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

Less Conservative Robust MPCPage 3 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:

Less Conservative Robust MPCPage 4 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

Less Conservative Robust MPCPage 5 II. Unsatisfactory Optimisation  Minimax optimisation:  Cost function:  Norm bounded disturbance:  Even optimisation effort across entire disturbance range - Unfair

Less Conservative Robust MPCPage 6 Weighted Maximum Concept  Weighted worst case  Optimising the weighted worst case

Less Conservative Robust MPCPage 7 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.

Less Conservative Robust MPCPage 8 Normal Distribution Approximation  Normal distribution is the limiting case of a discrete binomial distribution  Relationships:

Less Conservative Robust MPCPage 9 Optimisation With Weighted Maximum  Approximated weighted worst case:  Optimisation:

Less Conservative Robust MPCPage 10 Simulation Results  System Description  Cost function  An LP problem is equivalent to

Less Conservative Robust MPCPage 11 Simulation Results (Cont.)  Simulation Result I  Simulation Result II  Comparison Result

Less Conservative Robust MPCPage 12 III. Some Current Problems  Stability issues  More theoretical analyses  Probability distribution propagations

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