Date of Award
Doctor of Philosophy
Dr. Tom O'Mahony
Practical difficulties associated with the implementation of stabilizing robust model predictive control (MPC) laws are well known. The algorithms typically rely on the solution of the so-called min-max optimization problem. All such algorithms display a large online computational burden and often suffer excessive conservativeness. In this thesis, two original algorithms will be developed that address the conservativeness and complexity issues in min-max MPC.
The first algorithm is a min-max MPC based on the concept of closed-loop prediction. The synthesis procedure is realized using linear matrix inequalities and thus the implementation of the closed-loop min-max MPC control law can be performed by solving a semidefinite program (SDP) on-line. The primary advantages of the algorithm are that (i) the stability problems of many of the recent open-loop formulations are redressed (ii) the algorithm displays low computational complexity and (iii) reduced conservativeness is achieved relative to comparable approaches.
The second main contribution of this thesis is an approximate explicit algorithm for solving the closed-loop min-max MPC using multi-parametric SDP techniques. While the off-line computational complexity is significant, the proposed algorithm yields a real-time control law that reduces to a function evaluation problem which can be accelerated using binary search trees. Two approximation strategies, based on the value function and control input, are proposed and analyzed. Robust stability can be guaranteed and a user-defined upper bound on the approximation error can be established.
Finally, a number of simulation examples, one of which is an industrial collaboration on a permanent magnet synchronous motor, are presented to demonstrate and illustrate the properties and advantages of the proposed algorithms.
Cychowski, Marcin Tomasz, "Efficient Strategies for Robust Constrained Model Predictive Control" (2006). Theses [online].
Available at: https://sword.cit.ie/allthe/680