Abstract This paper presents the novelty RS (Risk-Sensitive) H 2 optimal control problem with criterion J 2 , showing the energy of the control spent into the process, H ∞ RS control approach with level of attenuation λ 1 is obtained, with cost criterion J ∞ . Robustness is added when hybridized H 2 ∕ H ∞ RS sub-optimal control problem is solved, as optimization approach, taking J 2 as cost function criterion, with H ∞ inequality constraint. The sub-optimal solution is obtained imposing that the H ∞ constraint holds with the equality sign. Values of the criterion J 2 versus exponential quadratic cost criterion J , (RS traditional criterion), illustrate advantages of exponential quadratic cost criterion J for different values of diffusion parameter ϵ into the state equation in the final time through an application to the model of the immune system. The experiments show the values of level of attenuation λ 1 in H ∞ RS control problem and hybrid H 2 ∕ H ∞ RS sub-optimal control problem which holds with equality sign. The results of the different experiments that were carried out show that the proposed methodology is feasible and meets the conditions required in H 2 , and H ∞ approaches.

中文翻译：

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一阶多项式系统的混合H2∕H∞次优随机风险敏感控制

摘要 本文提出了新的 RS (Risk-Sensitive) H 2 最优控制问题，其准则为 J 2 ，显示了过程中消耗的控制能量，获得了衰减水平为 λ 1 的 H ∞ RS 控制方法，并具有成本准则∞ 。在求解混合H 2 ∕ H ∞ RS 次优控制问题时增加了鲁棒性，作为优化方法，以J 2 作为代价函数准则，具有H ∞ 不等式约束。通过强加 H ∞ 约束和等号来获得次优解。标准 J 2 与指数二次成本标准 J 的值（RS 传统标准）说明了指数二次成本标准 J 对于扩散参数 ϵ 的不同值在最后时间通过应用到状态方程的优势免疫系统。实验表明，在H ∞ RS 控制问题和混合H 2 ∕ H ∞ RS 次优控制问题中，衰减水平λ 1 的值与等号成立。进行的不同实验的结果表明，所提出的方法是可行的，并且满足 H 2 和 H ∞ 方法所需的条件。