仿射非线性奇异系统的参数自适应控制

研究了一类含有未知参数的仿射非线性奇异系统的自适应控制问题.首先利用Lie导数及Lie括号,对仿射非线性奇异系统进行微分同胚变换,将非线性系统转化为一般线性奇异系统形式;然后基于参数自适应控制方法并结合线性矩阵不等式方法和Lyapunov稳定性理论,设计了自适应调节器方案,并给出系统在自适应调节器方案的作用下,系统在平衡点渐近稳定,参数渐近收敛的充分条件;最后给出数值算例,利用Matlab进行仿真,仿真结果证实了理论结果的有效性和可行性.

Parametric Adaptive Control for Affine Nonlinear Singular Systems

The parametric adaptive control problem was studied for a class of affine nonlinear singular systems with unknown parameter. Firstly, the affine nonlinear singular systems were transformed into generally linear singular systems via diffeomorphic transformation using Lie derivative and Lie bracket. Then, combined with LMI method and the Lyapunov stability theory, the parametric adaptive control method was used to construct an adaptive regulator. What's more, a sufficient condition was given under which the system was asymptotically stable at the point of equilibrium and parameter error was asymptotically convergent. Lastly, a simulation was constructed using Matlab, and the results of simulation showed the effectiveness and feasibility of the presented method.