Some Thoughts about Reducing the Conservativeness of Model

Predictive Control Huiying MU

Supervised by: Dr. Allwright

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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

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