最小相位不确定非线性系统的观测器设计

针对一类系统相对阶小于系统阶数的非线性系统,提出了一种基于输入输出线性化的观测器设计方法。首先考虑了模型已知时的非线性系统,通过微分同胚,将原系统变换为标准型,证明只要系统的零动态是局部指数稳定的,则基于估计误差的非线性动态方程是稳定的,即估计状态收敛到真实状态。然后分析了存在模型不确定性的系统的观测器设计问题,用RBF神经网络逼近不确定性,设计了神经网络加权系数的调整规律和Lyapunov函数,实现了含有不确定性时误差动态方程的渐近稳定性。仿真结果证明了算法的有效性。

Observer design for minimum phase uncertain nonlinear systems

An observer design approach based on input-output linearization for a class of nonlinear systems whose relative degree is less than its orders is proposed.First the nonlinear systems with no uncertainty is analysized and is transformed diffeomorphically into a canonical system,a given observer struction guarantees the observer error converges to zero provided zero dynamics is asympototically stable.Based on known system model and its Lyapunov function,the system with uncertainty is considered and a neural network is applied to approximate uncertain term.According to the update law of parameter and a modified Lyapunov function,the stability of system with uncertainty is proved.Simulations performed on a nonlinear system illustrate and clarify the approach.