Approximate Predictive Control of Polytopic Systems

Robust model predictive control algorithms often suffer from a high computational complexity due to the large number of variables and constraints involved in the optimiztion problems that are solved at every sampling instant. In this paper we propose an approximate control scheme for polytopic systems based on the interpolation of offline computed robust invariant tubes. The feasible set of the control scheme is the convex hull of all the sets in the invariant tubes. Online, the current control input is computed by interpolating between the control laws associated with these tubes. This interpolation requires the solution of an optimization problem. Compared with a direct solution of a robust model predictive control problem, the interpolation approach proposed in this paper requires much less computation time.