On Adaptive Control Of Nonlinear Systems With Unmodeled Dynamics

Along with the economic development and the advancement of technology, the requirements of the control systems continue to increase, the adaptive control problems of the nonlinear systems with unmodeled dynamics have received widespread attension of the control workers. The unmodeled dynamics widely exists in the practical control systems. If we ignore it in the controllers design, practical control results often can not reach the ideal requirements, even systems would be oscillate or divergent. One of the main methods is that, when the unmodeled dynamics satisfy exp-ISpS, an available dynamic signal is introduced to dominate the unmodeled dynamics. Combined backstepping design, dynamic surface technology, neural networks, adaptive control and output feedback control, several adaptive neual network control procedures is proposed for a class of nonlinear systems with unmodeled dynamics. The main work is as follows.Firstly, based on the backstepping design, a novel adaptive control scheme is proposed for a class of nonlinear strict feedback systems with unmodeled dynamics and unknown time-varying delays. The neural networks are used to approximate the unknown functions. An available dynamic signal is introduced to dominate the unmodeled dynamics. The unknown time-varying delays can be compensated for using appropriate Lyapunov-Krasovskii functional. Compared with the existing results, the proposed system model is more general, the restriction of the dynamic disturbances is relaxed, and the number of online adjusted parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is proved to be semi-globally uniformly ultimately bounded.Secondly, based on the principle of backstepping design, a novel adaptive control scheme is proposed for a class of nonlinear strict feedback systems with unmodeled dynamics and unknown function control gain. In this paper, an available dynamic signal is used to dominate the unmodeled dynamics. The problem of unknown control direction and the unknown function control gain is solved by using the property of Nussbaum function. The controller singularity problem is avoided by the use of integral Lyapunov function, which may be caused by time-varying gain functions. By using theoretical analysis, the closed-loop systems is proved to be semi-globally uniformly ultimately bounded.Thirdly, an adaptive dynamic surface control (DSC) procedure is proposed for a class of nonlinear systems in pure-feedback form with unmodeled dynamics. Neural networks are used to approximate the unknown continuous functions. A dynamic signal is introduced to dominate the dynamic disturbances. Compared with the existing literature, the proposed design scheme simplifies the processing procedure of the unmodeled dynamics, and cancels the assumption of the neural network approximation error to be bounded. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded.Lastly, a novel adaptive output feedback control procedure is proposed for a class of nonlinear systems with dynamic uncertainties and the unmeasured states. The neural networks are used to approximate the unknown nonlinear functions. K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By introducing the dynamic surface control technique, the over-parametrization problem is avoided. Compared with the existing literature, the proposed system model is more general, and the asymptotical tracking control is achieved, moreover, the number of online adjusted parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded.