The principle of maximum in the imitative control tasks

TL;DR

This paper explores the application of the maximum principle in optimal control for complex systems with unknown models, introducing a convergent delta-procedure for finite-step approximation of control parameters.

Contribution

It develops a delta-procedure based on the maximum principle that guarantees convergence and provides a practical method for optimal control in uncertain systems.

Findings

The delta-procedure converges to the optimal control solution.

The method is applicable even when system models are unknown.

Guidelines for choosing control discretization points are discussed.

Abstract

The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the problem for such systems where it is practically impossible to organize a control system because of an unknown model or because it is impossible to strictly follow the specified trajectories of control parameters in each particular case. A so-called delta-procedure is constructed that converges and allows one to obtain an approximation and optimal control of the system in a finite number of steps with a given accuracy delta. The theorem on the delta-procedure is proved and illustrative examples are given. Some features of the application of the proposed algorithm to real problems of simulation control are discussed, e.g. the optimal number of points dividing the time interval under consideration, and tasks for further individual research.