论文标题
线性离散时间系统具有稳定稳定性的线性离散时间系统的虚拟参考反馈调整，可确保基于设置成员资格
Virtual Reference Feedback Tuning for linear discrete-time systems with robust stability guarantees based on Set Membership
论文作者
论文摘要
在本文中，我们提出了一种新颖的方法，该方法允许以纯粹的基于数据的方式以及线性单输入和单输出系统设计，既稳定稳定又可以执行控制系统，以跟踪分段恒定参考信号。该方法同时使用（i）虚拟参考反馈调整来执行合适的性能以及（ii）提供A-Priori稳定稳定性保证的设置成员资格框架。实际上，通过集合成员身份识别获得了系统参数的不确定性集，其中提出了基于场景方法的算法来以概率方式估算通货膨胀参数。基于此集合，在优化问题中，线性矩阵不等式约束（线性成本函数依赖于虚拟参考反馈调整）中，强大的稳定性条件被执行。为了显示我们方法的一般性和有效性，我们将其应用于两个最广泛但最简单的控制方案，即通过（i）（i）静态馈电动作以及（ii）闭环中的集成器。由于设定的成员身份识别，提出的方法未完全指导。但是，不确定性集用于为闭环系统提供可靠的稳定性保证的唯一目标，并且它不直接用于性能优化，而这完全基于数据。参考两个仿真示例证明了开发方法的有效性。还与其他数据驱动方法进行了比较。
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.
