Extremal Problems for Infinite Order Parabolic Systems with Multiple Time-Varying Lags

eng Article in English DOI: 10.14313/PAR_258/23

send Adam Kowalewski AGH University of Krakow, Institute of Automatic Control and Robotics, Al. Mickiewicza 30, 30-059 Krakow, Poland

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Abstract

Extremal problems for infinite order parabolic systems with multiple time-varying lags are presented. An optimal boundary control problem for infinite order parabolic systems in which multiple time-varying lags appear in the state equations and in the boundary condition simultaneously is solved. The time horizon is fixed. Making use of Dubovicki–Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.

Keywords

boundary control, infinite order parabolic systems, multiple time-varying lags

Problemy ekstremalne dla systemów parabolicznych nieskończonego rzędu z wielokrotnymi zmiennymi opóźnieniami czasowymi

Streszczenie

Zaprezentowano ekstremalne problemy dla systemów parabolicznych nieskończonego rzędu z wielokrotnymi zmiennymi opóźnieniami czasowymi. Rozwiązano problem optymalnego sterowania brzegowego dla systemów parabolicznych nieskończonego rzędu, w których wielokrotne zmienne opóźnienia czasowe występują zarówno w równaniach stanu oraz w warunkach brzegowych typu Neumanna. Tego rodzaju równania stanowią w liniowym przybliżeniu uniwersalny model matematyczny dla procesów dyfuzyjnych. Korzystając z metody Dubowickiego-Milutina wyprowadzono warunki konieczne i wystarczające optymalności dla problemu liniowo-kwadratowego.

Słowa kluczowe

sterowanie brzegowe, systemy paraboliczne nieskończonego rzędu, wielokrotne zmienne opóźnienia czasowe

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