AI 中文总结
本文针对带输出反馈的网络多智能体线性二次差分博弈，提出输出反馈保证成本均衡（OF-GCE）的存在条件与综合算法，数值示例验证了方法的有效性。
AI 中文摘要
本文研究具有输出反馈信息结构的无限时域确定性线性二次差分博弈，考虑线性时不变动力学与定义在无限时域上的二次成本函数。我们首先证明，即使对于低维博弈，计算差分博弈中的输出反馈纳什均衡（OF-NE）也颇具挑战性。为解决该难题，我们引入差分博弈中的输出反馈保证成本均衡（OF-GCE）：在OF-GCE中，每个智能体寻求一种反馈策略，确保其成本保持在规定界限以下，同时满足均衡条件。我们基于一组耦合双线性矩阵不等式的可解性，推导OF-GCE存在的充要条件，提出一种基于线性矩阵不等式的迭代算法以综合OF-GCE策略，并进一步证明，当智能体拥有完整状态信息时，状态反馈保证成本均衡（SF-GCE）是OF-GCE的特例。数值示例验证了所提方法的有效性。
英文摘要
In this paper, we study infinite-horizon deterministic linear-quadratic difference games with an output feedback information structure. We consider linear time-invariant dynamics and quadratic cost functionals defined over an infinite horizon. We first demonstrate that computing an output feedback Nash equilibrium (OF-NE) in difference games is challenging, even for low-dimensional games. To address this difficulty, we introduce an output feedback guaranteed cost equilibrium (OF-GCE) for difference games. In an OF-GCE, each player seeks a feedback strategy that guarantees its cost remains below a prescribed bound while satisfying an equilibrium condition. We derive necessary and sufficient conditions for the existence of an OF-GCE in terms of the solvability of a set of coupled bilinear matrix inequalities. We provide a linear matrix inequality-based iterative algorithm for synthesizing OF-GCE strategies. We further show that the state feedback GCE (SF-GCE) is a special case of the OF-GCE when players have complete state information. Numerical examples illustrate the effectiveness of the proposed approach.
Comments11 pages, 4 figures
