Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Papers
Local Convergence of the Sequential Quadratic Method for Differential Games
Akio TanikawaHiro MukaiMin Xu
Author information
JOURNAL FREE ACCESS

2012 Volume 25 Issue 12 Pages 349-357

Details
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.

Content from these authors
© 2012 The Institute of Systems, Control and Information Engineers
Previous article Next article
feedback
Top