Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

• Main Authors: Olav Slupphaug, Lars Imsland, Bjarne A. Foss
• Format: Article
• Language: English
• Published: Norwegian Society of Automatic Control 2001-01-01
• Series: Modeling, Identification and Control
• Subjects: Robust control; Constrained control; Affine parameter-dependent models; Bilinear matrix inequalities; Semi-infinite programming
• Online Access: http://www.mic-journal.no/PDF/2001/MIC-2001-1-3.pdf
• ISSN: 0332-7353; 1890-1328

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.