一类非线性不确定系统的鲁棒自适应控制

Robust Adaptive Control for a Class of Uncertain Nonlinear Systems

针对一类同时含未建模动态、非线性不确定性和参数不确定性的非线性系统,研究它的鲁棒自适应控制问题。系统中含有的未建模动态是更广泛的输入到状态实践稳定,非线性不确定性满足三角界条件。在李雅普诺夫第二方法框架下,应用自适应反演技巧,显式地构造出光滑的部分状态反馈控制器。该鲁棒自适应控制器能保证对所有允许的不确定性闭环系统的信号全局一致径向有界,且输出收敛于原点的小领域。仿真结果验证了所得结论的有效性。

The problem of robust adaptive control is studied for a class of nonlinear systems subject to unmodeled dynamics,nonlinear uncertainties and parameter uncertainties.The more extensive unmodeled dynamics introduced is input-to-state practical stable（ISpS）,and unknown nonlinearities satisfy triangular bound conditions.In the framework of Lyapunov second method and applying tuning function adaptive backstepping theory,a smooth partial state feedback controller is explicitly constructed,which guarantees global uniform ultimate boundness for all states of closed-loop systems,and renders the output converge to a small neighborhood of the origin for all admissible uncertainties.Eventually a numerical example is given to illustrate the viability of the conclusion.