some thoughts about reducing the conservativeness of model predictive control huiying mu supervised...
TRANSCRIPT
Some Thoughts about Reducing the Conservativeness of Model
Predictive Control Huiying MU
Supervised by: Dr. Allwright
Less Conservative Robust MPCPage 2
Contents
I. Backgrounds :
II. Weighted Maximum:
III. Some Current Problems
•Robust Model Predictive Control
•Existing problems
•Undue optimisation•Weighted maximum concept•Disturbance description transformation•Normal distribution approximation•Optimisation with weighted maximum•Simulation Results
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I. Robust Model Predictive Control
The Concept of MPC• Receding horizon feedback control• Explicit use of plant model• On-line optimisation
A General Formulation• Plant model:
• Horizon length:
• Cost:
• Optimisation:
• Control:
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Existing Problems
Conservative• Minimax optimisation
• Small disturbance set, i.e.
• Short prediction horizon, i.e.
Computationally Expensive• State constraint satisfaction
• Non-linear/non-convex optimisation
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II. Unsatisfactory Optimisation
Minimax optimisation:
Cost function:
Norm bounded disturbance:
Even optimisation effort across entire disturbance range - Unfair
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Weighted Maximum Concept
Weighted worst case
Optimising the weighted worst case
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Disturbance Description Transformation
Tchebycheff Inequality: • The probability that is outside an arbitrary interval
is negligible if the ratio is sufficiently small.
A Normal equivalent to norm bounded• With appropriate mean and variance , a normal
distribution with density is equivalent to be norm bounded.
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Normal Distribution Approximation
Normal distribution is the limiting case of a discrete binomial distribution
Relationships:
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Optimisation With Weighted Maximum
Approximated weighted worst case:
Optimisation:
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Simulation Results
System Description
Cost function
An LP problem
is equivalent to
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Simulation Results (Cont.)
Simulation Result I
Simulation Result II
Comparison Result
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III. Some Current Problems
Stability issuesMore theoretical analysesProbability distribution propagations
The End
Thank you for your attention