Certainty-Equivalence Feedback Design With Polynomial-Type Feedbacks Which Guarantee ISS

The purpose of this note is to establish a certainty-equivalence feedback design for inverse optimally controlled affine systems. In particular, it is shown that a class of polynomial-type state feedbacks in conjunction with a globally asymptotically convergent observer leads to a globally asymptotically stable closed-loop. A key step in the proposed certainty-equivalence feedback design procedure is the identification of a new class of polynomial-type inverse optimal feedbacks which guarantees input-to-state stability (ISS) with respect to measurement errors. As a consequence, the proposed certainty-equivalence feedback design has the important feature that the state feedback is allowed to contain polynomial nonlinearities of arbitrarily high degree in the unmeasured states. This feature is illustrated on an example