Nonlinear Adaptive Neural Network Control Study

Most real-world systems present to be uncertain,intrinsically nonlinear, time-varying,and linear control system theory is insufficient to explicitly explain the complex dynamics features of nonlinear systems.Adaptive neural network has been proven to a powerful and effective method for controlling nonlinear systems with unknown functions.On the other hand,time delays are a common phenomenon in many practical control systems,which can be often found in industrial productions, network communication.In fact,delays can usually degrade system's performance and even cause system instability.In many practice,the effect of time delays is not be ignored and needs to be taken into account in the stability analysis and the control design for the nonlinear systems under study.Based on the current research findings on intelligent control of nonlinear systems,this thesis studies adaptive neural control for delay-free nonlinear systems and nonlinear time-delay systems.The main results of the thesis are divided into 6 chapters which are summarized as follows:1.A direct adaptive neural control is developed for a class of single-input-single-output(SISO) strict-feedback nonlinear systems.In the control design, radial basis function(RBF) neural network is used to approximate unknown virtual control signals rather than the unknown nonlinear functions.Backstepping is utilized to construct adaptive neural control for the systems under consideration and integral-type Lyapunov is employed to analyze the stability of the closed-loop system.The proposed scheme not only guarantees the boundedness of all the signals in the resulting closed-loop systems and good tracking performance,but also avoids the singularity problem of controller.It is worth to pointing out that the proposed scheme has the simple structure and less adaptive parameters.As a result, the computational burden of the scheme is alleviated,which might render our design scheme more suitable for practical applications.The developed design scheme is applied to design state-feedback controller for Brusselator chemical model and single-line flexible manipulator.Simulation results demonstrate the effectiveness of the proposed scheme.2.For a class of SISO strict-feedback nonlinear time-delay systems,backstepping and Lyapunov function are combined to develop an adaptive neural control scheme and Lyapunov-Krasovskii functional is used to compensate nonlinear time-delay terms. The designed controller guarantees the boundedness of all the signals in the closed-loop system.Simulation studies are given to illustrate the effectiveness of the proposed scheme.3.The tracking problem is addressed for a class of multiple-input-multiple-output (MIMO) strict-feedback nonlinear systems.According to the feature of the considered system with unknown nonlinear functions,RBF neural network and backstepping are combined to present a direct adaptive neural control scheme.The proposed scheme guarantees the boundedness of the closed-loop system and the racking performance.The character of the proposed scheme is that the designed controller has a simple structure and less adaptive parameters for a class of MIMO nonlinear systems.An inverted cart-pendulum and a two continuous stirred tank reactor process are used to illustrate the effectiveness of the proposed scheme.4.The neural approximation disturbance decoupling is solved for a class of MIMO strict-feedback nonlinear systems by backstepping design.Nonlinear functions and nonlinear time-delay functions in the considered systems are completely unknown, and RBF neural network is used to approximate unknown nonlinear functions.In each step of backstepping design,Lyapunov-Krasovskii functional are constructed to compensate all the nonlinear functions with delay of the step,thus all the time-delay term are completely compensated in the last step of backstepping.Then, an adaptive neural approximation disturbance decoupling control scheme is proposed.The proposed scheme guarantees the boundedness of the closed-loop systems,and renders a bounded approximate L₂ gain from the disturbance input to the output.Finally,the developed design scheme is applied to control a two continuous stirred tank reactor process.Simulation results illustrate the effectiveness of the method proposed.5.Direct adaptive neural tracking control is proposed for a class of completely non-affine pure-feedback nonlinear systems under a mild assumption,which are obtained by implicit function theorem and mean value theorem.In order to remove the restriction of the upper bound on the affine terms,a smooth function is introduced to compensate the interconnected term of the former step in backstepping design.Combining the backstepping technique with input-to-state stability analysis and small-gain theorem,the circular construction of controller is overcome in the design of adaptive neural control for the pure-feedback systems. The proposed control scheme not only guarantees the boundedness of all the signals in the closed-loop system and the tracking performance,but also provides a simple and effective way for controlling non-affine pure-feedback systems. Simulation studies are performed to demonstrate the effectiveness of the proposed scheme.6.Adaptive neural tracking control is presented for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays.The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state.A novel Lyapunov-Krasovskii functional is employed to compensate for the unknown function of current delayed state,which is effectively free from any restrictive assumption on unknown time-delay functions and overcomes the circular construction of controller from function approximator in the backstepping design.Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter.The proposed control scheme does not only overcome the difficulty in controlling non-affine pure-feedback systems,but also guarantee the boundedness of all the signals in the closed-loop system and the tracking performance.Simulation studies are provided to demonstrate the effectiveness of the proposed scheme.