Adaptive Tracking Control Based On Neural Network For Nonlinear Time-delay Systems

With the continuous development of the social productive forces and the increasingly rise of requirement for control performance, the control problems of uncertain nonlinear systems have received a great deal of attention, and a great many of achievements have been reported. It is well known that the time-delays widely exist in the practical control systems. The existence of time-delays has a significant effect on system performance. It cause singularity problems of controllers and may make the closed-loop system unstable. Therefore, the research on control of these systems has important practical significance. In this paper, combining Lyapunov-Krasovskii(L-K) functional, neural network approxi-mate ability and Lyapunov stability theory, some adaptive control schemes have been designed for a class of nonlinear time-delay systems. The main work is outlined as follows.Firstly, based on the principle of variable structure control and Nussbaum-type functions, two improved adaptive control schemes are proposed for a class of more gen-eral uncertain multi-input and multi-output(MIMO) nonlinear time-varying delay systems with unknown disturbances and nonlinear dead-zones. Neural networks are utilized to approximate the unknown nonlinear functions in the design. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii func-tionals. The proposed controller is continuous and does not cause the chattering pheno-menon. The restrictions of the control gain are relaxed by utilizing the quadratic-type Lyapunov function. The system under study is more universal. It is proved that the proposed design method is able to guarantee global uniform ultimate boundness of all the signals in the closed-loop system, and the output tracking error is proved to converge to a small neighborhood of the origin by theoretical analysis.Secondly, based on the approximation capability of the neural networks, a decen-tralized adaptive neural network control scheme is developed for a class of large-scale nonaffine nonlinear interconnected systems with unknown time-varying delays. The unk-nown nonaffine functions are separated by the mean value theorem, while the restrictions of the unknown time delays and the uncertain time-varying delay interconnections are relaxed by utilizing the Separation technique and the Young’s inequality in the design. The number of adjustable parameters is considerably reduced. In addition, time delay uncertainties are compensated for using Lyapunov-Krasovskii functionals. By the theo-retical analysis, all of the signals in the closed-loop system are shown to be bounded, while the output tracking errors converge to a small neighborhood of the origin.Thirdly, a decentralized adaptive neural network controller is developed for a class of large-scale nonaffine time-varying delays nonlinear systems with unknown control direc-tions and dead-zones inputs. The design is based on the property of Nussbaum-type fun-ctions and the approximation capability of the neural networks. The unknown nonaffme function is separated by the mean value theorem, while the restrictions of the unknown time delays and uncertainties time-varying delays interconnections are relaxed by utili-zing the Separation technique and Young’s inequality. In addition, the number of adjust-able parameters is considerably reduced. By the theoretical analysis, it is proved that all the signals in the interconnected closed-loop system with decentralized adaptive contro-llers are semi-globally uniformly bounded, and the output tracking errors converge to a small neighborhood of the origin.Lastly, based on the principle of variable structure control, an adaptive robust neural network control scheme is developed for a class of uncertain multivariable nonlinear state time-varying delay systems with unknown external disturbance uncertainties and input nonlinearities. Neural networks are utilized to approximate the unknown nonlinear func-tions in the design. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals. In addition, we will exploit a decom-position of the control gain matrix into a symmetric positive-definite matrix, a diagonal matrix with diagonal entries+1or-1and a unity upper triangular matrix. By the theor-etical analysis, it is proved that all the signals in the interconnected closed-loop system with decentralized adaptive controllers are semi-globally uniformly bounded, and the output tracking errors converge to a small neighborhood of the origin.