针对一类单输入单输出的非仿射纯反馈非线性切换系统,研究了一种在任意切换下的自适应控制策略.首先,引入中值定理处理系统的非仿射特性问题,并利用径向基函数神经网络逼近系统的未知非线性动态.然后,采用 Nussbaum函数处理系统控制增益未知的问题,且在反演设计的每一步引入低通滤波器以解决“微分爆炸”问题.最后,基于共同Lyapunov函数设计状态反馈控制器,并分析闭环系统的稳定性.所设计的控制器避免了切换发生时控制参数跳变和调节参数过多的问题,减少了计算负荷,可以保证闭环系统所有信号半全局一致有界,且跟踪误差可收敛到原点的一个较小邻域.仿真结果验证了控制策略的有效性.

Focusing on the issue of adaptive neural tracking control for a class of single input and single output unknown non-affine pure feedback nonlinear switching systems, the mean-value theorem was applied to deal with the non-affine problem successively, and the unknown nonlinear nonlinearities were approximated by radial basis function neural network. Next, the Nussbaum gain technique and the first-order filter were employed to solve the unknown control coefficients and the “explosion of complexity” problem. Finally, a state-feedback controller was proposed by using the common Lyapunov function approach, and the stability of the closed-loop system was analyzed. The proposed controller can decrease the number of learning parameters, and avoid parameter jump when the switch occurs, thus reduces the computational burden. The proposed controller can guarantee that all the signals in the closed-loop system are semi-globally, and the tracking error converges to a small neighborhood of the origin. The simulation results verify the feasibility and effectiveness of the approach.