不确定非线性系统的自适应神经网络跟踪控制

不确定非线性系统的自适应神经网络跟踪控制

[摘 要]

自适应backstepping控制技术在非线性系统控制综合中一直占有非常重要的位置。对于具有下三角形式的参数不确定非线性系统，该设计方法能够有效地解决这种系统的镇定以及跟踪控制等问题。但是实际中的系统所呈现的不确定性往往十分复杂，参数不确定这种简单的情况只是少有的一部分，当面对系统非线性完全未知时，传统的自适应backstepping方法将不再适用。而结合神经网络（NN）所诞生出来的自适应神经网络控制算法不仅继承了传统方法的精髓，同时还弥补了传统方法的不足。在现代智能算法中，神经网络有着强有力的函数逼近能力，正是从这一点出发，将神经网络和自适应backstepping设计方法相结合有效地解决含有完全未知函数的非线性系统的相关控制问题。

本论文基于自适应NN控制算法，主要研究了三类含有完全未知不确定性的非线性系统的跟踪控制问题，首先研究的是一类具有非严格反馈形式的切换非线性系统，通过将共同Lyapunov函数方法和自适应NN控制相结合，设计的状态反馈控制器能够保证目标信号被有界跟踪。然后针对的是一类高阶非线性系统，通过结合增加幂次积分和自适应NN控制技术解决了相应的跟踪控制问题。最后考虑了一类含有执行器死区非线性的切换随机系统，通过借助于处理随机系统的一套理论和方法（包括随机系统微分算子，随机系统的有界稳定性定义等）同时结合自适应NN控制方法，设计了一类状态反馈控制器，能够使系统输出能够几乎确定地有界跟踪目标信号

[关 键 词]：自适应控制；神经网络；切换系统；高阶系统；随机

系统

I

ADAPTIVE NN TRACKING CONTROL FOR UNCERTAIN

NONLINEAR SYSTEMS

ABSTRACT

Adaptive backstepping technique has been taken an important position in the control synthesis of nonlinear systems. For strict feedback nonlinear systems with parameter uncertainties, adaptive backstepping method can effectively solve the stabilization and tracing problem of such systems. However, most uncertainties in practical systems are very complex; parameter uncertainties just represent a small part of them. Traditional adaptive backstepping technique cannot be used when the system contain completely unknown uncertainties. Adaptive neural network (NN) control technique, as a NN algorithm-based design method, not only inherits the quintessence of traditional method, but also makes up the shortcomings of traditional adaptive backstepping technique. In modern intelligence algorithm, NN has shown its powerful ability in approximating nonlinear functions. Therefore, adaptive NN backstepping design method can effectively address the control problems of nonlinear systems with completely unknown uncertainties.

Based on adaptive NN control technique, the tracking control problems of three types of uncertain nonlinear systems with completely unknown uncertainties are considered in this paper. First, the bounded tracking problems of a class of switched nonstrict-feedback nonlinear systems are investigated by combing the common Lyapunov function method with adaptive NN technique, and the target signal can be bounded tracked by the system output under the designed state feedback controller. Then, the tracking control problems of a class of high order nonlinear systems are solved by using adding a power integrator and adaptive NN

II