Minimum Entropy Control for Time-Varying Systems Systems & Control: Foundations & Applications

Minimum entropy control has been studied extensively for linear time-invariant systems, both in the continuous-time an discrete-time cases. Controllers that satisfy a closed-loop minimum entropy condition are known to have considerable advantages over other optimal controllers. While guaranteeing an H-infinity norm bound, the entropy is an upper bound for the H 2 norm of the system, and thus minimum entropy controllers provide a degree of performance sacrificed by other H-infinity controllers.

These advantages make it desirable to extend the theory of minimum entropy control to other settings. In this book we provide a time-domain theory of the entropy criterion. For linear time-invariant systems, this time-domain notion of entropy is equivalent to the usual frequency domain criterion. Moreover, this time-domain notion of entropy enables us to define a suitable entropy for other classes of systems, including the class of linear time-varying systems.

Furthermore, by working with this time-domain definition of the entropy we are able to gain new interpretations of the advantages minimum entropy control. In particular we consider the connections between the time-varying analogues to the H2, H-infinity, and risk-sensitive control problem. This book is aimed at researchers in mathematical control theory.

It will be particularly attractive to those working in both H-infinity control theory as well as linear time-varying systems. While the approach used has its basis in operator theory, it can be followed easily by graduate students with a basis in linear systems theory.