On the optimal control of passive or non-expansive systems
Hughes, TH
Date: 26 March 2018
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers
Publisher DOI
Abstract
The positive-real and bounded-real lemmas solve
two important linear-quadratic optimal control problems for
passive and non-expansive systems, respectively. The lemmas
assume controllability, yet a passive or non-expansive system can
be uncontrollable. In this paper, we solve these optimal control
problems without making any ...
The positive-real and bounded-real lemmas solve
two important linear-quadratic optimal control problems for
passive and non-expansive systems, respectively. The lemmas
assume controllability, yet a passive or non-expansive system can
be uncontrollable. In this paper, we solve these optimal control
problems without making any assumptions. In particular, we
show how to extract the greatest possible amount of energy from
a passive but not necessarily controllable system (e.g., a passive
electric circuit) using state feedback. A complete characterisation
of the set of solutions to the linear matrix inequalities in
the positive-real and bounded-real lemmas is also obtained.
In addition, we obtain necessary and sufficient conditions for
a system to be non-expansive that augment the bounded-real
condition with new conditions relevant to uncontrollable systems.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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