This paper presents a safe robust policy iteration (SR-PI) algorithm to design controllers with satisficing (good enough) performance and safety guarantee. This is in contrast to standard PI-based control design methods with no safety certification. It also moves away from existing safe control design approaches that perform pointwise optimization and are thus myopic. Safety assurance requires satisfying a control barrier function (CBF), which might be in conflict with the performance-driven Lyapunov solution to the Bellman equation arising in each iteration of the PI. Therefore, a new development is required to robustly certify the safety of an improved policy at each iteration of the PI. The proposed SR-PI algorithm unifies performance guarantee (provided by a Bellman inequality) with safety guarantee (provided by a robust CBF) at each iteration. The Bellman inequality resembles the satisficing decision making framework and parameterizes the sacrifice on the performance with an aspiration level when there is a conflict with safety. This aspiration level is optimized at each iteration to minimize the sacrifice on the performance. It is shown that the presented satisficing control policies obtained at each iteration of the SR-PI guarantees robust safety and performance. Robust stability is also guaranteed when there is no conflict with safety. Sum of squares (SOS) program is employed to implement the proposed SR-PI algorithm iteratively. Finally, numerical simulations are carried out to illustrate the proposed satisficing control framework.

中文翻译：

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一个令人满意的控制设计框架，为受干扰的受约束系统提供安全和性能保证

本文提出了一种安全鲁棒策略迭代 (SR-PI) 算法来设计具有令人满意（足够好）性能和安全保证的控制器。这与没有安全认证的基于 PI 的标准控制设计方法形成对比。它还摆脱了现有的安全控制设计方法，这些方法执行逐点优化，因此是短视的。安全保证需要满足控制屏障函数 (CBF)，这可能与每次迭代 PI 中出现的贝尔曼方程的性能驱动 Lyapunov 解相冲突。因此，需要进行新的开发，以在 PI 的每次迭代中强有力地证明改进策略的安全性。所提出的 SR-PI 算法在每次迭代时将性能保证（由贝尔曼不等式提供）与安全保证（由稳健的 CBF 提供）相结合。贝尔曼不等式类似于令人满意的决策框架，并在与安全发生冲突时将性能牺牲与期望水平参数化。在每次迭代时都会优化这个愿望水平，以最大限度地减少对性能的牺牲。结果表明，在 SR-PI 的每次迭代中获得的令人满意的控制策略保证了稳健的安全性和性能。在不与安全冲突的情况下，也能保证稳健的稳定性。平方和 (SOS) 程序被用来迭代地实现所提出的 SR-PI 算法。最后，