{"ID":2900837,"CreatedAt":"2026-06-01T05:51:17.9442275Z","UpdatedAt":"2026-06-01T06:07:22.850459975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2605.30886","arxiv_id":"2605.30886","title":"Near-Optimal Mixed Strategy for Zero-Sum Linear-Quadratic Differential Games","abstract":"Deriving analytic solutions for optimal mixed strategies in zero-sum linear-quadratic differential games (ZSLQDGs) remains an open problem. In this paper, we analytically synthesize near-optimal mixed strategies for ZSLQDGs and establish rigorous performance certifications. Specifically, we construct a surrogate pure-strategy stochastic differential game (SDG) by matching the first two moments of the mixed strategies. This method achieves an $\\mathcal{O}(\\barπ^2)$ weak approximation of state distributions and expected costs with respect to the maximum commitment delay $\\barπ$. By analytically resolving the surrogate SDG, we derive closed-form optimal control laws for the matched moments. Crucially, we reveal that the surrogate game is governed by a Generalized Riccati Differential Equation (GRDE), which explicitly dictates a dynamic energy allocation law for variance injection. Building on these solutions, we propose a robust dual-routing architecture to execute the near-optimal mixed strategies. Furthermore, we certify that both the global value approximation error and the strategy suboptimality gaps are bounded by $\\mathcal{O}(\\barπ^{\\frac{1}{2}})$. Finally, numerical experiments on a double-integrator pursuit-evasion game illustrate the induced physical behaviors and validate the theoretical bounds.","short_abstract":"Deriving analytic solutions for optimal mixed strategies in zero-sum linear-quadratic differential games (ZSLQDGs) remains an open problem. In this paper, we analytically synthesize near-optimal mixed strategies for ZSLQDGs and establish rigorous performance certifications. Specifically, we construct a surrogate pure-s...","url_abs":"https://arxiv.org/abs/2605.30886","url_pdf":"https://arxiv.org/pdf/2605.30886v1","authors":"[\"Tao Xu\",\"Wang Xi\",\"Jianping He\"]","published":"2026-05-29T06:22:35Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}