Constrained predictive control of nonlinear plants via polytopic linear system embedding

This paper considers nonlinear system control via robust predictive controllers developed for constrained LTV systems with polytopic model uncertainties. The nonlinear systems dealt with are the ones whose trajectories can be embedded within those of a polytopic LTV system. This condition can be satisfied in bounded regions of the state space for a large class of nonlinear systems. In particular, we focus our attention on a robust predictive control scheme similar to the one recently developed by two of the authors for input-saturated polytopic LTV discrete-time systems, here extended so as to take into account also state constraints. The solution is based on the minimization, at each time instant, of an upper bound of the 'worst-case' infinite horizon quadratic cost under the constraint of steering the convex hull of the predicted state set into a feasible and robust positive invariant region. A condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants. The proposed predictive controller is proved to robustly quadratically stabilize input and state-constrained LTV polytopic systems, as well as any other embedded nonlinear system. Copyright (C) 2000 John Wiley & Sons, Ltd.