论文标题
普遍的遗憾最佳控制器合成受约束系统的最佳控制器合成
Generalised Regret Optimal Controller Synthesis for Constrained Systems
论文作者
论文摘要
本文提出了一种用于广义动态遗憾问题的合成方法，将严格因果控制器的性能与加权干扰下的最佳非因果控制器进行了比较。该框架涵盖了动态的遗憾问题，考虑到所产生的成本的差异以及考虑其比例的竞争比率，并且都被认为是对经典控制方法的本质自适应替代方案。此外，我们将合成扩展到了扰动上的点端界限的情况，并表明最佳解决方案并不比有界能量的最佳解决方案差，并且由恒定因子限制，这仅取决于干扰的重量。提出的基于优化的合成允许考虑受状态和输入约束的系统。最后，我们提供了一个数字示例，该示例将合成的控制器性能与$ \ Mathcal {h} _2 $ - 和$ \ MATHCAL {H} _ \ infty $ -Controllers进行了比较。
This paper presents a synthesis method for the generalised dynamic regret problem, comparing the performance of a strictly causal controller to the optimal non-causal controller under a weighted disturbance. This framework encompasses both the dynamic regret problem, considering the difference of the incurred costs, as well as the competitive ratio, which considers their ratio, and which have both been proposed as inherently adaptive alternatives to classical control methods. Furthermore, we extend the synthesis to the case of pointwise-in-time bounds on the disturbance and show that the optimal solution is no worse than the bounded energy optimal solution and is lower bounded by a constant factor, which is only dependent on the disturbance weight. The proposed optimisation-based synthesis allows considering systems subject to state and input constraints. Finally, we provide a numerical example which compares the synthesised controller performance to $\mathcal{H}_2$- and $\mathcal{H}_\infty$-controllers.
