Robust Local Stabilization of Nonlinear Systems With Controller-Dependent Norm Bounds: A Convex Approach With Input-Output Sampling
Robust Local Stabilization of Nonlinear Systems With Controller-Dependent Norm Bounds: A Convex Approach With Input-Output Sampling
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DOI：
10.1109/lcsys.2022.3229004
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发表时间：
2022-12
影响因子：
3
通讯作者：
Sze Kwan Cheah;Diganta Bhattacharjee;Maziar S. Hemati;R. Caverly
中科院分区：
文献类型：
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作者：
Sze Kwan Cheah;Diganta Bhattacharjee;Maziar S. Hemati;R. Caverly
这封信提出了一个框架，合成一个鲁棒全状态反馈控制器的系统未知的非线性。我们的方法特征的输入-输出行为的非线性的局部范数界使用可用的采样数据对应于一个已知的区域的平衡点。在这种方法中的一个挑战是，如果非线性有显式依赖于控制输入，先验选择的控制输入采样区域是必需的，以确定当地的范数界。这导致了一个“鸡和蛋”的问题，其中的本地范数界控制器的合成是必需的，但该区域的控制输入需要被表征之前不能知道的控制器的合成。为了解决这个问题，我们限制在采样区域内的闭环控制输入，同时合成控制器。由于所得到的综合问题是非凸的，三个半定规划（SDP）的主要问题，通过凸松弛，并构造了一个迭代算法，使用这些SDP的控制综合。两个数值例子证明了所提出的算法的有效性。
This letter presents a framework for synthesizing a robust full-state feedback controller for systems with unknown nonlinearities. Our approach characterizes input-output behavior of the nonlinearities in terms of local norm bounds using available sampled data corresponding to a known region about an equilibrium point. A challenge in this approach is that if the nonlinearities have explicit dependence on the control inputs, an a priori selection of the control input sampling region is required to determine the local norm bounds. This leads to a “chicken and egg” problem, where the local norm bounds are required for controller synthesis, but the region of control inputs needed to be characterized cannot be known prior to synthesis of the controller. To tackle this issue, we constrain the closed-loop control inputs within the sampling region while synthesizing the controller. As the resulting synthesis problem is non-convex, three semi-definite programs (SDPs) are obtained through convex relaxations of the main problem, and an iterative algorithm is constructed using these SDPs for control synthesis. Two numerical examples are included to demonstrate the effectiveness of the proposed algorithm.