Computation, approximation and stability of explicit feedback min-max nonlinear model predictive control

Authors:
Alexandra Grancharova;Tor A. Johansen
Affiliations:
Institute of Control and System Research, Bulgarian Academy of Sciences, Sofia, Bulgaria;Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

This paper presents an approximate multi-parametric Nonlinear Programming (mp-NLP) approach to explicit solution of feedback min-max NMPC problems for constrained nonlinear systems in the presence of bounded disturbances and/or parameter uncertainties. It is based on an orthogonal search tree structure of the state space partition and consists in constructing a piecewise nonlinear (PWNL) approximation to the optimal sequence of feedback control policies. Conditions guaranteeing the robust stability of the closed-loop system in terms of a finite l"2-gain are derived.