Distributed Cooperative Control and Optimization

presented by

Lihua Xie

School of EEE, Nanyang Technological University, Singapore

Email: elhxie@ntu.edu.sg

11 December 2014

Invited Session MoA08 Networked Controls and Games

Regular Session MoB08 Cooperative Systems

Regular Session MoC04 Nonlinear Control of Multi-Agent Systems

Regular Session MoC21 Distributed Robust Design

Regular Session TuA04 Distributed Control and Estimation

Panel Session TuB19 Collaborative Networked Organizations Principles; Decentralized and Distributed Control; Holonic Manufacturing Systems

Invited Session TuB20 Sustainable Networked Enterprises & Eco-Industrial Networking

Regular Session TuC04 Synchronization in Networked Systems

Regular Session WeA04 Decentralised Techniques for Estimation and Identification

Regular Session WeA11 Decentralized Control

Regular Session WeB01 Control of Microgrids

Regular Session WeB04 Networked Control with Time Delay

Regular Session WeB09 Networked Robotic Systems

Regular Session WeC04 Stochastic Approaches to Distributed Systems

Regular Session WeC16 Semantics in Enterprise Integration and Networking

Invited Session WeC17 Energy Management and Grid Interaction for Plug-In Electric Vehicles

Regular Session WeC23 Multi-Vehicle Systems

Regular Session ThA04 Advances in Consensus

Regular Session ThB04 Coordination of Multiple Vehicle Systems I

Regular Session ThB20 Telematics: Control Via Communication Networks

Invited Session ThB21 New Developments in Control and Optimization of Complex Systems

Regular Session ThC04 Coordination of Multiple Vehicle Systems II

Regular Session ThC13 Networked Systems

Regular Session ThC16 Control of Complex Systems

Regular Session FrA04 Control Over Networks

Invited Session FrA15 Data Acquisition and Processing: Bad Data and Cyber-Security in Smart Grids

Regular Session FrA18 Optimal Control of Distributed Systems

Regular Session FrB04 Adaptive Methods for Muti-Agent Systems

Regular Session FrB11 Distributed Control for Power Systems

2014 IFAC World Congress, Cape Town Number of sessions related to networked and distributed control (29)/ number of total sessions (341)=8.5%

CDC 2014, Los Angeles

Number of sessions related to networked and distributed control (35)/ number of total sessions (190)=18.42%

Invited Session MoA05 Large Scale and Distributed Optimization Invited Session TuB12 Mean Field Games II

Invited Session MoA06 New Control Approach for Power Networks Regular Session TuB17 Network Analysis and Control II

Invited Session MoA17 Controllability and Stability of Networked Control Systems I

Regular Session TuB18 Cooperative Control II

Regular Session MoA20 Consensus I Invited Session TuB20 Networked Control Systems: Consensus, Estimation and Security

Invited Session MoB05 Decentralized Coordination and Control Invited Session TuC05 Topics in Decentralized and Distributed Control

Invited Session MoB17 Controllability and Stability of Networked Control Systems II

Invited Session TuC17 Social and Economic Networks

Regular Session MoB20 Consensus II Regular Session TuC18 Cooperative Control III

Regular Session MoC05 Decentralized Control Regular Session TuC20 Synchronization

Invited Session MoC17 Dynamics in Social Networks: Opinions, Games and Optimization

Regular Session WeA17 Networked Control Systems I

Regular Session MoC20 Consensus III Regular Session WeA18 Computer Networks

Regular Session TuA05 Distributed Control I Regular Session WeB17 Networked Control Systems II

Invited Session TuA06 Smart Grid Solutions with Innovative Communication and Control Technologies

Invited Session WeB18 Coordination and Consensus Algorithms in Distributed Control Systems

Invited Session TuA12 Mean Field Games I Regular Session WeB20 Agents and Autonomous Systems II

Regular Session TuA17 Network Analysis and Control I Invited Session WeB21 Epidemics in Networks: Analysis and Control

Regular Session TuA18 Cooperative Control I Regular Session WeC07 Transportation Networks

Regular Session TuA20 Multi-Agent Systems Regular Session WeC17 Networked Control Systems III

Regular Session TuB05 Distributed Control II Regular Session WeC18 Sensor Networks

Why Distributed Control? -offer extended capabilities/force multiplier

Accomplish tasks not possible for single UAV/UGV

Complete tasks more efficiently and effectively

System of systems – more complex

Autonomy and collaboration are the key

Networked Multi-UAV Teaming: Challenges

Intelligent: Autonomous mission planning and execution

Collaborative: Efficient multi-UAV collaboration and teaming

Aware: Comprehensive, shared and predictive situational awareness

Responsive: Holistic contingency management

Robustness: Robust control against failures

(UAV, comm, wind, etc)

Steve et al.

