Extremal Problems for Second Order Hyperbolic Systems with Boundary Conditions Involving Multiple Time-Varying Delays

eng Article in English DOI: 10.14313/PAR_248/69

send Adam Kowalewski AGH University of Science and Technology, Cracow

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Abstract

Extremal problems for second order hyperbolic systems with multiple time-varying lags are presented. An optimal boundary control problem for distributed hyperbolic systems with boundary conditions involving multiple time-varying lags is solved. The time horizon is fixed. Making use of Dubovitski-Milyutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.

Keywords

boundary control, multiple time-varying delays, second order hyperbolic system

Problemy ekstremalne dla systemów hiperbolicznych drugiego rzędu z warunkami brzegowymi, w których występują wielokrotne zmienne opóźnienia czasowe

Streszczenie

Zaprezentowano ekstremalne problemy dla systemów hiperbolicznych z wielokrotnymi zmiennymi opóźnieniami czasowymi. Rozwiązano problem optymalnego sterowania brzegowego dla systemów hiperbolicznych drugiego rzędu, w których wielokrotne zmienne opóźnienia czasowe występują w warunkach brzegowych typu Neumanna. Tego rodzaju równania stanowią w liniowym przybliżeniu uniwersalny model matematyczny procesów fizycznych, w których ma miejsce przesyłanie sygnałów na odległość w liniach długich typu elektrycznego, hydraulicznego i innych. Korzystając z metody Dubowickiego-Milutina wyprowadzono warunki konieczne i wystarczające optymalności dla problemu liniowo-kwadratowego.

Słowa kluczowe

sterowanie brzegowe, systemy hiperboliczne drugiego rzędu, wielokrotne zmienne opóźnienia czasowe

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