavioral control

{ Fat-free mass

Fat mass

Navarro-Barrientos, J.E., D.E. Rivera, and L.M. Collins, "A dynamical model for describing behavioural interventions for weight loss and body composition change," "Mathematical and Computer Modelling of Dynamical Systems, Volume 17, No. 2, Pages 183-203, 2011.


•Inputs:-Diet

• Carbohydrates (CI)• Fat (FI)• Proteins (PI)• Sodium (Na)

-Physical Activity (PA; δ, in kcal/kg)• Outputs:

-Fat-Free Mass:•Lean Tissue Mass (LTM)•Extracellular Fluid (ECF)

-Fat Mass (FM)

Physiological Model: energy balance*

56

*Three compartment model based on work of K. Hall and C. Chow, NIDDK intramural scientists

Energy

Balance

Model

Behavioral

Model

Diet

Physical ActivityInte

rve

ntio

n a

cts

up

on

Attitude toward

the behavior

Subjective norm

Perceived

behavioral control

{ LTM

Fat mass

CI

FI

PI

Na ECF

Control Systems Engineering LaboratoryCSEL Physiological Model:

energy balance model (continued)

Model proposed by K. Hall and C. Chow (NIDDK Intramural Scientists). Daily

energy balance EB(t):EB(t) = EI(t)− EE(t),

EI(t) energy intake and EE(t) energy expenditure, both in kcal/d.

• Energy Intake EI:

EI(t) = a1CI(t) + a2FI(t) + a3PI(t)

CI, FI, PI carbohydrate, fat, and protein intakes all in grams/day, a1 =

4 kcal/gram, a2 = 9 kcal/gram, and a3 = 4 kcal/gram.

• Energy Expenditure EE:

EE(t) = βEI(t) + δBM + K + γLTMLTM(t) + γFMFM(t) +

ηFMd FM

dt+ ηLTM

d LTM

dt

δ is the physical activity coefficient (in kcal/kg), LTM lean tissue mass

and FM fat mass. K is a steady-state constant.

57

Control Systems Engineering LaboratoryCSEL Physiological Model:

energy balance model (continued)

Three-compartment model (FM , LTM and extra-cellular fluid ECF ):

d FM(t)dt

=(1− p(t))EB(t)

ρFM

d LTM(t)dt

=p(t)EB(t)

ρLTM

d ECF

dt=

∆Nadiet − ξNa(ECF − ECFinit)− ξCI(1− CI/CIb)[Na] τNa

,

p is given by the Forbes formula:

p =C

(C + FM); C = 10.4

ρLTM

ρFM.

For the extracellular fluid volume (in ml), ∆Nadiet is the change on sodiumin mg/d, CIb is the baseline carbohydrate intake, ECFinit is the initial ECFvolume and τNa = 2 is a time constant of two days.Finally, for the body mass:

BM(t) = FM(t) + LTM(t) + ECF (t).

58

Control Systems Engineering LaboratoryCSEL Weigh-IT+ Interactive Tool

Interactive tool that enables evaluating the three-compartment energy balance model; can be downloaded from http://csel.asu.edu/Weigh-IT

59

Control Systems Engineering LaboratoryCSEL Psychological model:

Theory of Planned Behavior (TPB)

Theory of Planned Behavior (TPB, Ajzen, 1985) says that behavior is influenced by intention, which in turn is influenced by:

• Attitude toward the behavior: determined by the strength of beliefs about the outcome (b) and the evaluation of the outcome (e).

• Subjective norm(s): determined by normative beliefs (n) and the motivation to comply (m).

• Perceived Behavioral Control: determined by the strength of each control belief (c) and the perceived power of the control factor (p).

