Research On Robust Adaptive Control For Uncertain Nonlinear Systems And Its Application

Studies on control scheme for the uncertain nonlinear system have important theoretical and practical significance because of the nonlinearity and uncertainty of actual system.A feedback linearization method is one of the main nonlinear system control technology.It makes nonlinear system convert to linear system,and then the linear system theory is used to the corresponding controller design.When the dynamic characters of controlled object are unknown,the neural network method can be applied to further realize neural network adaptive control of the unknown nonlinear systems.For several class of nonlinear system with uncertainty,we studied their robust adaptive control problem by applying the feedback linearization,adaptive control,neural network technique,Lyapunov stability theory and robust control method.The main content of this dissertation is divided into several parts as following:(1)Based on the adaptive feedback linearization method and Lyapunov stability theory,a new control scheme is proposed for a class of affine nonlinear systems with uncertainties.Firstly,we divided uncertain nonlinear systems into the nominal part and uncertain variation part,and then RBF(Radial Basis Function)neural network is applied to approximate unknown nonlinear function in the system.In this case,we can design a robust adaptive controller by using the neural network adaptive control and robust control.In addition,Lyapunov stability theory is applied to analysis the stability of the closed-loop system and to derive the update rule and adaptive law of neural network weight.The simulation examples show the effectiveness of the proposed method.(2)We designed a robust adaptive controller for a class of non-affine nonlinear systems with uncertainties.Firstly,we converted the non-affine nonlinear function into an affine nonlinear one based on mean value theorem,and then control problem for uncertain non-affine nonlinear systems into one for uncertain affine nonlinear systems.Secondly,we approximated the non-affine nonlinear function by using affine-type neural network and proposed further robust adoptive control method based on the affine-type neural network.If the state of controlled system can not be measured,we can design controller based on robust adaptation of the state observer.The theory proofs show that proposed control technology not only ensures the stability of the closed-loop system but also have a simple structure of controller and so overcome the controller singularity problem.Otherwise,this method can be applied to the affine nonlinear system.The simulation results show that this scheme is effective.(3)Based on the adaptive neural state feedback control method,the design of a robust adaptive state feedback controller is presented for a strict-feedback nonlinear system with unknown model.Firstly,the theory of characteristic equation is used for nonlinear state feedback control and then combines it with neural state feedback control technology.Compared with the traditional backstepping method,its structure is simpler and its robustness is stronger.In addition,this can be applied to the robust adaptive control of much uncertain nonlinear system.The application of Lyapunov stability theorem for this method may ensure system output tracking error and stability of total closed-loop system.Its feasibility is proved through the simulation examples.(4)The magnetic levitation system,double pendulum system and electromechanical system are selected for simulation analysis of the proposed method.The theoretical results in the thesis are successfully applied to various uncertain nonlinear systems,in which proved effectiveness of various controller.The simulation results suggest that the control method developed in this dissertation can be generally applied in the various nonlinear systems with uncertainty.Finally,the conclusion and the future work are discussed at the end of this paper.