ABSTRACT
The use of limiting equations in the analysis of qualitative properties of motion is applied here to the investigation of the optimal stabilization of mechanical systems with lumped parameters. The theorems obtained modify well-known results by weakening the conditions imposed on the derivative of the optimal Lyapunov function. This chapter presents a new approach based on a combination of the method of Lyapunov functions, the comparison technique and the method of limiting equations employed in solving the problems of controlled motion stabilization. In optimal control theory for a given system it is important to define the type of integrand in the quality criterion and the class of control forces so that the known Lyapunov function for the system without control can be applied to the system under control forces. The chapter gives an algorithm for solution of a large-scale system. This algorithm is based on the method of averaging from nonlinear mechanics together with the method of Lyapunov functions.
