arXiv 2304.005692023-04-02eess.SYcs.LGcs.SYmath.OC

具有输入约束的离散时间多维随机线性系统基于学习的自适应控制的稳定性界

Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraints

University of Melbourne（墨尔本大学）

Seth Siriya, Jingge Zhu, Dragan Nešić, Ye Pu

备注：: 21 pages, 1 figure, submitted to 62nd IEEE Conference on Decision and Control

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AI总结：

针对参数未知、含输入约束与无限随机干扰的离散时间多维线性系统，提出结合在线参数估计与饱和线性控制的确定性等价控制方案，并证明了闭环系统的高概率稳定性界。

摘要：

我们考虑在真实系统参数未知的情况下，具有有界控制输入约束和无限随机干扰的离散时间多维线性系统的自适应镇定问题。为应对这一挑战，我们提出了一种结合在线参数估计与饱和线性控制的确定性等价控制方案。在对系统和噪声过程施加额外假设的条件下，我们证明了闭环系统存在高概率稳定性界。最后，通过数值算例来阐明我们的结果。

英文摘要：

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To address this challenge, we propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control. We establish the existence of a high probability stability bound on the closed-loop system, under additional assumptions on the system and noise processes. Finally, numerical examples are presented to illustrate our results.

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