Rapid dynamical learning from neural control of sampled-data nonlinear systems via pseudo-inverse regression filter vector signal

Abstract

In this paper, a rapid neural learning control method utilizing a pseudo-inverse regression filter vector signal strategy is developed for sampled-data strict-feedback nonlinear systems, targeting enhancements in both neural learning speed and output tracking performance. Firstly, the consistency condition is proposed to ensure the stability of the sampled-data system, which is derived from the stability framework of the approximate model. Subsequently, a pseudo-inverse regression filter vector signal-based adaptive neural dynamic surface control (PIRFVB-ANDSC) is proposed by integrating digital first-order filter, regression filter and pseudo-inverse technique. Specially, a new form of NN weight updating law is built upon the pseudo-inverse regression filter vector signal. The persistent excitation (PE) level of the pseudo-inverse regression filter signal is verified to be independent of the system control gain function and PE level of Gaussian activation function which is convenient for performance analysis. Then, it is verified that PIRFVB-ANDSC effectively accelerates convergence of NN estimated weights and reduces the consumption of computing resources. The convergent weights are utilized to develop a disturbance observer-based neural learning dynamic surface control (DOB-NLDSC) to improve robustness. Finally, the simulation comparison demonstrates several key advantages of the scheme with some merits including the rapid NN learning speed, the enhanced tracking performance, and the strong robustness.