On certainty equivalence measurement feedback power gain control of nonlinear systems

This paper presents a theory for the design of measurement feedback controllers which achieve a prescribed power gain for the closed loop system. The theory can be implementable as nonlinear H^∞ control since the specifications are considerably less demanding. This weaker power gain design criteria appears to be very natural for designing systems with limit cycles or oscillatory behavior. Such issues were discussed by Dower et al. (1996, 1998) for state feedback power gain analysis and control and the results obtained here are based on that work and upon broadening the notion of “information state” or “cost to come” in the existing H^∞ theory. While our theory assumes certainty equivalence, theoretical work on more general controllers which do not require the certainty equivalence property is currently in progress