Synthesis of optimal deterministic feedback optimal control systems using iterative dynamic programming

Аuthors

Rodionova D. A.

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

e-mail: d.arya.rodionova@yandex.ru

Abstract

Nowadays optimal control problems arise in various branches of science. Optimal control synthesis is often applied to modelling manned motion of aerial vehicles in air-space systems. One of possible approaches to solving optimal control problems is the usage of metaheuristic optimal globalization methods. One of these methods is the Luus-Jakola global optimization method (random search with systematic reduction in the size of search region method). This method generates a sequence of iterations, each one sel ected fr om a neighborhood of the current position using a uniform distribution. With each iteration, the neighborhood decreases, and then increases again at the start of next pass. This methods converges with sufficient accuracy for global optimization problems and thus can be used in optimal control problems.

In this paper, the problem of feed-back optimal control for nonlinear deterministic systems was considered and an approach applying iterative dynamic programming is suggested. Iterative dynamic programming method can be applied to high-dimensional optimal control problems, such as the problems of finding optimal paths of aerial vehicles.

An algorithm for finding solution to feed-back optimal control problem using the iterative dynamic programming and Luus-Jakola methods is elaborated. The software environment for the algorithm is developed, which allows to apply the method to a number of typical problems and to analyze how parameters of the algorithms influence the accuracy of the obtained solution. Examples demonstrating method’s efficiency are provided, such as determining the maximum radius orbit transfer of a spacecraft in a given time. It is shown that the developed method is applicable to nonlinear feed-back optimal control problems and allows us to find the solution with sufficient accuracy in a reasonable amount of time.

Keywords:

random search, optimal control, continuous systems, iterative dynamic programming

References

1. Panteleev A.V., Metlitskaya D. V., Aleshina E.A. Metody global’noi optimizatsii. Metaevristicheskie strategii i algoritmy. (Global optimization methods. Metaheuristic strategies and algorithms), Moscow, Vuzovskaya kniga, 2013, 244 p.

2. Panteleev A.V. Primenenie evolyutsionnykh metodov global’noi optimizatsii v zadachakh optimal’nogo upravleniya determinirovannymi sistemami. (Usage of evolutionary global optimization methods in deterministic systems optimal control problems), Moscow, MAI, 2013, 160 p.

3. Panteleev A.V., Metlitskaya D. V. Avtomatika i telemekhanika, 2011, no. 11, pp. 117–129.

4. Panteleev A.V., Metlitskaya D. V. Vestnik Moskovskogo aviatsionnogo instituta, 2011, vol. 18, no. 4, pp. 102-113.

5. Luus, R., Jaakola T.H.I. Optimization by direct search and systematic reduction of the size of search region. American Institute of Chemical Engineers Journal (AIChE) V. 19 (4). 1973. pp.760—766.

6. Luus R. Iterative Dynamic Programming. — CRC Press.-2000, 344 p.

7. Bojkov R., Hansel B., Luus R. Application of direct search optimization to optimal control problems, Hungarian Journal of Industrial Chemistry, 1993, vol.21, pp.177—185.

8. Panteleev A.V., Rybakov K.A. Prikladnoi veroyatnostnyi analiz nelineinykh sistem upravleniya spektral’nym metodom (Applied probability analysis of nonlinear control systems using spectral method), Moscow, MAI-PRINT, 2010, 160 p.

9. Panteleev A.V., Rodionova D.A. Izvestiya instituta inzhenernoi fiziki, 2014, no.3(33), pp. 17-22.

Download