Energy

Balance

Model

Behavioral

Model

Diet

Physical Activity

Inte

rve

ntio

n a

cts

up

on

Attitude toward

the behavior

Subjective norm

Perceived

behavioral control

{ Fat-free mass

Fat mass

b

e

n

m

c

p

60

Control Systems Engineering LaboratoryCSEL Path Diagram for the

Theory of Planned Behavior

61

η = B η + Γ ξ + ζ

η1η2η3η4η5

=

0 0 0 0 00 0 0 0 00 0 0 0 0β41 β42 β43 0 00 0 β53 β54 0

η1η2η3η4η5

+

γ11 0 00 γ22 00 0 γ330 0 00 0 0

ξ1ξ2ξ3

+

ζ1ζ2ζ3ζ4ζ5

!5!4

"11

"22

"33

!1

!2

!3

AttitudeToward theBehavior

(!1)

Intention(!4)

Behavior(!5)

PerceivedBehavioral

Control(!3)

Behavioralbelief !

evaluationof outcome

("1 = b1 ! e1)

Normativebelief !

motivationto comply

("2 = n1 ! m1)

Controlbelief !power of

control belief("3 = c1 ! p1)

#41

#42

#43

#54

#53

SubjectiveNorm($2)

Control Systems Engineering LaboratoryCSEL Fluid Analogy for the

Theory of Planned Behavior

62

!"#!$%&$%'($

)&*+,'(-

.%%'%/0& 1)2

!41"1(t ! #4) !43"3(t ! #6)

(1 ! !41)"1

(1 ! !54)"4

!54"4(t ! #7)$5(t)

$1(t)

("3)("1)

("4)

("5)"5(t)

3##4

#4

3##4

#4

3##4

#4

3##4

#4

5/67&8%',&9(-:

3##4

#4

$2(t)

$3(t)("2)

!42"2(t ! #5) (1 ! !42)"2

$4(t)

%11&1(t ! #1)&1(t)

%22&2(t ! #2)&2(t)

%33&3(t ! #3) &3(t)

!53"3(t ! #8)

(1 ! !43 ! !53)"3

Valve

Resistance

Pipe

Control Systems Engineering LaboratoryCSEL Dynamic TPB Model

63

The conservation principle (Accumulation = Inflow − Outflow) leads to the

following system of differential equations:

τ1dη1

dt= γ11ξ1(t− θ1)− η1(t) + ζ1(t)

τ2dη2

dt= γ22ξ2(t− θ2)− η2(t) + ζ2(t)

τ3dη3

dt= γ33ξ3(t− θ3)− η3(t) + ζ3(t)

τ4dη4

dt= β41η1(t− θ4) + β42η2(t− θ5) + β43η3(t− θ6)− η4(t) + ζ4(t)

τ5dη5

dt= β54η4(t− θ7) + β53η3(t− θ8)− η5(t) + ζ5(t),

where:

τ1, · · · , τ5 are time constants,

η1, · · · , η5 are the inventories,

ξ1(t) = b1(t)e1(t), ξ2(t) = n1(t)m1(t), ξ3(t) = c1(t)p1(t),γ11, · · · , γ33 are the inflow resistances,

β41, · · · , β54 are the outflow resistances,

θ1, · · · , θ7 are time delays and ζ1, · · · , ζ5 are disturbances.

Control Systems Engineering LaboratoryCSEL Dynamic TPB Model:

simulation resultsSystem response for various step change increases in strength of beliefs to attitude:

0

20

40

60

80

Inte

ntio

n (

4)

0 5 10 15 20 25 30 350

10

20

30

40

50

t

Beha

vior

(5)

0

50

100

Inpu

t (1)

0

50

100

Attit

ude

(1)

b1=8, e1=8, 2nd order

b1=6, e1=6, 1st orderb1=4, e1=4

Model parameters:θ1 = · · · θ3 = 0, θ4 = · · · θ7 = 2τ1 = · · · τ3 = 1, τ4 = 2, τ5 = 4γij = 1, βij = 0.5, ζi = 0

ξ1 = b1 × e1 :(solid) b1 = 4, e1 = 4(dashed) b1 = 6, e1 = 6(dot-dashed) b1 = 8, e1 = 8

64

Control Systems Engineering LaboratoryCSEL Simulation Examples, Integrated Model

• Two simulation examples that illustrate the use of the integrated model are described in:

Navarro-Barrientos, J.E., D.E. Rivera, and L.M. Collins, "A dynamical model for describing behavioural interventions for weight loss and body composition change," "Mathematical and Computer Modelling of Dynamical Systems, Volume 17, No. 2, Pages 183-203, 2011.

