A robust constrained MPC scheme for nonlinear plants via norm-bounded linear differential inclusions embedding

Model predictive control strategies are described for solving set-point problems for nonlinear systems when pointwise-in-time input and/or state related inequality constraints have to be fulfilled. The trajectories of the nonlinear system are embedded within those of an auxiliary norm-bounded uncertain linear system in order to use simpler computational paradigms based on convex programming (LMIs). These MPC schemes are based on the minimization, at each time instant, of an upper bound on the worst case quadratic performance index. The conditions on the upper bound are obtained by means of the S-procedure. A control strategy based on N control free moves plus a feedback gain matrix is used. In order to demonstrate the effectiveness of the solution and the computational complexity reduction achievable, a numerical experiment is presented and contrasted to standard robust multi-model (polytopic) MPC schemes.