| Popis: |
Stability guarantees of the Externally forced switched (EFS) system in which switches occur deliberately to fulfill an exogenous reason is a crucial problem. High frequent switches, however, can cause instability in switched systems even when all closed-loop modes are stable. The control community has already addressed this classic problem with a known system model by designing a minimum dwell time. However, the gap still exists in the lack of such knowledge and especially when fast switching is deemed necessary. In this work, we aim to address the challenge in LQR setting and within the framework of our posed problem, in which, after a switch, the next mode reveals to switch to, and the task is to make the subsequent switching quickly while guaranteeing boundedness of state norm. We address the problem by designing an OFU-based algorithm that couples system identification and control design procedures. Parallel to the control design, our proposed algorithm also guarantees safe switches based on its estimated dwell time. With a provably tight dwell-time estimate error, we show that our proposed strategy achieves the expected regret of $\mathcal{O}(|\mathcal{M}|\sqrt{ns})$, where $ns$ and $|\mathcal{M}|$ are the total number of switches and the number of modes respectively, compared to the case when all parameters are known. To the best of the authors' knowledge, this is the first work for learning dwell time with guaranteed performance. |
