Observer-based optimal control for delta-domain LQ games with disturbances in finite/infinite time horizon

Yuan Yuan, Lei Guo
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Abstract

This paper addresses the observer-based composite control problem for a class of delta-domain LQ games with disturbances in both finite- and infinite-time horizon. In the presence of the disturbances, the Nash Equilibrium (NE) is revisited, and the scalar ε is proposed to describe the deviation of NE in such noise environment. A composite control strategy integrating the observer-based control and the feedback Nash strategies are developed such that NE can be achieved while compensating the matched disturbances. Sufficient conditions are given to ensure the existence of both the desired observer and the feedback Nash strategies in the delta-domain, and then the explicit expressions of such observer gain and Nash strategies are provided. An upper bound for the scalar ε is derived explicitly, and the corresponding convex optimization method is given to compute such epsilon level.
有限/无限时间范围内具有扰动的δ域LQ博弈的观测器最优控制
研究了一类具有有限和无限时域扰动的delta域LQ对策的基于观测器的复合控制问题。在存在干扰的情况下,重新研究了纳什均衡,并提出了标量ε来描述这种噪声环境下纳什均衡的偏差。提出了一种综合观测器控制和反馈纳什策略的复合控制策略,在补偿匹配扰动的同时实现NE。给出了期望观测器和反馈纳什策略在delta域存在的充分条件,并给出了期望观测器增益和反馈纳什策略的显式表达式。明确地导出了标量ε的上界,并给出了相应的计算ε水平的凸优化方法。
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