Contractive Model Predictive Control with Local Linearization for Nonlinear Systems

Most model predictive control (MPC) schemes in the literature designed for constrained nonlinear systems involve the solution of nonlinear programming problems (NLPs). Due to the difficulties inherent to solving NLPs and since MPC requires the optimal (feasible) solution to be computed on-line and at each time step, it is important to simplify the controller from a computational point of view. Furthermore, many nonlinear MPC controllers do not provide any stability or performance guarantees for the closed-loop system. In this paper we propose a stabilizing MPC controller which can be implemented as a quadratic programming (QP) problem. Because we use local linear approximations of the nonlinear plant for prediction and because stability is guaranteed through the introduction of an additional state constraint in the optimization called contractive constraint, this scheme has been denoted contractive MPC with local linearization.

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