Research On The Control Problems For Nonlinear Systems With Uncertain Disturbances

As is well-known,disturbances such as external environmental disturbances,noise disturbances,internal friction of mechanical systems and power systems are common in various practical systems,and these practical systems are inherently nonlinear.Hence,it is of great practical significance to improve system's anti-disturbance ability and obtain better control performance.In recent years,based on nonlinear stability theory,Lyapunov function,backstepping technique,disturbance observer-based control and other design tools,the control design of uncertain nonlinear systems has achieved remarkable results.However,most of the existing results need to impose strong assumptions and the system considered has certain limitations.Based on this,this paper will further design and analyze the nonlinear control systems with uncertain disturbances.The main contents include:1.The practically finite-time(PFT)control problem is concerned for nonlinear sys-tems subject to mismatching disturbances.Without any extra assumptions on system nonlinearities,a composite controller is developed by introducing a disturbance observer and finite-time control technique.Based on the designed controller and Lyapunov stabili-ty theory,the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance.Furthermore,as a byproduct of the proposed design method,the disturbance observer-based PFT control for high-order nonlinear systems is also possible.To the best of the authors'knowledge,it is the first PFT control result for high-order nonlinear systems with external disturbances.Finally,an application example of a single-link robot system and a numerical example are presented to demonstrate the effectiveness of the proposed scheme,respectively.2.The global output-feedback tracking control problem is addressed for nonlinear time-delay systems in the presence of unmeasurable disturbances.Firstly,for nonlinear time-delay systems with input saturation,without any growth assumptions,the full-state observer and auxiliary system are introduced to handle unmeasurable states and satu-rated input,respectively.Then,an output-feedback controller is designed to make the closed-loop system globally uniformly ultimately bounded(GUUB).Furthermore,non-linear time-delay systems containing unmeasurable disturbances and input saturation is considered.To handle the unmeasurable states and disturbances,the composite state observer and disturbance observer are constructed.Based on these two observers,an output-feedback controller is designed by introducing an auxiliary system to eliminate the effect of input saturation,which ensures the closed-loop system to be GUUB.Par-ticularly,instead of converging to an arbitrarily small neighborhood of zero as in related results,the tracking error is bounded by the function of saturation input error and de-sign parameters.Finally,a chemical reactor system is presented to demonstrate the effectiveness and usefulness of the proposed scheme.3.The adaptive finite-time control is devoted to a class of stochastic nonlinear systems with unknown noise of covariance.The traditional nonlinear growth conditions are removed through the Taylor expansion formula,the negative effect generated by unknown covariance noise is compensated by combining adaptive control technique with backstepping recursive design.We firstly design an adaptive state-feedback controller which guarantees the closed-loop system globally asymptotical stability in probability.Then,a novel smooth adaptive state-feedback controller is skillfully designed and analyzed with the help of the adding a power integrator method and stochastic finite-time stability,which further makes the closed-loop system finite-time stable in probability.Finally,a simple pendulum system is simulated to demonstrate the effectiveness of the proposed control scheme.4.The globally feedback control is investigated for stochastic nonlinear time-delay systems.Firstly,the globally adaptive state-feedback control problem is addressed for a more general class of stochastic nonlinear systems with an unknown time-varying delay and perturbations.Without imposing any assumptions on the time-varying delay,an adaptive state feedback controller is skillfully designed by using adaptive backstepping control technique.Then,based on Lyapunov-Razumikhin lemma and stochastic stability theory,it is proven that the constructed controller can guarantee the closed-loop system to be globally asymptotically stable(GAS)in probability.Furthermore,for stochastic nonlinear time-delay system with input delay and unmeasurable system states,the growth assumptions are removed through a technical lemma.Based on this,by introducing an auxiliary system and using Lyapunov-Krasovskii functional,the adverse effects generated by input saturation and time-varying delay are eliminated.Then,based on state-observer and backstepping recursive design,an output-feedback controller is constructed to render the closed-loop system globally bounded almost surely.Particularly,different from the existing results,the tracking error is ensured to be tuned by the design parameters and input saturation error in the mean quartic sense.Finally,a stochastic chemical reactor time-delay system is established to demonstrate the effectiveness of the proposed scheme.