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Precise integration method for solving noncooperative LQ differential game. (English) Zbl 1299.49063

Summary: The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

MSC:

49N70 Differential games and control
91A23 Differential games (aspects of game theory)
91A10 Noncooperative games
65K10 Numerical optimization and variational techniques
93B52 Feedback control
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