A group time-optimal tasks of aerial vehicles

Аuthors

Bortakovsky A. S.^1*, Shchelchkov K. A.^2**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Udmurt State University, UdSU, Universitetskaya str., Izhevsk, 426034, Russia

*e-mail: asbortakov@mail.ru
**e-mail: incognitobox@mail.ru

Abstract

The goal of the study consists in developing methods for forming the time optimal control laws for groups of objects. The problems of group performance find practical application in the field of controlling the groups of manned and unmanned aerial vehicles. There are also applications in biology and robotics. In the theory of optimal control such problems are new and insufficiently explored. The article considers four group performance problems. They are the task of simultaneous achieving one goal by a group of objects, the task of managing a group with its leader selection, the task of achieving several goals with a single or multiple sequential separation of active control objects from the carrier. The solution of these rather simple academic tasks allows developing and testing methods for optimal position control synthesis, which can be implemented in complex applied problems.

Optimal positional control developing is based on the method of dynamic programming, consisting in finding the price function (the Hamilton-Jacobi-Bellman function). In the problems under consideration, the centralized management of a group is based on the optimal decentralized positional control of individual mobile objects. The price function is formed from auxiliary functions, i.e. partial price functions for individual objects of the group.

The result of this work is the solution of the assigned group time-optimal problems, as well as the methods of constructing the price function and optimal positional control. The developed methods can be employed in the aerospace field while planning the aircraft groups’ application.

For theoretical studies in the field of optimal control of the groups of mobile objects, the solved problems can be employed as testing ones. The developed methods of the price function constructing can be employed for solving other more complex problems. Given that even in academic examples the solution is being found numerically, the application of the proposed methods of synthesis indissolubly related to the development of the appropriate approximate algorithms, as well as programs for the numerical implementation of these algorithms.

Keywords:

optimal control, time-optimal problem, centralized group management, decentralized group management

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