The solution of the optimization problem on the network model process

Аuthors

Shmelev V. V.

Mlitary spaсe Aсademy named after A.F. Mozhaisky, Saint Petersburg, Russia

e-mail: valja1978@yandex.ru

Abstract

Automated process control necessarily implies the formation of five components: the objective and constraints (resources) of a process, alternatives and the selection criteria in the performance of the process and a model of the process. The paper proposes a structural and logical approach to the synthesis, verification, monitoring and control of process models. Each step of the process is represented as a universal network structure, built on the principles of Petri nets. This versatile network structure of the operation is the distinctive feature of structural and logical approach. Simulation capabilities approach, taking into account the modifications introduced Petri nets sufficiently match the complexity of logical relationships of various technological processes. The network structure is graphically represented in the notations of Petri nets, and formalized by means of set-theoretic approach.

To enable optimal process control shows the version of the mathematical structure of the selection of the optimal control on a simulated process. The structure comprises a set-theoretic model of the controlled process, a variety of options tuples layouts input position universal network structures that act as control actions, a set of relations that limit choice and reflecting the technological, technical, territorial, resource, space-time requirements, as well as a set of relations of preference ( performance), determine the choice of the optimal tuple. Marking the universal structure of the operation is the output position information on the current status of the operation.

As an example of solving the optimization problem management process represented a universal network structure, the features of the application of the method of dynamic programming-ing. In accordance with generally accepted procedures using the method of dynamic programming in the elements, and the notation of the proposed model of the process considered the construction of a multi-step management process with the production on it optimal control problem. Then analyzes the elementary approach to the problem of having excessive computational complexity. Formulated and proved the principle of optimality of Bellman. Formalizes the reverse and direct the procedure for calculating the optimum process control.

The scope of application of the developed structural and logical approach and created its model-based information technology support system may be the process of decision-making in complex technical systems. The ability to solve optimization problems using the proposed model can greatly increase the effectiveness of such systems.

Keywords:

model of the process, Petri nets, mathematical structure selection, the dynamic programming method

References

1. Shmelev V.V. Aviakosmicheskoe priborostroenie, 2015, vol. 4, pp. 78–93.

2. Shmelev V.V., Manujlov YU.S. Trudy MAI, 2015, no 6(84): http://www.mai.ru/science/trudy/published.php?ID=63140

3. Kotov V.E. Seti Petri. (Networks of the Petri), Leningrad, Nauka, 1984, 160 p.

4. Ohtilev M.YU. Osnovy teorii avtomatizirovannogo analiza izmeritel’noj informacii v real’nom vremeni. Sintez sistemy analiza. (Basic theory of the automated analysis of the measuring data in real time. Synthesis analysis system), Sankt-Peterburg, Military Space Academy A.F.Mozhayskogo, 1999, 162 p.

5. URL: http://cpntools.org/download

6. Kristensen, L.M., Christensen, S., Jensen, K. The Practitioner’s Guide to Coloured Petri Nets. Int. J. Softw. Tools Technol. Transf. 1998, no 2(2), pp. 98–132.

7. Shmelev V.V., Manujlov YU.S., Rahimov R.R., Bogdanov A.V. Nauchnoe obozrenie, 2015, no 19, pp. 156 — 161.

8. Reznikov B.A. Sistemnyj analiz i metody sistemotekhniki. CHast’ 1. Metodologiya sistemnyh issledovanij, modelirovanie slozhnyh sistem. (Systems analysis and systems engineering techniques. Part 1. Methodology for System Studies, simulation of complex systems), MO SSSR, 1990, 522 p.

9. Zakirov R.G. Trudy MAI, 2014, no. 78: http://www.mai.ru/science/trudy/published.php?ID=53665

10. Rodionova D.A. Trudy MAI, 2015, no. 84: http://www.mai.ru/science/trudy/published.php?ID=63137

11. Chernous’ko F.L. Sorosovskij obrazovatel’nyj zhurnal, 1998, no. 2, pp. 139 — 144.

12. Manujlov YU.S., Kalinin V.N., Goncharevskij V.S., Delij I.I., Novikov E.A. Upravlenie kosmicheskimi apparatami i sredstvami nazemnogo kompleksa upravleniya. (Management spacecraft and ground control complex), Sankt-Peterburg, Military Space Academy A.F.Mozhayskogo, 2010, 609 p.

13. Syrin S.A., Tereshchenko T.S., Shemjakov A.O. Trudy MAI, 2015, no. 82: http://www.mai.ru/science/trudy/published.php?ID=58745

Download