基于收缩理论的一类非线性系统自适应动态面控制

Contraction theory-based adaptive dynamic surface control for a class of nonlinear systems

针对一类不确定非线性参数严反馈系统,提出基于收缩理论的自适应动态面控制方法.动态面控制器设计保证了各子系统关于状态误差部分收缩;对不确定参数构造收缩自适应律,并利用收缩下的奇异摄动分析降阶处理子系统,确保降阶前后状态误差间的偏差及滤波误差有界;通过分层子系统的收缩鲁棒性分析,证明了原闭环系统状态半全局收敛到以期望轨迹为中心的球域内,保证了跟踪误差及自适应估计有界.刚性机械臂系统仿真验证了所提出方法的有效性.

For a class of uncertain nonlinear systems in the parametric strict feedback form, an adaptive dynamic surface control method based on the contraction theory is proposed. Every subsystem is partially contracting in the state error by designing the dynamic surface controller. The adaptive estimation via contraction is designed for the uncertain parameters.Moreover, the contraction-based singular perturbation analysis is used to reduce the subsystem dynamics, which ensures the differences of the state errors between the original and the reduced subsystems＇ and the differences of the filters are bounded.By analyzing the contraction-based robustness of the hierarchical interconnection of the subsystems, it is proved that the states of the original closed-loop system can semi-globally converge to a ball centered about the desired trajectory, and it is guaranteed that both of the tracking error and adaptive estimation are bounded. Finally, simulation results of the rigid-link electrically driven robot manipulators system show the effectiveness of the proposed method.