Minimum entropy control for time-varying systems

Dr. Pablo Iglesias-Visiting Faculty, Electrical and Computer Engineering, Johns-Hopkins University

Minimum entropy control has been studied extensively for linear time-invariant systems, both in the continuous-time and 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 $H_\infty$ 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 $H_\infty$ controllers. These advantages make it desirable to extend the theory of minimum entropy control to other settings.

In this talk 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 of minimum entropy control. In particular we consider the connections between the time-varying minimum entropy control problem and the time-varying analogues to the $H_2$, $H_\infty$ and risk-sensitive control problem.

We will also show how the techniques of the entropy control problem can be used to generalize Bode's sensitivity integral for time-varying systems.