AI 中文总结
研究任意切换下切换系统的鲁棒控制问题,提出联合合成反馈策略及其闭环值函数上界的框架，利用路径完备图和可达性图概念，结合函数得到策略及上界，通过半定规划等方法求解，实验证明该方法对反馈控制和模型预测控制均实用。
AI 中文摘要
本文研究了具有性能保证的任意切换下切换系统的鲁棒控制。我们提出了一个框架，该框架联合合成一个反馈策略及其相应无限时域闭环值函数的一个经认证的上界。所提出的上界不仅能证明合成策略的性能，还能在控制器合成过程中进行优化。具体而言，我们的方法将函数与路径完备图的节点相关联，并沿其边强制实施基于图的贝尔曼不等式。利用新引入的可达性图的概念，这些函数被组合成一个反馈策略及其相应闭环值函数的经认证上界，该上界表示为图索引函数的逐点最小 - 最大组合。对于具有二次阶段成本的线性切换系统，所提出的框架允许基于半定规划和交替优化的易于处理的计算公式。数值实验，包括建筑温度调节基准测试，证明了所提出方法对于使用合成策略进行直接反馈控制以及使用经认证上界作为终端成本进行模型预测控制的实际有用性。
英文摘要
This paper addresses the robust control of switched systems under arbitrary switching with performance guarantees. We propose a framework that jointly synthesizes a feedback policy and a certified upper bound on its corresponding infinite-horizon closed-loop value function. The proposed upper bound not only certifies the performance of the synthesized policy, but can also be optimized during controller synthesis. More precisely, our approach associates functions with the nodes of a path-complete graph and enforces graph-based Bellman inequalities along its edges. Exploiting a newly introduced notion of reachability graph, these functions are combined into both a feedback policy and a certified upper bound on its corresponding closed-loop value function, expressed as a pointwise min-max combination of the graph-indexed functions. For linear switched systems with quadratic stage costs, the proposed framework admits tractable computational formulations based on semidefinite programming and alternating optimization. Numerical experiments, including a building temperature regulation benchmark, demonstrate the practical usefulness of the proposed approach both for direct feedback control using the synthesized policy and for model predictive control using the certified upper bound as a terminal cost.
CommentsSubmitted to Automatica
