基于DSC后推法的非线性系统的鲁棒自适应NN控制

针对一类具有不确定系统函数和方向未知的不确定增益函数的非线性系统, 提出了一种鲁棒自适应神经网络控制算法. 本算法采用RBF神经网络(Radial based function neural network, RBF NN)逼近模型不确定性, 外界干扰和建模误差采用非线性阻尼项进行补偿, 将动态面控制(Dynamic surface control, DSC)与后推方法结合, 消除了反推法的计算膨胀问题, 降低了控制器的复杂性; 尤其是采用Nussbaum函数处理系统中方向未知的不确定虚拟控制增益函数, 不仅可以避免可能存在的控制器奇异值问题, 而且还能使得整个系统的在线学习参数显著减少, 与DSC方法优点结合, 使得控制算法的计算量大为减少, 便于计算机实现. 稳定性分析证明了所得闭环系统是半全局一致最终有界(Semi-global uniformly ultimately bounded, SGUUB)的, 并且跟踪误差可以收敛到原点的一个较小邻域. 最后, 计算机仿真结果表明了本文所提出控制器的有效性.

DSC-backstepping Based Robust Adaptive NN Control for Nonlinear Systems

A systematic procedure for synthesis of robust adaptive neural network control is proposed for a class of strict- feedback nonlinear systems with both unknown system nonlinearities and unknown virtual control gain nonlinearities. By employing radial based function neural network (RBF NN) to approximate uncertain nonlinear system functions, and nonlinear damping item to compensate for both external disturbance and modeling error, and by combining dynamic surface control (DSC) with backstepping technique and Nussbaum gain approach, the algorithm can not only overcome both the "explosion of complexity" problem inherent in the backstepping method and the possible "controller singularity" problem, but also reduce dramatically the number of on-line learning parameters, thus reducing the computation load of the algorithm correspondingly and making it easy in actual implementation. The stability analysis shows that all closed-loop signals are semi-global uniformly ultimately bounded (SGUUB), with the tracking error converging to a small neighborhood of the origin by appropriately choosing design constants. Finally, simulation results are presented to show the effectiveness of the proposed algorithm.