Adaptive Stabilization of Controlled Mechanical Systems in the Conditions of Unknown Parametric Drift

Abstract

The present chapter deals with the study of an important but least known case in the theory of parametric estimation of controlled MS, the case when the vector of unknown system parameters, or that of unknown perturbations affecting the control object, is an unknown (uncontrollable, nonmeasurable) vector function of time. Certain models of solving the problems of adaptive stabilization and optimization under parametric drift conditions, based on utilizing the formalism of Lyapunov functions, were given in earlier researches under a variety of restrictions, for example on the information about the drift model and the rate of change of the parameters. The dominant difficulties that occur in these problems of forming convergent estimation algorithms, concern the proof of the fact that the Lyapunov function monotonically decreases on the trajectories of the controlled process.