Optimal control problem of a dynamic system with control and phase variable constraints and its numerical solution. 2.

Abstract

An analytical and numerical solution of the optimal controlling of a linear dynamic system with quadratic functional, fixed endpoints, constraint on control and quadratic phase constraint are obtained. The difficulties of studying and numerical solving such problems are related, firstly, to the problem of matching sections of the optimal trajectory, and secondly, to the software implementation of numerical procedures and the need for accounting the constraints on control and on the phase variable. Optimality conditions are used in the form of Lagrange multipliers principle. An explicit expression for the Lagrange functional multiplier is obtained. Received an explicit expression for the Lagrange functional factor. The times of entry of the optimal trajectory to the boundary of the phase constraint and exit from it were calculated by solving equations for conjugating the ends of the trajectory sections. Optimal control and trajectory have a "composite" form, due to the docking of parts of the trajectory passing outside the phase limitation and lying on it. In the case of a quadratic phase limitation, graphs of optimal controls and trajectories at different parameter values are given. The algorithm can be used to solve control problems and design structures of control devices when studying applied problems of constructing technical, economic, military systems of optimal and extreme control of the