Data-Driven Synthesis of Optimization-Based Controllers for Regulation of Unknown Linear Systems
Data-Driven Synthesis of Optimization-Based Controllers for Regulation of Unknown Linear Systems
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DOI：
10.1109/cdc45484.2021.9682795
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
G. Bianchin;M. Vaquero;J. Cortés;E. Dall’Anese
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文献类型：
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作者：
G. Bianchin;M. Vaquero;J. Cortés;E. Dall’Anese
本文提出了一个数据驱动的框架来解决与未知线性动力系统相关的时变优化问题。在许多现代工程应用中，做出在线控制决策来调节动态系统以解决优化问题是一个中心目标。然而，现有的方法严重依赖于系统动力学的精确知识，因此在设计控制器之前需要一个初步的系统辨识阶段。在这项工作中，我们利用行为理论的结果表明，线性系统的稳态传递函数可以从数据样本计算，而无需任何知识或估计的系统模型。然后，我们使用这种数据驱动的表示设计控制器，灵感来自梯度下降优化方法，调节系统的凸优化问题的解决方案，而不需要任何知识的时变干扰影响模型方程。结果是定制的成本函数满足Polyak-Jasojasiewicz不等式。
This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to regulate a dynamical system to the solution of an optimization problem is a central goal in many modern engineering applications. Yet, the available methods critically rely on a precise knowledge of the system dynamics, thus mandating a preliminary system identification phase before a controller can be designed. In this work, we leverage results from behavioral theory to show that the steady-state transfer function of a linear system can be computed from data samples without any knowledge or estimation of the system model. We then use this data-driven representation to design a controller, inspired by a gradient-descent optimization method, that regulates the system to the solution of a convex optimization problem, without requiring any knowledge of the time-varying disturbances affecting the model equation. Results are tailored to cost functions satisfy the Polyak-Łojasiewicz inequality.