Distributed task

assignment

Formation, coverage control, etc

Distributed estimation, fusion, etc

• Determinism of data transmission, interferences, fading and

time-varying throughput, packet drops, etc

• Protocols: Contention based, time based control, hybrid,

event-triggered?

• Whom, when and what to communicate (topology and

bandwidth limitation)?

• Security

Some Challenges Relating to Control

6

Dynamics and disturbances

• Heterogeneity, uncertainties, disturbances

Communications

Control and optimization

• Coupling between communications and control

• Constraints in control, computation and communications

• Global vs. local

Formation Control

UAV 1

Robust MPC

UAV 2

Robust MPC

UAV 3

Robust MPC

… Robust MPC

Tracking control

7

Indoor

Outdoor..\..\Videos\UAV\Outdoor UAV\2UAV-Circle.mp4

1 1q u

2 2q u

3 3q u

n nq u

1 1,max| |iu u ,1 ,1 ,| |i j i jq q r ,1iq

Communication Channel Models

AWGN Channel (satellite

comm, air-to-air, optical comm)

1log(1 )

2C

2/ . (constant)nP

Fading Channel (urban,

underwater comm)

n(t) is white Gaussian with

variance

Power of channel input is

bounded by

Signal-to-noise ratio (SNR):

2.n

n(t) is white Gaussian with

variance

Power of channel input is

bounded by

Channel side information:

Instantaneous SNR:

2.n

.P

2

2

( ). (time-varying)

n

P t

( ).t

.P

8

Network Topology and Data Rate

• Communication network is essential for MAS.

• Both network topology and data rate are to be considered.

• Controllability and observability of networked systems

• Relation between topological structure of network and

global control objectives is largely unknown (Xiao and

Boyd, 2004; Chen and Zhang, 2011).

• Optimal topology search often leads to computationally

intractable solutions.

• Limited research on data rate for MAS except simple lower

order dynamics.

– Ahlswede, “Network information flow,” IEEE Trans. Information Theory, vol. 46, no. 4, 2000.

– R. Koetter and Medard, “An algebraic approach to network coding,” IEEE/ACM Trans. Networking, vol. 11, no.

5, 2003

i encoding transmission decoding j

States are real-valued，but only

finite bits of information are

transmitted at each time-step

( )ijx t( )ix t

{ , , }G V E A

Data Rate and Network Topology

Key issue: Joint design of coder/decoder and control protocol to

minimize data rate for distributed consensus

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Existing work:

• n – bit sufficient for distributed consensus of n-th order

integrator dynamics (Li et al., 2011; Li and Xie, 2012; Qiu

and Xie (2013))

• Convergence rate

• For general dynamics, network topology (You and Xie

(2012)

2

2exp ,2

NN

N

KQQ

N

Limitations:

• Synchronization between transmitter and receiver

• Generation of data rate to general dynamics remains

challenging

• Topology in relation to and scalability

• Topology and data rate are dealt with separately

• Performance control

1( )

1

u Nj

j N

QA

Q

2log | ( ) |u

iR A

NQ

SISO Stabilizability (Elia, 2005):

MIMO case corresponds to block-diagonal uncertainties and is

difficult

MIMO with Comm-Control Co-design (Xiao, Xie, Qiu, 2012):

Consensus over identical fading channels (Xu, Xiao, Xie, 2014)

2

MS 22

1log 1 log ( ).

2C M A

Consensus over AWGN and Fading Channels

• Consensus over AWGN channels can be achieved by

decaying gains (Li and Zhang, Liu and Xie, 2011)

• Consensus over fading remains largely open

2

MS 2 221

1log 1 log ( ).

2

i

i

m

i

C M A

22

2 2

1 11 1 ,

1 1 ( )

N

N

Q

Q M A

Distributed Optimization - Coverage Control and Search

Motivation

• Cooperative surveillance and search

• Air-net communication coverage

video1 video2

Problem Formulation

• F: Device-specific, location-

orientation –dependent, overlap

• : Density function

• How to solve this nonlinear

optimization in a distributed way.

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Distributed Optimization - Separable Cost Function

1

1

min ( ), s.t. ...m

i i m

i

f x x x X

( ) ( ) ( )( ) ( ) ( ) ( )ii i ij j i X i i i ij

x t u t a t x x P x x t f x Distributed localization

Rendezvous

Algorithm:

• Convergence to global optimum can be

guaranteed by properly choosing

• How to handle local constraints such as

obstacles

• How to handle control input constraints

• Locally coupled cost functions such as

overlapping in sensing

( )t

Control Research in the Future

Demand- driven To address challenges facing mankind; clean &

sustainable energy, energy efficiency, transportation,

healthcare, environment: Interdisciplinary, high

complexity

Technology- driven Leverage om ultra-rich information arising from

extraordinary sensing, communication, and computing

capabilities (Internet of Things, CPS, data analytics) as

well as advances in devices

Curiosity - driven

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