Research On Contraction Theory-based Nonlinear Control And The Application In The UAV

Nonlinear control system which is a widespread phenomenon in each domain of the scientific research and the real life has an important theoretical and practical significance,and becomes one of the topics in the research of control theory.Lyapunov method which is a common theory in the traditional nonlinear system analysis focuses on the stability of the equilibrium,namely whether the system can automatically return to the equilibrium in the presence of small disturbance.Contraction theory is a more recent tool for analyzing the convergence behavior of nonlinear systems in the state-space form.As a nonlinear stability theory,contaction analysis which is based on the continuum mechanics and differential geometry,in contrast to Lyapunov analysis,does not require to known what the nominal motion or the equilibrium is,so it is a more promising analysis method.Aiming at the contraction theory-based nonlinear control and the application in the UAV,this dissertation expands the following research in three areas:From the view of the trajectory convergence,a contraction-based adaptive backstepping control method is proposed for the control problem of nonlinear systems in parametric strict feedback form with uncertain parameters.At first,the virtual and actual control inputs are designed according to the combination structure between the sub-systems,which guarantees the contraction of the system,and then the adaptive estimations are designed for the uncertain parameters of each sub-system using contraction-based adaptive lemma.Both of the facts that the system outputs can converge to the desired trajectory and the parameter adaptive estimations are bounded are guaranteed.For a class of uncertain nonlinear system in parametric strict feedback form,an adaptive dynamic surface control method based on contraction theory is proposed in this paper.Every subsystem is partially contracting in the state error by designing the dynamic surface controller.The adaptive estimation via contraction is designed for the uncertain parameters.Moreover,the contraction-based singular perturbation analysis is used to reduce the subsystem dynamics.This ensures the differences of the state errors between the original and the reduced subsystems and the differences of the filters are explicitly bounded.By analyzing the contraction-based robustness of the hierarchical interconnection of the subsystems,it is proven that the states of the original closed-loop can semi-globally converge to a ball centered about the desired trajectory,and it is guaranteed that both of the tracking error and adaptive estimation are bounded.For the uncertain helicopter attitude model,the multivariable contraction-based backstepping control is applied to control the single helicopter attitude mode in the Lagrangian form according to the eigenvalue analysis.And then on the basis of communication topological,the multivariable contraction-based backstepping control is extended to the synchronization control of the multiple helicopters attitude model.The simulation examples demonstrate the effectiveness of this method.