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

Authors: Olav Slupphaug, Lars Imsland and Bjarne A. Foss,
Affiliation: NTNU, Department of Engineering Cybernetics and ABB
Reference: 2001, Vol 22, No 1, pp. 29-52.

Keywords: Robust control, Constrained control, Affine parameter-dependent models, Bilinear matrix inequalities, Semi-infinite programming, Nonlinear model predictive control

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 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.

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  title={{Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach}},
  author={Slupphaug, Olav and Imsland, Lars and Foss, Bjarne A.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}