OPTIMAL CONTROL AS CONDITIONAL VARIATIONAL PROBLEM WITH VARIABLE RIGHT ENDPOINT

Abstract

Subject of research. We consider dynamical system optimal control problem relating to a class of conditional variation problems with variable endpoints. Variational method is applied for research of the elastic mechanical system with controllable spring stiffness. Methods. The classical calculus of variational methods is used, which includes a variation of auxiliary functional and corresponding Euler equations. In solving a general conditional variation problem, the obtained differential system of equations in closed form is studied for design of an optimal control system for the initial dynamic object with a given quality functional. Main results. Results of unconstrained optimization are generalized to the case with additional differential (nonholonomic) constraints. Transversality condition in the variational problem is formulated in terms of local programming. An optimal control algorithm is constructed in the elastic oscillator model example, and the value of finite transition period is found. Practical relevance. The proposed approach can be used in optimal control design for dynamical systems. This optimization scheme can be also applied to controlled dynamic systems, when operation time is not fixed in advance.

Keywords

• variable endpoint
• performance functional
• optimal control
• functional variation
• transversality condition