A New Algorithm for Computing the Stabilizing Solution of General Periodic Time-Varying Stochastic Game-Theoretic Riccati Differential Equations

TL;DR

This paper introduces a novel iterative algorithm for solving a broad class of periodic time-varying stochastic Riccati equations in zero-sum differential games, with proven convergence and verified effectiveness.

Contribution

The paper presents a dual-layer matrix iteration method that reformulates complex Riccati equations into interconnected subproblems, enabling stable solutions for time-varying stochastic games.

Findings

Algorithm converges rigorously to stabilizing solutions.

Numerical experiments confirm effectiveness and stability.

Provides a unified framework for complex Riccati equations.

Abstract

We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer matrix-valued functions iteration sequences, which reformulate the original problem into a set of interconnected bilevel subproblems. By sequentially computing the maximal periodic solutions to the Riccati differential equations associated with each subproblem, we derive the stabilizing periodic solutions for the original problem and rigorously prove the algorithm's convergence. Numerical experiments verifies algorithm effectiveness and stability. This study provides a unified numerical framework for solving a wider range of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations.