Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications
Online ISSN : 2188-4749
Print ISSN : 2188-4730
The 43rd ISCIE International Symposium on Stochastic Systems Theory and Its Applications (Oct. 2011, Shiga)
Local Convergence of the Sequential Quadratic Method for Differential Games
Akio TanikawaHiro MukaiMin Xu
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2012 Volume 2012 Pages 11-18

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Abstract

For computing a Nash (saddle point) solution to a zero-sum differential game for a general nonlinear system, Mukai et al. presented an iterative Sequential Quadratic-Quadratic Method (SQQM) as follows. Given a solution estimate, they defined a subproblem which approximates the original problem up to the second order around the solution estimate. They proposed to replace the subproblem with another subproblem in order to obtain a game problem with only a linear dynamics by removing the quadratic terms in the system dynamics and adding them to the payoff function as in Lagrangian function. We can now solve this subproblem conveniently by a Riccati equation method. We then update the solution estimate by adding its Nash solution to the current solution estimate for the original game. Through our extensive experiments, we observed not only local convergence of the SQQM but also much faster convergence of the SQQM than the iterative methods based on lower order approximations such as the Sequential Linear-Quadratic Method (SLQM). In this paper we will establish local convergence of the SQQM.

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© 2012 ISCIE Symposium on Stochastic Systems Theory and Its Applications
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