Optimal discrete systems of automatic type approximate synthesis

Аuthors

Nemychenkov G. I.

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

e-mail: grigorian_05@list.ru

Abstract

The work regards discrete systems of automate type (SAT), which serve as mathematical models of control units in the form of an automata with memory. Discrete system of automate type models the switching control of complex dynamic systems operating modes, and is one of the hybrid systems components [1]. A discrete system of automate type is described by recurrence equations or containments, and serves as a control units mathematical model in the form of an automata with memory. It is one of the components of dynamic systems with automata part [2, 3], as well as logical-dynamic [4, 5, 6] and hybrid systems [1, 7]. A hybrid system means a system where the processes have several levels of heterogeneous description, while the system state is characterized by ever changing or discretely changing components [8]. One can encounter such systems solving applied problems concerning mechanical and electric power control systems, as well as control problems of aircraft, technological processes, and computer network traffic and in many other areas.

The aim of this work is development of software and algorithmic support for the synthesis of positional control based of sufficient optimality conditions.

The software and algorithmic support for the synthesis of one-dimensional and two-dimensional systems of automate type was developed. The algorithm operation was analyzed using academic examples with known analytical solution.

Certain restrictions on the number of switching count occur very often, while solving the aircraft movement control problems.

For example, a satellite transfer from a low circular orbit to higher (geostationary) one, requires the upper stage «breeze-M». The permissible of the upper stage cruise engine firing should not exceed 10. Thus, if the engine state (on/off) is described by a discreet system, the total number of system switching would, naturally, be limited. Such restrictions can be accounted for during switching systems synthesis [9, 10]. Implementation of switching systems for satellite active stabilization problems to describe the jet engine operation allows accounting for inefficient fuel consumption while its firing and cut-off [6].

The author developed the discreet SAT synthesis algorithm, described by recurrence containment, and consisting in conditional cost functions construction. The bundled software for SAT with single or repeated switching synthesis. An academic example was solved for 2-dimensional discreet SAT synthesis.

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Keywords:

discrete system, optimal control, optimal control synthesis algorithm

References

1. Cassandras C.G., Pepyne D.L., Wardi Y. Optimal Control of a Class of Hybrid Systems // IEEE Trans. Aut. Con. 2001. V.46. № 3. P. 398–415.

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9. Bortakovskii A.S., Konovalova A.A. Izvestiya RAN. Teoriya i sistemy upravleniya, 2014, no.5, pp. 38-70.

10. Bortakovskii A.S., Konovalova A.A. Izvestiya RAN. Teoriya i sistemy upravleniya, 2013, no.1, pp. 18-44.

11. Kofman A., Anri-Laborder A. Metody i modeli issledovaniya optimizatsii. Tselochislennoe programmirovanie (Methods and optimization model studies. Integer programming), Moscow, Mir, 1976, 432 p.

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