Optimality of robust disturbance-feedback strategies

Journal article (2016)

Authors

E.J. Trottemant OLD Intelligent Control & Robotics
C.W. Scherer University of Stuttgart
M. Mazo OLD Intelligent Control & Robotics
Research Group
OLD Intelligent Control & Robotics
Relaxation LMI Affine strategies Disturbance-feedback control Min-max problem
More Info
expand_more

Published Date

2016

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Research Group

OLD Intelligent Control & Robotics

Abstract

Summary In this paper, robust disturbance-feedback strategies for finite time-horizon problems are studied. Linear discrete-time systems subject to linear control, state constraints, and quadratic objective functions are considered. In addition, persistent disturbances, which enter the system additively and are contained in a polytopic set, act on the system. The synthesis of robust strategies leads in the case of the traditional robust state-feedback and open-loop min-max strategies to, respectively, nonconvex problems or conservatism. However, robust disturbance-feedback problems can easily be reformulated as convex problems and solved by tractable linear matrix inequalities. Hence this approach bypasses the nonconvexity issue while maintaining the advantages of feedback strategies. As a key result, it is shown that both sources of conservatism attributed to this approach, namely, the relaxation method and the affine parametrization, can be removed at the expense of an increase in computational effort.