Abstract
In this paper, we derive sufficient relative minimum conditions for discrete-continuous control systems on the base of Krotov’s sufficient optimality conditions counterpart. These conditions can be used as verification conditions for suggested control mode and enable one to construct new numerical methods.
Highlights
IntroductionHybrid systems, which include systems with variable structure [1], discrete-continuous [2], logic-dynamic [3, 4], impulsive [5], and some other systems, firmly took their place in the theory of optimal control
We consider a class of optimal control problems, which is characterized by the change of descriptions with time in terms of controlled differential systems
It allows us to verify that the proposed solution of the optimal control problem provides a local minimum for the functional
Summary
Hybrid systems, which include systems with variable structure [1], discrete-continuous [2], logic-dynamic [3, 4], impulsive [5], and some other systems, firmly took their place in the theory of optimal control. They are sometimes referred to as “heterogeneous”. A considerable part of scientific conferences and journals are devoted to that field They propose corresponding mathematical models and methods of investigation for each type of such systems. We consider a class of optimal control problems, which is characterized by the change of descriptions with time in terms of controlled differential systems For this class, a two-level model of a discrete-continuous system (DCS) is proposed in [2, 6–8]. We derive sufficient relative minimum conditions that can be used for the evaluation of the proposed solution and enable one to construct new numerical methods
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