Extremal problems for parabolic systems with time-varying lags

• Autorzy: Kowalewski A.

Identyfikatory

DOI

10.24425/119078

• Języki publikacji: EN

Abstrakty

EN

Extremal problems for parabolic systems with time-varying lags are presented. An optimal boundary control problem for parabolic systems in which time-varying lags appear in the state equations and in the boundary conditions 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.

Słowa kluczowe

EN

boundary control; parabolic systems; time-varying lags

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2018
• Tom: Vol. 28, No. 1
• Strony: 89--104
• Opis fizyczny: Bibliogr. 11 poz., wzory

Twórcy

autor

Kowalewski A.

• AGH University of Science and Technology, Institute of Automatics and Robotics, 30-059 Cracow, al. Mickiewicza 30, Poland

Bibliografia

• [1] E. S. Gilbert: An iterative procedure for computing the minimum of a quadratic form on a convex set. SIAM J. Control, 4(1), (1966), 61-80.
• [2] I. V. Girsanov: Lectures on the Mathematical Theory of Extremal Problems. Publishing House of the University of Moscow, Moscow, 1970 (in Russian).
• [3] A. Kowalewski and M. Miśkowicz: Extremal problems for time lag parabolic systems. Proceedings of the 21st Int. Conf. on Process Control, Strbske Pleso, Slovakia, (2017), 446-451.
• [4] A. Kowalewski: Extremal problems for distributed parabolic systems with boundary conditions involving time-varying lags. Proc. of the 22nd Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, (2017), 447-452.
• [5] A. Kowalewski: Optimal control of parabolic systems with time-varying lags. IMA J. Math. Control and Information, 10(2), (1993), 113-129.
• [6] A. Kowalewski: Boundary control of distributed parabolic system with boundary condition involving a time-varying lag. Int. J. Control, 48(6), (1988), 2233-2248.
• [7] A. Kowalewski: Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays. AGH University of Science and Technology Press, Cracow, 2001.
• [8] A. Kowalewski and J. Duda: On some optimal control problem for a parabolic system with boundary condition involving a time-varying lag. IMA J. Math. Control and Information, 9(2), (1992), 131-146.
• [9] J. L. Lions: Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin, 1971.
• [10] J. L. Lions and E. Magenes: Non-Homogeneous Boundary Value Problems and Applications. vols. 1 and 2, Springer-Verlag, Berlin, 1972.
• [11] V. P. Maslov: Operators Methods, Moscow, 1973 (in Russian).

Uwagi

EN

The research presented here was carried out within the research programme AGH University of Science and Technology, No. 11.11.120.396.

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).