Resumen de Minimax strategy in approximate model predictive control
Andrei Pavlov, Iman Shames, Chris Manzie
It is known that a model predictive control law for a linear dynamical system with a linear or quadratic cost function can be explicitly computed as a piece-wise affine function. However, the number of regions required grows rapidly with the horizon length, the number of states and constraints limiting the deployment of explicit solutions to relatively small MPC problems, and motivating approximate solutions requiring less storage for online implementation. Unfortunately, the offline computation required to generate the approximate solution can be very high using many existing algorithms. In this paper, we propose a new procedure to generate the approximate solution based on barycentric interpolation whilst retaining a (less conservative) certification of the controller. This novel certification procedure requires solving a number of small-scale multiparametric linear programs together with convex optimization problems. During the online implementation of the approximate MPC, only a small linear program has to be solved to evaluate the control law. The efficacy of the proposed approach is demonstrated through both simulation and also in application to a canonical cart–pole stabilization problem.