• Simulation Example 1: Using the model to better understand variability in participant response;

• Simulation Example II: Using the model to better understand the proper sequence of intervention components;

65

Control Systems Engineering LaboratoryCSEL Integrated Model, Simulation Example:

Understanding Participant Variability

66

Representative male participant with initial conditions: BM = 100 kg, FM =30 kg, LTM = 45 kg and ECF = 25 liters.

Intervention acts upon: beliefs about healthy eating habits (from b1 = 7 tob1 = 10) and healthy physical activity (from b1 = 1 to b1 = 3).

Three Scenarios:

i) Complete assimilation, τ1 = 0.1, β41 = 1, θ7 = 0.

ii) Partial assimilation, τ1 = 20, β41 = 0.5, θ7 = 15.

iii) Noisy partial assimilation, ζ1 ∼ N(0, 20) for EI and ζ1 ∼ N(0, 50) for PA.

Additional parameters:

• Behavioral variables: ξ2 = ξ3 = 50,

• Delays: θ1 = · · · = θ6 = 0, θ8 = 0,

• Time constants: τ2 = · · · = τ5 = 0.1,

• Inflow and outflow resistances: γij = 1 and βij = 0.5.


Behavioral Response

0

20

40

60

Attit

ude

(1)

0

20

40

60

80

Inte

ntio

n (

4)

0 20 40 60 80 100 120 140 160 1800

10

20

30

40

Beha

vior

(5)

time (days)

0

5

10Be

liefs

abo

ut h

ealth

yea

ting

habi

ts

0

5

10

Belie

fs a

bout

hea

lthy

phys

ical

act

ivity

0

20

40

60

Attit

ude

(1)

20

40

60

80

Inte

ntio

n (

4)

1=0.1

1=20

1=20, 1~N(0,20)

41=1

41=0.5

41=0.5, 1~N(0,20)

0 20 40 60 80 100 120 140 160 18010

20

30

40

Beha

vior

(5)

time (days)

7 =0

7 =15

7 =15, 1~N(0,20)

1=0.1

1=20

1=20, 1~N(0,50)

7 =0

7 =15

7 =15, 1~N(0,50)

41=1

41=0.5

41=0.5, 1 N(0,50)

Energy Intake Physical Activity

67

Integrated Model, Simulation Example:Understanding Participant Variability


Physiological Response

68

2500

3000

3500

EI (k

cal/d

)

0 20 40 60 80 100 120 140 160 1800.5

1

1.5

(kca

l/kg/

d)

time (days)

90

95

100

BM (k

g)

42

44

46

FFM

(kg)

21

26

31

FM (k

g)

24.4

24.5

24.58

ECF

(kg)

1=0.1, 41=1, 7=0

1=20, 41=0.5, 7=15

1=20, 41=0.5, 7=15,w noise

Integrated Model, Simulation Example:Understanding Participant Variability


• Excessive Gestational Weight Gain (GWG) increases risk factors for pregnancy complications such as gestational diabetes, macrosomia, preeclampsia, and birth defects.

• Over the past 20 years, the percentage of women gaining over 40 lbs (18 kg) during pregnancy has increased by 30%.

• Our approach relies on dynamical systems modeling to predict weight change during pregnancy, incorporating both physiological and psychological factors:

- Physiological model: maternal-fetal energy balance model.

- Psychological model: mechanistic model inspired by the Theory of Planned Behavior (TPB).

