控制方向未知的高次非线性系统的鲁棒自适应控制

Robust adaptive control of high order nonlinear systems with unknown control directions

研究了一类具有不可控不稳定线性化的非线性系统的自适应控制问题.该类系统的控制方向未知且含有不确定时变非线性参数.应用Nussbaum-type增益技术和adding a power integrator递推设计方法,设计了一种鲁棒自适应状态反馈控制器.所设计的控制器能够保证闭环系统的所有信号全局一致有界,且系统的状态渐近趋于零.除了假设未知参数及不确定性有界外,所设计的控制策略不需要控制系数的任何先验知识.仿真例子验证了算法的有效性.

The problem of adaptive control for a class of nonlinear systems with uncontrollable and unstabilizable linearization is studied in this paper. The class of systems have unknown time-varying virtual control coefficients and uncertain time-varying nonlinear parameters. A robust adaptive state feedback controller is designed by employing the Nussbaum-type gain technique and adding a power integrator design approach. The controller guarantees all signals of the closed-loop system to be globally uniformly bounded. Especially, the state signals asymptotically converge to zero. The proposed design method does not require any a prior knowledge of the unknown control coefficients except for their bounds. The effectiveness of the proposed algorithm is verified by a simulation example.