Model Predictive Control for discrete fuzzy systems via iterative quadratic programming

Takagi-Sugeno fuzzy models are exact representations of nonlinear systems in a compact region. Guaranteed-cost linear matrix inequalities produce controllers which minimize a shape-independent bound on a quadratic cost; however, the controller has a fixed structure (possibly suboptimal), say a Parallel Distributed Compensator (PDC), and does not allow input saturation. By posing the problem as a Model Predictive Control one, the ideas of terminal set, terminal controller and feasible set can be used in order to improve the performance of usual guaranteed-cost controllers for Takagi-Sugeno systems via Quadratic Programming. A Polya-based approach has been introduced in order to (conservatively) transform the invariant set problem into a polytopic one, as well as computing the controller feasibility region. The optimal controller is computed iteratively.