Prevention of Excessive GWG

69


!"#$%&'(")*+#',-.'/01#2

34#)

5114)40"*2'-6&748*2'58)494)&

-6&748*258)494)&',-.'/01#2

!"#$%&'.*2*"8#'/01#2

:*);<$##'/*77

:*)'/*77

3#84740"'=>2#7

(? (@(A

BA

BC

B?'

D#4%6)

(E (F

BC

B?' (")#$9#")40"-6&748*2'G#7740"'(H

(")#$9#")40"''3#249#$&3&"*I487

(C

!"#$%&'(")*+#'G#2<'=#%>2*)40"

-6&748*2'58)494)&'G#2<'=#%>2*)40"

JBA'

JBA'

(H

!!

"

BA

"

&?'

&?'

&C'

&A'

Conceptual Model for Gestational Weight Gain Interventions

70


• Data from study described in McCarthy et al., Addiction, Vol. 103, pgs. 1521-1533, 2008. Active drug is buproprion SR.

• 11 week study; randomization (n = 463)

- Drug: Drug, Placebo

- Counseling: Yes, No

• Treatment Conditions:

- Active Drug with Counseling (AC; n=101)

- Active Drug, No Counseling (ANc; n = 101)

- Placebo with Counseling (PC; n =100)

- Placebo, No Counseling (PNc ; n =101)

• T = 42 daily observations for each participant

71

Smoking Cessation Intervention

Control Systems Engineering LaboratoryCSEL Fluid Analogy for Mediation Analysis

!"#

$##%

#%

$##%

#%

M(t)

T (t)aT (t ! !1)

e1(t)

e2(t)

Y (t)

c!T (t ! !2)

bM(t ! !3) bM(t) (1 ! b)M(t)

Y (t)!"#$%

&%'(')"*+%

,(-%

72

τ1dM

dt= a T (t− θ1)−M(t) + e1(t)

τ2dY

dt= c� T (t− θ2) + b M(t− θ3)− Y (t) + e2(t).

T

M

Yc!

a b

e1

e2

Path Diagram:

Time constant (!) and delay (θ) variables are essential features in this dynamic model representation for mediation.

Quitting

Craving

Cigs Smoked


0 5 10 15 20 25 30 35 40 450

5

10

15

20Outcome: Cigs Smoked, Cohort Averages

Active Drug with CounselingPlacebo with No Counseling

0 5 10 15 20 25 30 35 40 4515

20

25

30Mediator: Craving

0 5 10 15 20 25 30 35 40 450

0.5

1

Treatment (Quit = 1,Yes; Quit = 0, No)

Study Time (Day)

Smoking Cessation Intervention Drug and Placebo Group Average Data

• Comparison of average cigarettes smoked and craving scores for two treatment groups (active drug with counseling (blue) vs. placebo-no counseling (red)).

73

Cigs Smoked

Craving

Quitting


0 5 10 15 20 25 30 35 40 450

10

20

30Outcome: Cigs Smoked

Participant A, Active Drug with CounselingParticipant B, Placebo with No Counseling

0 5 10 15 20 25 30 35 40 450

10

20

30

40Mediator: Craving

0 5 10 15 20 25 30 35 40 450

0.5

1


Study Time (Day)

Representative Participants“A” and “B”

74• Participant “A” from drug group (blue); participant “B” from placebo group (red)

Cigs Smoked

Craving

Quitting


Sheet1

l!"#"$%&# Cohort AverageDrug with Cou

, Active nseling

Cohort Avwith No

erage, Placebo Counse ing

Participant A, Active Drug with Counseling

Participant B, Placebo with No Counseling

'&()"#*+$,)#$-./ 86.12 63.74 65.70 47.7001#2*3&$,)#$-./ 84.85 88.05 74.02 58.88

" -11.088 -3.779 -18.539 2.611

4 7.669 17.090 6.009 1.722

5 0.281 0.001 0.001 13.424

" -3.275 -28.014 -7.314 107.12526 -15.873 -10.979 -11.880 6.119

7 0.507 0.001 0.188 9.5118 -0.087 -0.286 0.004 -0.762

9 0.782 0.977 0.001 0.006

Page 1

Parameter Estimation Summary

• Parameter estimation performed using the Process Models feature in Matlab’s System Identification Toolbox (one-step ahead prediction-error minimization for continuous differential equation structures).

