Discussion And Research On Adaptive Neural Network Control Of Discrete-Time Nonlinear System

It has been proved that neural network can approximate any nonlinear continuous function to the desired accuracy in a compact set. Based on this nature of neural networks, many scholars have carried out some active research in the adaptive neural network control. Currently, most research focused on continuous-time nonlinear system. However, discrete-time nonlinear systems than the continuous-time system can more accurately describe the actual controlled object, hence the control schemes of discrete-tiem systems has the important theoretical and practical significance.In discrete-time domain, a major drawback of the existing adaptive NN control methods is that there are too many adaptive parameters needed to be tuned on-line, especially for nonlinear MIMO discrete-time higher-order systems, the learning time tends to be unacceptably large and the time-consuming process is unavoidable. Considering this defect, based on Lyapunov's stability theory, the main works are as followsFirst, adaptive state feedback neural network (NN) control be investigated for two classes of signal-input signle-output (SISO) discrete-time nonlinear systems. Throgh the transformation of the systems, the control schemes avoid the so-called controller singularity problem in adaptive control. By suitably choosing the design parameters, the closed-loop systems are proven to be semi-globally uniformly ultimately bounded (SGUUB) and the propsed methods needs only less parameters to be adjusted online, therefore, it can reduce on-line computation burden. Simulation examples are employed to illustrate the effectiveness of the proposed algorithm.Further, adaptive output feedback nerual network (NN) control is proposed for a class of second order discrete-time nonlinear systems. The NN backstepping approach is utilized to design the adaptive output feedback controller. The non-causal problem encountered during the control design is overcomed by using the neural network approximation desired controller. The adaptive output feedback controller needs only to adjust less adaptive parameters, therefore, it is clear that the proposed schemes can reduce on-line computation burden. Simulation studies show the effectiveness of the newly proposed schemesFinally, adaptive output feedback NN control is presented for a class of multi-input multi-output (MIMO) discrete-itme nonlinear systems. By introducing the mapping to be diffeomorphism, the considered MIMO systems can be transformed into the input–output representation. Effective output feedback adaptive control is developed using backstepping, based on Lyapunov analysis method, it is proven that the closed-loop system is stable in the sense that semi-globally uniformly ultimately bounded (SGUUB). In contrast to the existing results, the advantage of the developed scheme is that the quantity of the adjustable parameters is hugely alleviated. The effectiveness of the developed scheme is illustrated by a simulation example.