Optimal boundary control problems of retarded parabolic systems

• Autorzy: Kowalewski A. , Krakowiak A.
• Języki publikacji: EN

Abstrakty

EN

Optimal boundary control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.

Słowa kluczowe

EN

boundary control; parabolic systems; time delays; linear quadratic problem; quadratic programming method

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2013
• Tom: Vol. 23, no. 3
• Strony: 261--279
• Opis fizyczny: Bibliogr. 15 poz., wzory

Twórcy

autor

Kowalewski A.

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

autor

Krakowiak A.

• Technical University of Cracow, Institute of Mathematics, 31-155 Cracow, ul. Warszawska 24, Poland

Bibliografia

• [1] H. T. Banks and A. Manitius: Projection series for retarded functional differential equations with application to optimal control problems. J. Differential Equations, 18 (1975), 296-332.
• [2] A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter: Representation and Control of Infinite Dimensional Systems. 1, 2 Birkhauser, Boston 1993.
• [3] M. C. Delfour: The linear quadratic optimal control problem for hereditary differential systems:theory and numerical solution. Applied Mathematical Optimization, 3 (1977), 101-162.
• [4] E. S. Gilbert: An interative procedure for computing the minimum of quadratic form on a convex set. SIAM J. Control, 4 (1966), 61-80.
• [5] G. Knowles: Time optimal control of parabolic systems with boundary conditions involving time delays. J. Optimiz. Theor. Applics., 25 (1978), 563-574.
• [6] A. Kowalewski: Application of Conical Approximations to Optimal Control Problems for Systems described by Partial Differential Equations of Hyperbolic Type. Ph. D. thesis, University of Mining and Metallurgy, Cracow 1976.
• [7] A. Kowalewski: Boundary control of distrbuted parabolic systems with boundary condition involving a time - varying lag. Int. J. Control, 48 (1988), 2233-2248.
• [8] A. Kowalewski: Optimization of parabolic systems with deviating arguments. Int. J. Control, 72 (1999), 947-959.
• [9] A. Kowalewski and A. Krakowiak: Optimal distributed control problems of retarded parabolic systems. Archives of Control Sciences, 19 (2009), 279-293.
• [10] A. Krakowiak: Boundary control of retarded parabolic systems. Control andCybernetics. 40 (2011), 164-178.
• [11] J. L. Lions: Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin 1971.
• [12] J. L. Lions and E. Magenes: Non-Homogeneous Boundary Value Problems and Applications. 1, 2 Springer Verlag, Berlin 1972.
• [13] K. Malanowski: Some Applications of Fourier Method to Optimal Control Problems for Systems Described by Partial Differential Equations. Papers of the Institute of Organization and Management, Series B, Bulletin No. 3, Warsaw 1974 (in Polish).
• [14] N. E. Nahi and L. A. Wheeler: Optimal terminal control of continuous system via successive approximation of the reachable set. IEEE Trans. Automatic Control, 12 (1967), 515-521.
• [15] P. K. C. Wang: Optimal control of parabolic systems with boundary conditions involving time delays. SIAM J. Control, 13 (1975), 274-293.