τ1τ2d2M

dt2+ (τ1 + τ2)

dM

dt+M(t) = a (T (t) + τa

dT

dt)

τ3 τ4d2Y

dt2+ (τ3 + τ4)

dY

dt+ Y (t) = c� (T (t) + τ3

dT

dt) + b (M(t) + τ4

dM

dt)

75

Control Systems Engineering LaboratoryCSEL Dynamical Model Fits for

Cohort Averages

0 5 10 15 20 25 30 350

5

10

15

20Outcome: Cigs Smoked, Cohort Averages

Model Active Drug with CounselingData Active Drug with CounselingModel Placebo with No CounselingData Placebo with No Counseling

0 5 10 15 20 25 30 3515

20

25

30Mediator: Craving

Model Active Drug with CounselingData Active Drug with CounselingModel Placebo with No CounselingData Placebo with No Counseling

0 5 10 15 20 25 30 350

0.20.40.60.8

1


Study Time (Day)

76


0 5 10 15 20 25 30 350

5

10

15

20Outcome: Cigs Smoked, Single Subjects

Model Active Drug with Counseling

Data Active Drug with Counseling

Model Placebo with No Counseling

Data Placebo with No Counseling

0 5 10 15 20 25 30 350

10

20

30

40

50Mediator: Craving

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1


Study Time (Day)

Dynamical Model Fits for Participants “A” and “B”:

77


Summary and Conclusions• Behavioral interventions, when modeled as dynamical systems, will benefit

from a control engineering perspective.

• Applying a dynamical systems approach will require intensive measurement and a recognition of the input/output nature of phenomena associated with behavioral interventions.

• Connections between behavioral theory (represented via path diagrams) and dynamical systems can be established using fluid analogies. This was demonstrated for the Theory of Planned Behavior and statistical mediation.

• A hypothetical adaptive intervention based on Fast Track has been simulated using a rule-based controller (“IF-THEN” decision rules) vs. engineering-based PID (Proportional-Integral-Derivative) decision algorithms.

• System identification and model predictive control offers significant advantages as a means for implementing adaptive, time-varying behavioral interventions.

78

Control Systems Engineering LaboratoryCSEL Upcoming Courses

• ChE 561 Advanced Process Control: to be offered spring 2012

• ChE 461/598 Introduction to Process Dynamics and Control: to be offered fall 2012

• ChE 598 Introduction to System Identification: to be offered spring 2013.

79


Acknowledgments• Linda M. Collins, Ph.D., The Methodology Center and Dept. of Human

Development and Family Studies, Penn State University.

• Susan D. Murphy, Ph.D., Department of Statistics, Department of Psychiatry, and Institute for Social Research, University of Michigan.

• Naresh Nandola, Ph.D. (currently with ABB-Bangalore) and J. Emeterio Navarro-Barrientos, Ph.D. (currently with School of Mathematical Sciences, ASU)

• Ph.D. students: Sunil Deshpande, Kevin Timms, Yuwen Dong, and Jessica Trail.

Support from NIH-NIDA (National Institute on Drug Abuse) and NIH-OBSSR (Office of Behavioral and Social Sciences Research),

Grants K25DA021173 and R21DA024266

80


Control Systems Engineering LaboratoryCSEL References

• Behavioral interventions as dynamical systems; connections to path diagrams and use of system identification techniques:

• Navarro-Barrientos, J.E., D.E. Rivera, and L.M. Collins, "A dynamical model for describing behavioural interventions for weight loss and body composition change," "Mathematical and Computer Modelling of Dynamical Systems, Volume 17, No. 2, Pages 183-203, 2011.

