论文标题
一种系统级别的方法，以遗憾最佳控制
A System Level Approach to Regret Optimal Control
论文作者
论文摘要
我们提出了一种基于优化的方法，用于为具有潜在的对抗性干扰以及已知或对抗性初始条件的线性系统综合动态遗憾最佳控制器。动态遗憾被定义为系统成本的真正成本与在任何输入序列中都可以最佳实现的成本之间的差异，这些序列对给定的干扰能量有充分了解所有未来的干扰。此问题公式可以看作是经典$ \ Mathcal {H} _2 $ - 或$ \ Mathcal {H} _ \ infty $ -control的替代方法。所提出的控制器合成基于系统级参数化，该参数允许将动态遗憾问题重新定义为半明确的问题。这产生了一个新的框架，可以考虑结构化的动态遗憾问题，这些问题尚未在文献中考虑。对于在干扰上已知的椭圆形界限，我们表明，与仅使用有界能量假设相比，动态遗憾界限可以得到改善，并且最佳动态遗憾结合的最大差异最大，最多会差异为$ \ frac {2}π$与计算的解决方案。此外，提出的框架允许保证状态和输入约束满意度。
We present an optimisation-based method for synthesising a dynamic regret optimal controller for linear systems with potentially adversarial disturbances and known or adversarial initial conditions. The dynamic regret is defined as the difference between the true incurred cost of the system and the cost which could have optimally been achieved under any input sequence having full knowledge of all future disturbances for a given disturbance energy. This problem formulation can be seen as an alternative to classical $\mathcal{H}_2$- or $\mathcal{H}_\infty$-control. The proposed controller synthesis is based on the system level parametrisation, which allows reformulating the dynamic regret problem as a semi-definite problem. This yields a new framework that allows to consider structured dynamic regret problems, which have not yet been considered in the literature. For known pointwise ellipsoidal bounds on the disturbance, we show that the dynamic regret bound can be improved compared to using only a bounded energy assumption and that the optimal dynamic regret bound differs by at most a factor of $\frac{2}π$ from the computed solution. Furthermore, the proposed framework allows guaranteeing state and input constraint satisfaction.
