Stabilizing model predictive control of time-varying non-linear systems using linear matrix inequalities

The paper presents a stabilizing model predictive control (MPC) scheme for time-varying non-linear systems subject to input constraints. A state-feedback MPC law is computed by minimizing an upper bound of infinite horizon performance objective, which is formulated as a convex optimization involving linear matrix inequalities constraints. Time-varying linear dynamic approximation is used to derive the stability of the closed-loop system. In particular, a suboptimal algorithm of stabilizing MPC for time-varying non-linear systems is provided to decrease the online computation burden. The performance and effectiveness of the proposed approaches is illustrated by some comparisons with MPC algorithms based on linear polytopic descriptions.