Robust Model Predictive Controller for Uncertain Piecewise Affine Systems

This paper considers discrete-time, uncertain piecewise affine systems affected by both polytopic parameter variations and bounded disturbances, where the uncertainty can be presented in a polytopes framework. A new Robust Model Predictive Control (RMPC) algorithm based on polyhedral techniques that checks the attainability of a state space region is presented. The developed approach computes in its first stage the maximal set in the state space from which states can be driven to the target region while taking into account the system's uncertainties. Thereafter, a RMPC algorithm that guarantees to drive the system states from the maximal set to the target region is proposed. The proposed algorithm not only gives a simple and fast sub-optimal solution which considerably reduces the online computation, it guarantees the feasibility and the stability of the solution. The proposed algorithms are applied in simulation to a two-tank example.