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International Journal of Differential Equations
Volume 2011 (2011), Article ID 319375, 13 pages
Existence of Solutions of a Riccati Differential System from a General Cumulant Control Problem
1Department of Electrical & Computer Engineering, Kettering University, Flint, MI 48504, USA
2Department of Mathematics, Bradley University, Peoria, IL 61625, USA
Received 31 May 2011; Accepted 15 November 2011
Academic Editor: A. M. El-Sayed
Copyright © 2011 Stanley R. Liberty and Libin Mou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. Mou, S. R. Liberty, K. D. Pham, and M. K. Sain, “Linear cumulant control and its relationship to risk-sensitive control,” in Proceedings of the 38th Allerton Conference on Communication, Control, and Computing, pp. 422–430, 2000.
- K. D. Pham, S. R. Liberty, and M. K. Sain, “Linear optimal cost cumulant control: a k-cumulant problem class,” in Proceedings of the 36th Allerton Conference on Communication, Control, and Computing, pp. 460–469, 1998.
- K. D. Pham, M. K. Sain, and S. R. Liberty, “Cost cumulant control: state-feedback, finite-horizon paradigm with application to seismic protection,” Journal of Optimization Theory and Applications, vol. 115, no. 3, pp. 685–710, 2002.
- M. K. Sain, C. H. Won, and B. F. Spencer Jr., “Cumulant minimization and robust control,” in Stochastic Theory and Adaptive Control, T. E. Duncan and B. Pasik-Duncan, Eds., Lecture Notes in Control and Information Sciences, pp. 411–425, Springer, Berlin, Germany, 1992.
- M. K. Sain, C. H. Won, B. F. Spencer Jr., and S. R. Liberty, “Cumulants and risk-sensitive control: a cost mean and variance theory with application to seismic protection of structures,” in Advances in Dynamic Games and Applications, J. A. Filar, V. Gaitsgory, and K. Mizukami, Eds., vol. 5 of Annals of the International Society of Dynamic Games, pp. 427–459, Birkhäuser, Boston, Mass, USA, 2000.
- M. J. Zyskowski, M. K. Sain, and R. W. Diersing, “State-feedback, finite-horizon, cost density-shaping control for the linear quadratic Gaussian framework,” Journal of Optimization Theory and Applications, vol. 150, no. 2, pp. 251–274, 2011.
- P. Whittle, Risk-sensitive optimal control, John Wiley & Sons, New York, NY. USA, 1990.
- S. R. Liberty and R. C. Hartwig, “On the essential quadratic nature of LQG control-performance measure cumulants,” Information and Computation, vol. 32, no. 3, pp. 276–305, 1976.
- G. P. Papavassilopoulos and J. B. Cruz, Jr., “On the existence of solutions to coupled matrix Riccati differential equations in linear quadratic Nash games,” IEEE Transactions on Automatic Control, vol. 24, no. 1, pp. 127–129, 1979.
- S. R. Liberty and L. Mou, “Estimation of maximal existence intervals for solutions to a Riccati equation via an upper-lower solution method,,” in Proceedings of the 39th Allerton Conference on Communication, Control, and Computing, pp. 281–282, 2001.
- G. Freiling, S.-R. Lee, and G. Jank, “Coupled matrix Riccati equations in minimal cost variance control problems,” IEEE Transactions on Automatic Control, vol. 44, no. 3, pp. 556–560, 1999.