Finite-time State Estimation Analysis And Control Of Nonlinear Time-delayed Systems

Linear control is a mature subject with a long research history.But in actual control problems,nonlinear systems are more common.Systems are inevitably affected by a series of factors such as time-delay,external disturbance,uncertainty,and diversity.Therefore,researches on nonlinear systems are very necessary and challenging.In the past few decades,the problem of state estimation of nonlinear systems has received a lot of attention.The so-called state estimation refers to the estimation of the internal state of systems based on the available measurement data.Generally,the data obtained by measuring the input and output of systems can only reflect the external characteristics of the system,and the dynamic law of systems needs to be described by internal state variables.In actual engineering,the internal state variables of systems that describe the dynamics of systems are usually not directly measured.Therefore,state estimation is essential in many control systems.In control problems,the stable performance of systems is very important.The steady-state performance of systems is represented by many definitions of stability,but the transient performance of systems cannot be presented.However,transient performance is very important in some control problems,and systems are required to satisfy the given control requirements within a limited time.In this context,the research of finite-time control is worthy of attention.The finite-time control is an advanced control method which compared with the traditional control,finite-time control systems have faster convergence time,stronger anti-interference and better robustness.This paper focuses on the finite-time state estimation and control of nonlinear systems,and carries out state estimation and finite-time stability for different types of nonlinear systems.The control method studied in this paper is applied to RLC circuit systems and high-speed train systems.Finally,the research of this paper is verified by simulation,and the results proved the effectiveness of the research method.The research content and innovations of this article are mainly as follows:1)The finite-time state estimation problem of nonlinear discrete systems with disturbances and time-delays is considered,and bounded disturbances are added into the measurement output of nonlinear systems.The finite-time state estimator with various disturbances and time-delays is designed.According to the Lyapunov stability theory,finite-time stability theory,and H_?bounded theory,the H_?finite-time bounded criterion of the estimation error systems is obtained.2)The finite-time state estimation problem of nonlinear continuous systems with time-varying delays and disturbances is considered.In order to reduce the waste of communication resources caused by data transmission,finite-time state estimators based on an event trigger mechanism are designed.According to the Lyapunov stability theory,the finite-time stability theory,and based on the event trigger mechanism,the finite time bounding criterion of the estimation error systems is obtained.The influence of the trigger threshold on the upper limit of error systems is considered,the designed state estimator can be adapted to different control requirements.3)The problem of finite-time state estimation of chaotic RLC circuit systems are considered,and under the condition of time-delay and external interference in this circuit,according to Lyapunov stability theory,finite-time stability theory,and event-triggered mechanism,the finite-time bounding criterion of the chaotic RLC circuit estimation error system are obtained.4)Considering the problem of finite-time sample-data control of high-speed train systems,the high-speed train systems are regarded as a whole,and the displacement and speed error between each car of the high-speed train are mainly studied,and the sampling periods are converted into time-varying delays.The problem of finite-time sampling data control of high-speed train systems is transformed into a problem of stability analysis of time-varying delay systems.According to the Lyapunov stability theory and the finite-time stability theory,finite-time bounded criterions for the dynamic error system of high-speed train systems with time-varying delay and disturbance are obtained.