Direct Model Reference Adaptive Control for Tracking Contracting Nonlinear Systems
Direct Model Reference Adaptive Control for Tracking Contracting Nonlinear Systems
复制标题
DOI：
10.1109/cdc42340.2020.9303884
复制
发表时间：
2020-12
期刊：
影响因子：
--
通讯作者：
N. P. Hyun;M. Petersen;R. Wood
中科院分区：
文献类型：
--
作者：
N. P. Hyun;M. Petersen;R. Wood
针对非线性控制仿射系统，提出了一种新的直接模型参考自适应控制(DMRAC)来跟踪收缩的非线性参考模型。假定不确定性的结构包括输入上的乘性未知参数。收缩参考模型允许使用确定性等价原理(CEP)来设计简单控制器，这一工具通常不能用于非线性系统，因为它在这些系统上的弱点。所提出的控制器被构造为最小化从估计的对象向量场到期望的收缩向量场的距离，这利用了收缩参考模型的优点。即使所提出的控制器不能完全匹配真实的收缩向量场，自适应控制器和自适应律的共同作用使得黎曼距离渐近于零且参数误差有界。此外，将所提算法推广到使用基于控制收缩度量(CCM)的控制器来构造收缩参考模型的情况。以全驱动摆为例，说明了该算法的有效性。
In this paper, a new direct model reference adaptive control (DMRAC) for nonlinear control affine systems is proposed to track a contracting nonlinear reference model. The structure of the uncertainty is assumed, including a multiplicative unknown parameter on the input. The contracting reference model enables the use of the certainty equivalence principle (CEP) for designing the simple controller, a tool which often cannot be used for nonlinear systems due to its weakness on these systems. The proposed controller is constructed to minimize the distance from the estimated plant vector field to the desired contracting vector field, which leverages the benefits of the contracting reference model. Even though the proposed controller does not perfectly match the true contracting vector field, the combined efforts of the adaptive controller and the adaptation law make the Riemannian distance asymptotically approach zero with bounded parameter error. In addition, the proposed algorithm is extended to the case of using a control contraction metric (CCM) based controller to construct the contracting reference model. A fully actuated pendulum example is studied to illustrate the effectiveness of the algorithm.