Design of feedback control by an optimal control approach relies on the solutions of the Hamilton‐Jacobi‐Bellman (HJB) equation, while this equation rarely admits analytical solutions for arbitrary choices of the performance measure. An inverse optimal feedback design approach is proposed here in which analytical solutions are explored for the HJB equation that optimize some meaningful, but not necessarily ideal, performance measure. Such performance measure is exclusively selected from a family of cost functionals with an intended structural constraint which inherently yields analytical solutions to the HJB equation. This family includes a set of free parameters which are exploited to construct cost functionals adequately representing the design requirements. The structural constraint imposed on this cost functional family indeed narrows down the scope of the proposed method; yet, it is shown by several examples that this method can successfully address certain classes of feedback design problems.

中文翻译：

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反馈控制设计的逆最优方法：探索Hamilton-Jacobi-Bellman方程的解析解

通过最优控制方法设计的反馈控制设计依赖于汉密尔顿·雅各比·贝尔曼（HJB）方程的解，而该方程很少接受对性能指标的任意选择的解析解。本文提出了一种逆向最优反馈设计方法，其中探索了针对HJB方程的分析解决方案，该解决方案优化了一些有意义但不一定理想的性能指标。此类性能度量仅从具有预期结构约束的成本函数族中选择，这些结构固有地会产生HJB方程的解析解。该系列包括一组免费参数，这些参数可用于构建足以代表设计要求的成本功能。对该成本函数族施加的结构约束确实缩小了所提出方法的范围；但是，通过几个示例表明，该方法可以成功解决某些类别的反馈设计问题。