On Adaptive Control Of Uncertain Nonlinear Systems With Time-varying Delays And Unmodeled Dynamics

In the practical engineering systems,most control systems present to be intrinsically nonlinear,uncertain and time-varying,existing control theory cannot be directly applied to the nonlinear systems with complex features.On the other hand,time delays and unmod-eled dynamics are common phenomena in the real-world systems,which can be often found in industrial production and networked systems.If not properly control,time delays and unmodeled dynamics can deteriorate system performance and even make the system insta-bility.In fact,in order to extend the existing control strategies to nonlinear systems with time-varying delays and unmodeled dynamics,some severe restrictions are usually imposed,which often results in the conservatism in the process of controller design.It is imperative to introduce the new methods or improve the existing techniques to reduce the conservatism.Based on the existing works,this thesis utilizes the neural networks' universal approxima-tion property to investigate two control problems with time delays and unmodeled dynamics.One is the problem of adaptive control for uncertain nonlinear systems;the other one is the distributed coordinated control problem of uncertain nonlinear multi-agent systems.details can be seen as follows:1.A novel robust adaptive neural control scheme is proposed for a class of uncertain time-varying delayed nonlinear systems with dead-zone input and unmodeled dynamics.In the process of controller design,radial basis function neural networks are employed to approximate the unknown nonlinear functions obtained by Young's inequality.By combining adaptive backstepping method,an adaptive neural tracking controller is fi-nally developed.By constructing the exponential Lyapunov-Krasovskii functional,the state time-varying delay uncertainty is compensated for without requiring the known in-formation of its upper bound functions.Using Young's inequality and RBFNNs,the assumptions with respect to unmodeled dynamics are relaxed.It is worth pointing out that only one learning parameter needs to be tuned at each step of the recursive design,thus the computational burden can be alleviated.2.The problems of adaptive neural network tracking control for uncertain nonstrict-feedback nonlinear systems with multiple time-varying delays are investigated.First,we con-sider the nonstrict-feedback nonlinear systems with unmodeled dynamics and multiple time-varying delays.Adaptive backstepping technique,neural networks' approximation theory and quadratic Lyapunov function method are combined to develop a robust adap-tive control scheme.The character of the proposed control strategy is that the newly developed Lyapunov-Krasovskii functionals not only appropriately deal with the mul-tiple state time-varying delays,but also make the delayed nonlinearities free from any assumptions.In addition,by utilizing variable separation technique and bounding func-tions' monotonously increasing property,the restrictive assumption of the dynamic dis-turbance with respect to unmodeled dynamics is relaxed.Second,the tracking control problem is addressed for a class of switched nonstrict-feedback nonlinear systems with multiple time-varying delays.It is proved that the tracking error of adaptive neural control systems is bounded with common Lyapunov function method and Lyapunov-Krasovskii functional method.Compared with the existing results,only one adaption parameter needs to be tuned regardless of the number of the the switched subsystems by introducing a novel continuous function at each step of the recursive design.As a result,the computational burden is alleviated,which is much more practical for application.3.The problem of adaptive error-constrained neural tracking control for uncertain nonstrict-feedback systems in the presence of unknown symmetric output dead-zone and input saturation.A Nussbaum type function is introduced to handle the singularity prob-lem of discontinuity function of dead-zone output model.A barrier Lyapunov function is exploited to solve the problem of tracking control without violating the error con-straints.With the help of auxiliary first-order filters,the dimensions of neural network input are reduced in each recursive design.It is rigorously shown that the proposed output-constrained controller guarantees that all the closed-loop signals are semiglobal uniformly ultimately bounded and the tracking error never violates the output constraint.A Brusselator chemical model and the dynamic model of the electromechanical system are used to illustrate the feasibility and effectiveness of the proposed control method.4.The problem of distributed consensus control for uncertain nonlinear multi-agent sys-tems is investigated.First,we consider the uncertain pure-feedback nonlinear multi-agent systems,neural networks are employed to compensate the unknown nonlinear functions,adaptive dynamic surface control and Lyapunov stability theory are com-bined to develop a distributed consensus control scheme.Furthermore,the problem of distributed consensus control for a class of pure-feedback nonlinear multi-agent systems with unmodeled dynamics is considered.By introducing an available dynamic signal,the obstacle caused by unmodeled dynamics is conquered.The distributed dynamic sur-face controllers are designed to ensure that the output of each follower synchronize with the leader.A numerical example is provided to illustrate the feasibility of the proposed control scheme.