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Optimality of robust disturbance‐feedback strategies
Author(s) -
Trottemant E. J.,
Scherer C. W.,
Mazo M.
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3360
Subject(s) - control theory (sociology) , mathematical optimization , affine transformation , robust control , computer science , disturbance (geology) , convex optimization , relaxation (psychology) , output feedback , state (computer science) , regular polygon , conservatism , full state feedback , mathematics , control (management) , control system , algorithm , engineering , psychology , paleontology , social psychology , geometry , artificial intelligence , pure mathematics , electrical engineering , biology , politics , law , political science
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. Copyright © 2015 John Wiley & Sons, Ltd.