APM  Vol.3 No.8 , November 2013
Saddle Point Solution for System with Parameter Uncertainties

In this paper, we consider dynamical system, in the presence of parameter uncertainties. We apply max-min principles to determine the saddle point solution for the class of differential game arising from the associated dynamical system. We also provide sufficient condition for the existence of this saddle point.

Cite this paper: A. Bankole and T. Obiwuru, "Saddle Point Solution for System with Parameter Uncertainties," Advances in Pure Mathematics, Vol. 3 No. 8, 2013, pp. 685-688. doi: 10.4236/apm.2013.38092.

[1]   B. Abiola, “Control of Dynamical System in the Presence of Bounded Uncertainty,” Unpublished Ph.D. Thesis, Department of Mathematics, University of Agriculture, Abeokuta, 2009.

[2]   S. Gutman, “Differential Games and Asymptotic Behaviour of Linear Dynamical System in the Presence of Bounded Uncertainty,” Ph.D. Thesis, Department of Engineering, University of California, Berkeley, 1975.

[3]   A. B. Xaba, “Maintaining an Optimal Steady State in the Presence of Persistence Disturbance,” Ph.D. Dissertation, University of Arizona, Tucson, 1984.

[4]   C. S. Lee and Leitmann, “Uncertain Dynamical Systems: An Application to River Pollution Control,” Modelling and Management, Resources Uncertainty Workshop, EastWest Centre, Honolulu, 1985.

[5]   H. Kwakernaak, “Linear Optimal Control Systems,” Wiley-Interscience, New York, 1972.

[6]   F. H. Clarke, “Optimization of Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts,” John Wiley & Sons, Inc., New York, 1983.

[7]   R. F. Hart, S. P. Sethi and R. G. Vickson, “A Survey of the Maximum Principle for Optimal Control Problems with State Constraints,” SIAM Review, Vol. 37, No. 2, 1995, pp. 181-218.

[8]   T. Haberkorn and E. Trélat, “Convergence Results for Smooth Regularizations of Hybrid Nonlinear Optimal Control Problems,” SIAM Journal on Control Optimization, Vol. 49, No. 4, 2011, pp. 1498-1522.

[9]   R. Vinter, “Optimal Control, Systems & Control: Foundations & Applications,” Birkauser, Boston, 2000.