Asymptotics of solution for singularly perturbed nonlinear discrete periodic optimal control problems

• Autorzy: Kurina G. , Nekrasova N.
• Języki publikacji: EN

Abstrakty

EN

The asymptotic expansion of the solution of a singularly perturbed nonlinear discrete time periodic optimal control problem is constructed as series with respect to non-negative integer powers of a small parameter. The terms of asymptotic expansion are the solutions of optimal control problems which are essentially simpler than the original perturbed problem. The solvability of the perturbed problem is established in the neighborhood of a solution of the simpler non-perturbed problem of the lower dimension. The estimates are obtained for the proximity of the approximate solutions to the exact one. The nice property is proved, namely, the values of the minimized functional do not increase when higher-order approximations to the optimal control are used. Numerical examples are given in order to illustrate the method proposed.

Słowa kluczowe

EN

asymptotic methods; discrete time systems; optimal control

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2008
• Tom: Vol. 34, no 1
• Strony: 23--37
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Kurina G.

autor

Nekrasova N.

• Voronezh State Forestry Academy ul. Timirjazeva 8, 394613 Voronezh, Russia,

Bibliografia

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• [3] Dmitriev M.G., Kurina G.A., Singular perturbations in control problems, Avtomatika i Telemehanika, 2006, No. 1, (in Russian).
• [4] Gaipov M.A., Asymptotic expansion of the solution of a nonlinear discrete optimal control problem with small step-size without restrictions on the control (formalism), I. Izv. Akad. Nauk TSSR, Ser. Fiz.-Tekhn., Khim. i Geol. Nauk, 1990, No. 1, (in Russian).
• [5] Kurina G.A., Asymptotic expansion of solutions of optimal control problems for discrete weakly controllable systems, J. Appl. Maths Mechs., Vol. 66, No. 2 [Prikl. Mat. Mekh., Vol. 66, No. 2 (in Russian)], 2002.
• [6] Kurina G.A., Nekrasova N.V., Asymptotic solution of discrete periodic singularly perturbed linear-quadratic problem. Generalized Solutions in Control Problems. Proc. IFAC Workshop GSCP-2004 and satellite events, Pereslavl-Zalessky, Russia, Moscow: Fizmatlit, 2004.
• [7] Kurina G.A., Nekrasova N.V., Asymptotic solution of singularly perturbed nonlinear discrete periodic optimal control problem, Proc. 44th IEEE Conference on Decision and Control, and European Control Conference ECC ‘05, Seville, Spain, 2005,
• [8] Kurina G.A., Shchekunskikh S.S., Asymptotic solution of nonlinear periodic optimal control problem with state equation singularly perturbed by matrix, Differencial’nye Urav-neniya, Vol. 41, 2005, No. 10, (in Russian).
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