1. Some Thoughts about Reducing the Conservativeness of Model Predictive Control Huiying MU Supervised by: Dr. Allwright

2. 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

3. 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:

4. 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

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

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

7. 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.

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

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

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

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

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

13. The End Thank you for your attention