Model predictive control of nonlinear systems using piecewise linear models

We consider the problem of controlling nonlinear systems which are modeled as a set of piecewise linear (PL) or affine systems using model predictive control (MPC). The paper reviews recent results on the analysis and control of PL systems, which can model a wide range of practically relevant nonlin ear systems. Using techniques from the theory of linear matrix inequalities (LMIs), we develop a multiple model MPC technique involving a sequence of local state feedback matrices, which minimize an upper bound on the 'worst- case' objective function. The resulting problem, which utilizes a single qu adratic Lyapunov function and multiple local state-feedback matrices, can b e cast as a convex optimization problem involving LMIs. Several extensions of this technique involving approximating the local regions by ellipsoids o r polytopes, and their respective advantages and disadvantages, are discuss ed. (C) 2000 Elsevier Science Ltd. All rights reserved.