基于集合隶属度的鲁棒稳定性保证线性离散系统的虚拟参考反馈整定

William D'Amico, M. Farina
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引用次数: 1

摘要

在本文中,我们提出了一种新的方法,允许以纯粹基于数据的方式设计线性单输入和单输出系统,用于跟踪分段恒定参考信号的鲁棒稳定和执行控制系统。该方法同时使用(i)虚拟参考反馈调优(Virtual Reference Feedback Tuning)来实现合适的性能,以及(ii)集合成员框架来提供先验的鲁棒稳定性保证。通过集合隶属度辨识得到系统参数的不确定性集,并提出了一种基于情景方法的算法,以概率的方式估计膨胀参数。在此基础上,以线性代价函数依赖于虚拟参考反馈调优的优化问题的线性矩阵不等式约束来实现鲁棒稳定性条件。为了展示我们方法的通用性和有效性,我们将其应用于两种最广泛使用但最简单的控制方案,即通过(i)静态前馈动作和(ii)闭环积分器实现跟踪。由于集合隶属度的识别,该方法不是完全直接的。然而,不确定性集的使用仅仅是为了为闭环系统提供鲁棒稳定性保证,而不是直接用于性能优化,而是完全基于数据进行优化。通过两个仿真算例验证了所提方法的有效性。并与其他数据驱动方法进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Virtual Reference Feedback Tuning for linear discrete-time systems with robust stability guarantees based on Set Membership
In this paper we propose a novel methodology that allows to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant reference signals. The approach uses both (i) Virtual Reference Feedback Tuning for enforcing suitable performances and (ii) the Set Membership framework for providing a-priori robust stability guarantees. Indeed, an uncertainty set for the system parameters is obtained through Set Membership identification, where an algorithm based on the scenario approach is proposed to estimate the inflation parameter in a probabilistic way. Based on this set, robust stability conditions are enforced as Linear Matrix Inequality constraints within an optimization problem whose linear cost function relies on Virtual Reference Feedback Tuning. To show the generality and effectiveness of our approach, we apply it to two of the most widely used yet simple control schemes, i.e., where tracking is achieved thanks to (i) a static feedforward action and (ii) an integrator in closed-loop. The proposed method is not fully direct due to the Set Membership identification. However, the uncertainty set is used with the only objective of providing robust stability guarantees for the closed-loop system and it is not directly used for the performances optimization, which instead is totally based on data. The effectiveness of the developed method is demonstrated with reference to two simulation examples. A comparison with other data-driven methods is also carried out.
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