TAILIEUCHUNG - Control of stage by stage changing linear dynamic systems
In this paper, the control problems of linear dynamic systems stage by stage changing and the optimal control with the criteria of quality set for the whole range of time intervals are considered. The necessary and sufficient conditions of total controllability are also stated. The constructive solving method of a control problem is offered, as well as the definitions of conditions for the existence of programmed control and motions. The explicit form of control action for a control problem is constructed. | Yugoslav Journal of Operations Research 22 (2012), Number 1, 31-39 DOI: CONTROL OF STAGE BY STAGE CHANGING LINEAR DYNAMIC SYSTEMS . BARSEGHYAN Yerevan State University Armenia, Yerevan barseghyan@ Received: October 2011 / Accepted: November 2011 Abstract: In this paper, the control problems of linear dynamic systems stage by stage changing and the optimal control with the criteria of quality set for the whole range of time intervals are considered. The necessary and sufficient conditions of total controllability are also stated. The constructive solving method of a control problem is offered, as well as the definitions of conditions for the existence of programmed control and motions. The explicit form of control action for a control problem is constructed. The method for solving optimal control problem is offered, and the solution of optimal control of a specific target is brought. Keywords: Control problem, optimal control, dynamic system, stage by stage changing. MSC: 37N35, 93C05, 49J15, 93C15 1. INTRODUCTION Problems of control, and an optimal control of objects on the set of operational states have an important role, theoretical and applied, for instance, in the case of the change of dynamic model’s parameters due to the operation of system. These problems are typical for the energy-efficient and thermal devices, the machinery with electricity cables and other mechanisms of industrial-technological purpose. In particular, the dynamic model of controllable object with the change of operational state confined, when time intervals are strictly limited, is considered in [1, 2]. Both in the ordinary control problems and the problems of dynamic systems changing stage by stage, the challenges of phased controllability, control, and optimal control emerge [3-6]. The control and optimal control problems of linear dynamic V. R. Barseghyan / Control of Stage by Stage 32 systems and stage by stage changing linear dynamic systems are .
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