Sufficient optimality conditions for continuous-discrete systems with multiple instantaneous switchings of the discrete part

Abstract

A continuous-discrete system in which the motion of the continuous part is described by differential equations and the behavior of the discrete part is described by recurrences is considered; multiple instantaneous switchings are allowed. Such systems are called hybrid, and they occupy an intermediate position between continuous-discrete systems with single switchings and logicaldynamical systems. Sufficient optimality conditions under constraints on the number of switchings of the discrete part are obtained. Equations for the synthesis of the optimal closed loop control are derived. Application of the optimality conditions is illustrated by examples.

Methodology of the Construction of Computational Scenarios for Modeling Extreme States in Living Systems

“…The term hybrid system refers to a wide variety of all structures with switches, different breaks, and regular impulses [ 12 ]. Hybrids include logic–dynamic systems in which the discrete part is described by logical variables [ 13 ]. We prefer to talk about our calculations as about predictively redefinable changes in the state of the system.…”