STOCHASTIC OPTIMAL STABILIZATION OF ADAPTIVE MECHANICAL SYSTEMS

The problem of optimal adaptive stabilization of nonlinear mechanical systems subject to white-noise perturbations is investigated and solved. In particular, a control system is synthesized such that a local quadratic objective functional is minimized, the controlled system is stabilized about the null position, and the adjustable parameters converge to the true values in probability. It is shown that the choice of Bellman function (stochastic Lyapunov function) in quadratic form with a kinetic energy matrix is conducive to the synthesis of an optimal adaptive stabilization system.