Sufficient conditions of optimality of the automaton part of the logical-dynamical system

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

“…It was shown in [22] that, in optimal control problems for LDSs in distinction from continuous [26], discrete [27,28], discrete-continuous [29], impulse [17,18], and switched [11][12][13][14][15][16] systems, there appears a new type of minimizing sequences that leads to processes with instantaneous multiple switchings of states of the logical (discrete) part. Examples show that such processes are not exceptions encountered only in special systems.…”

“…Logical-dynamical systems (LDSs) are a variant of hybrid systems; the discrete part in such systems is described by logical variables (see [8,[19][20][21][22][23][24][25]). The logical part of such a system is a finite state machine (FSM) with memory that controls the dynamical part.…”

Sufficient Optimality Conditions for Discrete Automaton Type Systems with Instantaneous Multiple Switchings

“…As in logic-dynamic systems, optimal processes with instantaneous multiple switchings can arise in automaton type systems [2]. Such processes are limits of minimizing sequrences in which the switching times tend to a limit without violating their mutual arrangement.…”

“…The discrete automaton type systems constitute a part of dynamical systems with an automaton part [1, 2], logic-dynamic systems [3]-[7], and hybrid systems [8]- [13]. Unlike the classical models of discrete systems [14,15], where the states are changed (switched) at prescribed (switching) times, the states of discrete automaton type systems can be switched at artibtary times [16,17].As in logic-dynamic systems, optimal processes with instantaneous multiple switchings can arise in automaton type systems [2]. Such processes are limits of minimizing sequrences in which the switching times tend to a limit without violating their mutual arrangement.…”

“…The discrete automaton type systems constitute a part of dynamical systems with an automaton part [1,2], logic-dynamic systems [3]- [7], and hybrid systems [8]- [13]. Unlike the classical models of discrete systems [14,15], where the states are changed (switched) at prescribed (switching) times, the states of discrete automaton type systems can be switched at artibtary times [16,17].…”