Minimum Time Problem for Co-operative Parabolic System with Control-State Constraints
Mathematical Modelling and Applications
Volume 1, Issue 1, October 2016, Pages: 1-7
Received: Sep. 6, 2015;
Accepted: Sep. 17, 2015;
Published: Oct. 12, 2016
Views 4519 Downloads 262
Mohammed Shehata, Department of Mathematics, Faculty of Science, Jazan University, Kingdom of Saudi Arabia
In this paper, the minimum time problem for differential systems of parabolic type with distributed control and control - state constraints are considered. The minimum time problem is replaced by an equivalent one with fixed time and the necessary optimality conditions of time-optimal control are obtained by using the generalized Dubovitskii-Milyutin Theorem (see ).
Minimum Time Problem for Co-operative Parabolic System with Control-State Constraints, Mathematical Modelling and Applications.
Vol. 1, No. 1,
2016, pp. 1-7.
W. Kotarski, Characterization of Pareto optimal points in problems with multi equality constraints, Optimization 20 (1989), 93–106.
I.V.Girsanov, Lectures on mathematical theory of extremum problems. New York: Spring-Verlag.(1972).
I.V. Girsanov, Lectures on mathematical theory of extremum problems. New York: Spring-Verlag.(1972).
R.A. Adams, Sobolev Spaces, Academic Prees, New York, (1975).
J. Fleckinger, J. Hernandez and F.DE. Thelin, On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems, Rev.R.Acad.Cien.Serie A.Mat. 97,2 (2003), 461-466.
Lions, J. L. (1971). Optimal control of systems governed by partial differential equations. Band: Springer-verlag.
Lions, J. L., & Magenes, E. (1972). Nonhomogeneous boundary value problem and applications. New York: Spring-Verlage.
D.G.Luenberger, Optimization by vector space methods. New York: Wiley. (1969).
W. Kotarski, Some problems of optimal and pareto optimal control for distributed parameter systems. Katowice, Poland: Reports of Silesian University, 1668. (1997).
Ahmed Zabel & Maryam Alghamdi(2011). Garding’s Inequality for Elliptic Differential Operator with Infinite Number of Variables. International Journal of Mathematics and Mathematical SciencesVol 2011,-10.
Fattorini, H. O. (1998). Infinite dimensional optimization theory and opotimal control. Cambridge: Cambridge University Press
Wang, P. K. C. (1975). Optimal control of parabolic systems with boundary conditions involving time delays. SIAM Journal of Control and Optimization,13, 274-293.
Wong, K. H. (1987). Optimal control computation for parabolic systems with boundary conditions involving time delays. Journal of Optimization Theory and Applications,53, 475-507.
El-Saify, H. A., Serag. H. M., & Shehata, M. A. (2009). Time-optimal control for co-operative hyperbolic systems involving Laplace operator. Journal of Dynamical and Control systems 15(3), 405-423.
El-Saify, H.A., Shehata,M.A. Time-Optimal Control of Petrowsky Systems with Infinitely Many Variables and Control-State Constraints Studies in Mathematical Sciences Vol. 2, No. 1, 2011, pp. 01-15.
Kotarski, W., El-Saify, H. A., & Shehata, M. A. (2007). Time optimal control of parabolic lag system with infinite variables. Journal of the Egyptian mathematical society,15(1), 21-34.
Mohammed Shehata, Some time-optimal control problems for co-operative hyperbolic systems with distributed or boundary controls. Journal of Mathematical Sciences: Advances and Applications. vol 18, No 1-2,(2012),63-83.
Mohammed Shehata, Time -optimal control problem for co-operative parabolic systems with control in initial conditions, Advances in Pure Mathematics Journal, 3, No 9A,(2013),38-43.
Mohammed Shehata, Dirichlet Time-Optimal Control of Co-operative Hyperbolic Systems Advanced Modeling and Optimization Journal. Volume 16, Number 2, (2014),355-369.
Byung Soo Lee, Mohammed Shehata, Salahuddin, Time -optimal control problem for co-operative parabolic systems with strong constraint control in initial conditions, Journal of Science and Technology, Vol.4 No.11,(2014).
Mohammed Shehata, Time-optimal control of 4-th order systems.Proceedings of The 4-th International Conference on Computer Science and Computational Math ematics (ICCSCM 2015), 250-255.
Mohammed Shehata, Abo-el-nour N. Abd-alla, M.A. Bakhit Time-optimal control of parabolic systems involving operator of 4th order. SYLWAN Journal.Vol. 159,Issue. 8 (2015).
Mohammed Shehata, Time-optimal Neumann boundary Control of 4th Order Systems. CIENCIA E TECNICA Journal.Vol. 30, (2015).
H. A. El-Saify and M. A. Shehata. Time optimal control problem for parabolic systems involving different types of operators. Journal of The Egyptian Mathematical Society. Vol 17 (2009).
W. Kotarski, H. A. El-Saify and M. A. Shehata, “Time Optimal Control of Parabolic lag Systems with an Infinite Number of Variables,” Journal of the Egyptian Mathematical Society, Vol. 15,No. 1, (2007), pp. 21-34.