ESTIMATING THE QUALITY FUNCTIONAL IN OPTIMAL CONTROL VARIATIONAL CALCULUS TASKS UNDER THE CHANGES OF THE LEFT-HAND ARGUMENT OF BOUNDARY CONDITION

Abstract

Estimating the quality functional in optimal control variational calculus tasks under the changes of boundary condition is considered.

In control systems, there is a certain permissible change of the controlled parameter based on which the control system is designed. Unlike ordinary control systems, in optimal control systems, there is another indicator - the quality functional (optimality criteria), which also depends on the controlled parameters. Therefore, the permissible range of changes of controlled parameters in optimal control systems should be determined based on the quality functional value’s tolerances. Therefore, estimating the quality functional under the changes of boundary conditions has theoretical and practical importance. It is particularly important for problems solved by numerical methods because it is quite simple for problems solved analytically.

In this article, the estimation methods of the quality functional under the changes of left-hand argument of boundary condition in the form of Taylor series with an accuracy of the second member in optimal control variational calculus tasks solved by the indirect numerical method are developed. According to the developed method, both the optimization function and the quality functional are functions of the left-hand argument of boundary condition. In other words, the boundary condition parameter is an argument of the optimization function. The mathematical apparatus for determining the specified series coefficients has been developed. These coefficients depend on the partial derivatives of the optimization function by boundary parameter. The boundary conditions for partial derivative functions of the optimal function by boundary parameters, and the determination methods for these functions using the known optimal function are studied. The truth of the Taylor series coefficients, and the algorithm for their determination are shown experimentally.