Extremal Problems for Infinite Order Parabolic Systems with Boundary Conditions Involving Integral Time Lags

eng Artykuł w języku angielskim DOI: 10.14313/PAR_246/37

wyślij Adam Kowalewski , Marek Miśkowicz AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering

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Abstract

Extremal problems for integral time lag infinite order parabolic systems are studied in the paper. An optimal boundary control problem for distributed infinite order parabolic systems in which integral time lags appear in the Neumann boundary conditions is solved. Such equations constitute in a linear approximation a universal mathematical model for many diffusion processes (e.g., modeling and control of heat transfer processes). The time horizon is fixed. Using the Dubovicki-Milutin framework, the necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance indexes and constrained control are derived.

Keywords

boundary control, infinite order parabolic systems, integral time lags

Problemy ekstremalne dla parabolicznych systemów nieskończonego rzędu z warunkami brzegowymi, w których występują całkowe opóźnienia czasowe

Streszczenie

Zaprezentowano ekstremalne problemy dla systemów parabolicznych nieskończonego rzędu z całkowymi opóźnieniami czasowymi. Rozwiązano problem optymalnego sterowania brzegowego dla systemów parabolicznych nieskończonego rzędu, w których całkowe opóźnienia czasowe występują w warunkach brzegowych 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

całkowe opóźnienia czasowe, sterowanie brzegowe, systemy paraboliczne nieskończonego rzędu

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