Approximate calculation of reachable sets for linear control systems with different control constraints

Author:

Zykov I.V.1

Affiliation:

1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract

The paper considers the problem of approximate construction of reachability sets for a linear control system, when the control action is constrained simultaneously by geometric and several integral constraints. A variant of the transition from a continuous to a discrete system is proposed by uniformly dividing the time interval and replacing the controls at the step of dividing them with their mean values. The convergence of the reachability set of the approximating system to the reachability set of the original system in the Hausdorff metric is proved as the discretization step tends to zero, and an estimate is obtained for the rate of convergence. An algorithm for constructing the boundary of reachable sets based on solving a family of conic programming problems is proposed. Numerical simulation has been carried out.

Funder

Ministry of Science and Higher Education of the Russian Federation

Publisher

Udmurt State University

Subject

Social Sciences (miscellaneous),Social Sciences (miscellaneous),Clinical Psychology,Social Psychology,Law,Sociology and Political Science,Social Sciences (miscellaneous),Clinical Psychology,Marketing,Business and International Management,Small Animals,Small Animals,Applied Psychology,Gender Studies,Religious studies,Gender Studies,Applied Microbiology and Biotechnology,Biotechnology,Applied Microbiology and Biotechnology,Biotechnology

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