Approximate synthesis of optimal control of trajectory pencils of continuous deterministic systems with incomplete feedback

Аuthors

Panteleev A. ^*, Karane M. S.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: avpanteleev@inbox.ru
**e-mail: mmkarane@mail.ru

Abstract

The problem of finding an approximate optimal control for deterministic control systems with incomplete feedback on measured variables described by ordinary differential equations is considered. The initial conditions are given in the form of a set of initial states, so the problem of controlling a pencil of trajectories generated by this set and the control law used is considered. To describe the set of initial states, as well as the position of this pencil over time, smooth finite functions are used, the values of which characterize the density of traces of trajectories inside the pencil.
This task is relevant because it allows you to cover a wider class of applied problems. The uncertainty of setting the initial state of the system or the lack of complete information about the state of the system is often found in practice, for example, due to a malfunction of measuring devices or an error in the measurements obtained.
Sufficient conditions for е-optimality are formulated and proven, expressions are obtained for finding an a priori estimate of the proximity of the desired control to the optimal one, and a method for parameterizing the problem of satisfying sufficient conditions based on the spectral representation of unknown basis functions is proposed. A step-by-step algorithm for searching for approximate optimal control using sufficient conditions and multi-agent  optimization algorithms is presented. Based on the proposed approach, software to analyze the effectiveness of this approach has been developed. Two model examples are solved, in which estimates of the proximity of the control laws to the optimal solution are obtained and the results of an analysis of the behavior of the corresponding pencils of trajectories are presented.

Keywords:

optimal control, trajectory pencils, sufficient optimality conditions, multi-agent optimization algorithms

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