• Riley, W.T., D.E. Rivera, A.A. Autienza, W. Nilsen, S. Allison, and R. Mermelstein,"Health behavior models in the age of mobile interventions: are our theories up to the task?" Translational Behavioral Medicine: Practice, Policy, Research, Vol. 1, No. 1, pgs. 53 – 71, March 2011.

• Deshpande, S., N. Nandola, D.E. Rivera, and J. Younger, “A control engineering approach for designing an optimized treatment plan for fibromyalgia,” Proceedings of the 2011 American Control Conference, San Francisco, CA, June 29 - July 1, 2011.

• Great introductory paper on adaptive interventions:

• Collins, L.M., S.A. Murphy, and K.L. Bierman, “A conceptual framework for adaptive preventive interventions,” Prevention Science, 5, No. 3, pgs. 185-196, Sept., 2004.

81

Control Systems Engineering LaboratoryCSEL References (Continued)

• Control engineering for adaptive interventions:

• Rivera, D.E., M.D. Pew, and L.M. Collins, “Using engineering control principles to inform the design of adaptive interventions: a conceptual introduction,” Drug and Alcohol Dependence, Special Issue on Adaptive Treatment Strategies, Vol. 88, Suppl. 2, May 2007, Pages S31-S40.

• Rivera, D.E., M.D. Pew, L.M. Collins, and S.A. Murphy, “Engineering control approaches for the design and analysis of adaptive, time-varying interventions,” Technical Report 05-73, The Methodology Center, Penn State (also available from http://csel.asu.edu/AdaptiveIntervention)

• Nandola, N. and D.E. Rivera, “A novel model predictive control formulation for hybrid systems with application to adaptive behavioral interventions,” Proc. of the 2010 American Control Conf., Baltimore, MD, June 30 - July 2, 2010, pgs. 6286-6292 (available through IEEE Xplore)

• Zafra-Cabeza, A. , D.E. Rivera, L.M. Collins, M.A. Ridao, and E. F. Camacho, “A risk-based model predictive control approach to adaptive interventions in behavioral health,” IEEE Transactions on Control Systems Technology, in press (available through early access IEEE Xplore).

• Deshpande, S., N. Nandola, D.E. Rivera, and J. Younger, “A control engineering approach for designing an optimized treatment plan for fibromyalgia,” Proceedings of the 2011 American Control Conference, San Francisco, CA, June 29 - July 1, 2011.

82

Control Systems Engineering LaboratoryCSEL References (Continued)

• Some tutorial presentations that may be of interest:

• Rivera, D.E., “Engineering control theory: can it impact adaptive interventions?” tutorial presentation at 2010 Society for Prevention Research workshop, June 1, 2010. Can be downloaded from http://csel.asu.edu/adaptiveintervention (select item 9).

• Rivera, D.E., “A brief introduction to system identification,” Penn State Methodology Center Brown Bag presentation, March 20, 2008. Can be downloaded from http://csel.asu.edu/controleducation (select item 10).

• Rivera, D.E., “An introduction to mechanistic models and control theory,” tutorial presentation at the SAMSI Summer 2007 Program on Challenges in Dynamic Treatment Regimes and Multistage Decision-Making, June 18 - 29, 2007. Can be downloaded from http://csel.asu.edu/controleducation (select item 9).

• My first paper in the control engineering area:

• Rivera D.E., M. Morari, and S. Skogestad, “Internal model control: PID controller design,” Ind. Eng. Chem. Proc. Des. Dev., 1986, 25(1), 252-265.

• Sunil Deshpande’s MS thesis:

• “A control engineering approach for designing an optimized treatment plan for fibromyalgia,” MS thesis, Electrical Engineering, Arizona State U., 2011.



Thank you for your attention!

84

dynamic modeling / control engineering dynamical systems and

Documents