Asymptotics of the Solution to the Minimization Problem of the Integral Quadratic Performance Index on Trajectories of a Quasi-Linear System

Abstract

The problem of minimizing an integral quadratic performance index on the trajectories of a quasi-linear dynamic system with a small parameter multiplying the nonlinearities subject to terminal constraints is considered. Asymptotic approximations of the optimal control in this problem in the form of open loop control and feedback are constructed. The computations are reduced to solving the unperturbed linear-quadratic problem, integrating systems of linear differential equations, and finding the roots of nonsingular linear algebraic systems.