Adaptive Control Of Discrete-time Nonlinear Systems Via Backstepping

Backstepping design of nonlinear systems is a kind of structural technique, usuallyused with Lyapunov-based adaptive law to drive the whole closed loop system to thedesired dynamic and static properties. In respect of designing robust/adaptive controllerfor uncertain systems, backstepping techniques have predominant advantages,especially when the disturbances or uncertainties don't satisfy the matching conditions.And the universal approximation property of neural networks (called NN for short)makes them have huge potentiality in dealing with high nonlinearity and criticaluncertainty. So combining with the two methods to design adaptive neural networkcontroller is a very active topic of study research now. And what is more, adaptivecontrol for nonlinear discrete-time systems is a very challenging problem. The adaptive backstepping control of discrete-time nonlinear systems is discussed inthis paper. Firstly, background of the development of adaptive control theory and thehistory and current situations of discrete-time nonlinear adaptive control systems areintroduced. And the fundamental principles and structural methods of backsteppingtechniques for discrete-time systems are given along with the parameter estimationalgorithms and some important stability results. Secondly, adaptive NN control for aclass of strict-feedback discrete-time nonlinear systems with unknown functions isinvestigated via backstepping. The functional uncertainties are resolved by awavelet-based neural network (called WNN for short) function approximator. Then arobust adaptive backstepping controller without overparametrization is proposed, whichshows the stability and tracking properties of the closed loop systems. Moreover, anadaptive iterative learning control (called ILC shortly) scheme is put forward in thedirection of discrete time domain by employing high-order neural networks (shortlycalled HONNs) to a class of unknown nonlinear discrete-time systems. Theε -trackingare achieved. The efficiency and characteristic of the proposed scheme are also shownthrough a simulation example. Lastly, adaptive backstepping control of multi-variablediscrete-time nonlinear systems is studied. The stability of the closed loop system isanalyzed by applying the Key Technical Lemma and the properties of the projectionalgorithm to the multiple-input multiple-output (MIMO for short) system with twothree-order subsystems. Problem existing in the adaptive backstepping control forMIMO nonlinear discrete-time systems are also illustrated.