%0 Journal Article
%T Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach
%A Olav Slupphaug
%A Lars Imsland
%A Bjarne A. Foss
%J Modeling, Identification and Control
%D 2001
%I Norwegian Society of Automatic Control
%R 10.4173/mic.2001.1.3
%X 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 nonconvex 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.
%K Robust control
%K Constrained control
%K Affine parameter-dependent models
%K Bilinear matrix inequalities
%K Semi-infinite programming
%U http://www.mic-journal.no/PDF/2001/MIC-2001-1-3.pdf