Adaptive Control of Uncertain Coupled Mechanical Systems

Abstract

A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems Σ with n degrees of freedom and nc < n control inputs. Each system has the structure of two coupled subsystems with nc and nr degrees of freedom, respectively: a prototype being an uncertain flexible structure with n degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom, nc < n in number. Two nonlinear adaptive feedback strategies are described, with (i) continuous and (ii) discontinuous state dependence, which guarantee (i) a form of practical stability and (ii) asymptotic stability of the zero state.