Adaptive Backstepping Neural Network Control For Several Classes Of Nonlinear Systems

Nonlinear control theory has always been one of the focuses in automatic control com-munity during the last two decades. Especially the adaptive backstepping neural networkcontrol theory, encompounded by backstepping technique and neural network approxima-tion theory, has attracted much attention of many researchers and some important resultshave been obtained. However, there still exist some open issues need to be further inves-tigated. This dissertation is devoted to study the extension of the adaptive backsteppingneural network control scheme to the stochastic nonlinear and discrete-time nonlinear con-trol areas. Some important control theories, such as stability theory of stochastic di?er-ential equations and time-delay functional di?erential equations, as well as decentralizedcontrol theory of interconnected large-scale systems are combined with the adaptive back-stepping neural network control scheme to address the problems of output-feedback controland tracking control for several classes of stochastic nonlinear systems and discrete-timenonlinear systems. Details are as follows:1. Via the circle criterion, a new nonlinear observer is introduced to the stochasticnonlinear systems to estimate the unmeasured states, thus the problem of output-feedbackcontrol can be solved for the stochastic nonlinear strict-feedback system with unmeasuredstates. The main merit of this nonlinear observer lies in that it not only can eliminatethe Lipschitz restriction on the state-dependent nonlinearities of the traditional output-feedback control design, but also can solve the high-gain problem of the linear observer.Most results of the dissertation are based on this technique.2. An output-feedback stabilization control scheme is designed for a class of uncertainstochastic nonlinear strict-feedback systems with unmeasured states, where the adaptivebackstepping neural network control method is combined with the technique of nonlinearobserver design. By constructing a state-quartic and parameter-quadratic Lyapunov func-tion, the closed-loop system can be proved to be stable in probability. Moreover, here onlya neural network is employed to compensate for all unknown nonlinear upper boundingfunctions depending on the system output, which simpli?es the existing adaptive neuralnetwork control schemes.3. The adaptive backstepping neural network control scheme is extended to thestochastic nonlinear time-delay systems. Firstly, based on the circle criterion and the adap-tive backstepping neural network control method, a nonlinear observer is introduced andall the unknown upper bounding function depending on the system output is integratedto be compensated only by a neural network, such that the restriction of the prelimi-nary knowledge of the output-dependent nonlinear upper bounding functions is removed.Then,this idea is further extended to the problem of output-feedback stabilization for a class of uncertain stochastic nonlinear strict-feedback systems with discrete and distributeddelays.4. The adaptive backstepping neural network control scheme is extended to thestochastic nonlinear interconnected systems. Firstly, using decentralized nonlinear ob-server to estimate the unmeasured states and combining with the backstepping technique,for each subsystem only a neural network is employed to compensate for all unknown up-per bounding functions which depend on the respective subsystem outputs, and then theproblem of decentralized stabilization is solved for a class of large-scale stochastic nonlinearstrict-feedback systems. Secondly, by constructing a state-quartic and parameter-quadraticLyapunov-Krasovskii functional and combining with the technique of Young's inequality,the controller designing di?culty of the It?o terms, delay terms and the coupling terms ofall subsystems is removed, so that the problem of adaptive output-feedback stabilization isdealt with for the interconnected stochastic nonlinear delay system.5. The adaptive tracking control problems are considered for a class of discrete-timenonlinear systems with unknown periodically time-varying parameters. By combining withthe neural network approximation technique and Fourier series expansion (FSE), the sys-tems are transformed into a class of simpler linear parametric strict-feedback systems withunknown constant parameters. Then, via the existing discrete-time nonlinear backstep-ping design technique, the adaptive controller can be designed for the new systems, whichcan ensure all the signals of the closed-loop systems are bounded for all bounded initialconditions, reference signals and external disturbances. In addition, a small-in-the-meantracking error can be achieved.