Uncertainty modelling and robust output feedback control of nonlinear discrete systems: a mathematical programming approach

Abstract

We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter-dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite) series of ordinary linear programs. Additionally, the system representation includes control and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter-dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this non-convex feasibility problem is proposed. Complexity of the design method and some special cases such as state feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state-feedback model predictive control with robust stability. Copyright © 2000 John Wiley & Sons, Ltd.