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. (c) 2005 Elsevier B.V. All rights reserved.

A separation result for systems with feedback constraints / Battilotti, Stefano. - In: SYSTEMS & CONTROL LETTERS. - ISSN 0167-6911. - STAMPA. - 55:5(2006), pp. 369-375. [10.1016/j.sysconle.2005.07.008]

A separation result for systems with feedback constraints

BATTILOTTI, Stefano
2006

Abstract

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. (c) 2005 Elsevier B.V. All rights reserved.
2006
control constraints; measurement feedback; nonlinear systems
01 Pubblicazione su rivista::01a Articolo in rivista
A separation result for systems with feedback constraints / Battilotti, Stefano. - In: SYSTEMS & CONTROL LETTERS. - ISSN 0167-6911. - STAMPA. - 55:5(2006), pp. 369-375. [10.1016/j.sysconle.2005.07.008]
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