This article is cited in 5 papers

Optimal control of linear systems with interval constraints

V. M. Aleksandrov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

Abstract: For linear systems with interval constraints, a method for computing a time-optimal control is proposed. The method is based on transforming a quasi-optimal control. The properties and features of the quasi-optimal control are examined. A technique is described for dividing the domain of initial conditions into reachable sets over different times and for approximating each set by a family of hyperplanes. An iterative method for computing an optimal control with interval constraints is developed. The convergence of the method is proved, and a sufficient condition for the convergence of the computational process is obtained. The radius of local quadratic convergence is found. Numerical results are presented.

Key words: optimal control, quasi-optimal control, interval constraints, time-optimal control, reachable set, adjoint system, convergence, iterative process.

UDC: 519.626

MSC: Primary 49M20; Secondary 49M05

Received: 07.08.2014
Revised: 16.11.2014

DOI: 10.7868/S004446691505004X

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:5, 749–765

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