Synthesis of optimal control of linear logic-dynamical systems

Mathematics


Аuthors

Bortakovsky A. S.1*, Pegachkova E. A.2**

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: asbortakov@mail.ru
**e-mail: pegachkova@mail.ru

Abstract

We consider the optimal control problem for logic-dynamical systems whose dynamical part is given by linear differential equations and whose logic part is defined by linear finite difference equations modeling the automaton with memory. The quality of the control is determined by a quadratic objective functional. This setting is analogous to the classical Letov-Calman problem of analytic construction of optimal regulator. The equations on the synthesis function and on feedback optimal control are derived. We show that the optimal control of the dynamical part is provided by a linear regulator (similarly to the classical case), and optimal control of the logical part is determined by recurrent equation. We describe several examples of these optimal processes including those which require countable set of switches of the logical part.


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