In this article, the mixed H₂/H_∞ performance optimization is first formulated as a nonzero‐sum game, of which the sufficient condition guaranteeing the existence of the Nash equilibrium is derived using the Hamilton–Jacobi (HJ) theory. Then, Hamiltonian‐driven inequalities are presented to evaluate the H₂ and H_∞ performances. Using this Hamiltonian‐inequality driven approach, the coupled HJ equations arising from finding the Nash equilibrium are relaxed to the HJ inequality constraints. A novel mixed policy iteration (PI) algorithm is developed that uses sum‐of‐squares (SOS) program in policy evaluation step, and consists of an H₂ performance improvement step and an H_∞ performance guarantee step. This constrained‐driven approach allows us to present a PI algorithm that takes into account both robustness and performance objectives. Finally, a numerical simulation is carried out to highlight the efficacy of the proposed framework.

中文翻译：

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使用平方和的混合动力H2 /H∞性能的汉密尔顿驱动的自适应动态规划

在本文中，所述混合ħ ₂ / ħ _∞性能优化，首先配制为非零和游戏，其中使用汉密尔顿-雅可比（HJ）理论导出的充分条件保证纳什均衡的存在。然后，哈密顿驱动不等式被呈现给评估ħ ₂和ħ _∞性能。使用这种哈密顿不等式驱动的方法，将找到纳什均衡所产生的耦合HJ方程放宽到HJ不等式约束。开发了一种新颖的混合策略迭代（PI）算法，该算法在策略评估步骤中使用平方和（SOS）程序，并且由H ₂组成。性能改进步骤和H ^ _∞性能保证的一步。这种受约束驱动的方法使我们能够提出同时考虑健壮性和性能目标的PI算法。最后，进行了数值模拟，以突出提出的框架的有效性。