标题： 无限时域不确定线性二次微分博弈中的软约束输出反馈保证成本均衡 显示英文标题

标题： Soft-constrained output feedback guaranteed cost equilibria in infinite-horizon uncertain linear-quadratic differential games

摘要： 在本文中，我们研究具有输出反馈信息结构的无限时域线性二次不确定微分博弈。我们假设受确定性外部扰动影响的线性时不变名义动态，玩家的风险偏好通过无限时域上的软约束二次成本准则来表达。我们证明了文献中可用于存在软约束输出反馈纳什均衡（SCONE）的条件过于严格，甚至在低维博弈中也难以满足。为解决这个问题，我们借鉴次优控制的思想，引入了软约束输出反馈保证成本均衡（SCOGCE）的概念。在SCOGCE中，玩家的最坏情况成本被指定的成本配置所上界，同时保持均衡性质。我们表明，SCOGCE策略形成一个更大的均衡策略类；也就是说，每当存在SCONE时，它同时也是SCOGCE。我们证明了SCOGCE存在的充分条件与一组耦合双线性矩阵不等式的可解性有关。利用半定编程松弛，我们提供了基于线性矩阵不等式的SCOGCE策略合成迭代算法。最后，我们通过数值例子说明了SCOGCE控制器的性能。 显示英文摘要

摘要： In this paper, we study infinite-horizon linear-quadratic uncertain differential games with an output feedback information structure. We assume linear time-invariant nominal dynamics influenced by deterministic external disturbances, and players' risk preferences are expressed by a soft-constrained quadratic cost criterion over an infinite horizon. We demonstrate that the conditions available in the literature for the existence of a soft-constrained output feedback Nash equilibrium (SCONE) are too stringent to satisfy, even in low-dimensional games. To address this issue, using ideas from suboptimal control, we introduce the concept of a soft-constrained output feedback guaranteed cost equilibrium (SCOGCE). At an SCOGCE, the players' worst-case costs are upper-bounded by a specified cost profile while maintaining an equilibrium property. We show that SCOGCE strategies form a larger class of equilibrium strategies; that is, whenever an SCONE exists, it is also an SCOGCE. We demonstrate that sufficient conditions for the existence of SCOGCE are related to the solvability of a set of coupled bi-linear matrix inequalities. Using semi-definite programming relaxations, we provide linear matrix inequality-based iterative algorithms for the synthesis of SCOGCE strategies. Finally, we illustrate the performance of SCOGCE controllers with numerical examples.