Abstract
This chapter presents an extension of cost-cumulant control theory over a finite horizon for a class of stochastic zero-sum differential games wherein the evolution of the states of the game in response to decision strategies selected by two players from sets of admissible controls is described by a stochastic linear differential equation and a standard integral-quadratic cost. A direct dynamic programming approach for the Mayer optimization problem is used to solve for a multi-cumulant based solution when both players measure the states and minimize the first finite number of cumulants of the standard integral-quadratic cost associated with this special class of differential games. This innovative decision-making paradigm is proposed herein to provide not only a mechanism in which the conflicting interests of noncooperative players can be optimized, but also an analytical tool which is used to provide a complete statistical description of the global performance of the stochastic differential game.
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Pham, K.D. (2007). Multi-cumulant Control for Zero-Sum Differential Games: Performance-Measure Statistics and State-Feedback Paradigm. In: Pardalos, P.M., Murphey, R., Grundel, D., Hirsch, M.J. (eds) Advances in Cooperative Control and Optimization. Lecture Notes in Control and Information Sciences, vol 369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74356-9_3
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DOI: https://doi.org/10.1007/978-3-540-74356-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74354-5
Online ISBN: 978-3-540-74356-9
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