A separation result for systems with feedback constraints

In this paper we propose a certainty equivalence principle for the stabilization of nonlinear systems via measurement feedback, which clarifies the connection between the solution of a couple of Hamilton Jacobi inequalities (HJIs) and the design constraints imposed on the control and the estimation error fed back in the control loop by the observer itself. Once a solution of these HJIs has been found a measurement feedback controller can be directly implemented. This controller has different features with respect to classical controllers: in classical control schemes an observer consists of a “copy” of the system plus a term proportional to the error between the actual measurement and the “estimated” measurement. Here, we allow a term which is a nonlinear function of this error. This result is particularly powerful in conjunction with step-by-step strategies as illustrated by an application to feedforward systems.