Research On H_? Control Of Two Types Of Time-delay Hamiltonian Systems

In actual production and life,time-delay phenomena exist widely,such as delays in the transmission and processing of signals in the network,delays in physical changes in elasticity,and incubation periods in infectious diseases in biology.On the other hand,the system often suffers from disturbances from the external environment.The existence of time-delay phenomena and external disturbances not only make the analysis and synthesis of the system complicated and difficult,but also an important factor that leads to the deterioration and instability of the actual control system.Therefore,the robust control design of the time-delay system has become an important research topic in the control field.In recent years,a large number of research results have emerged.Among them,the problem of control and stability based on time-delayed Hamiltonian systems is a research hot spot.As we all know,the port-controlled Hamiltonian system describes an open system that not only has energy dissipation,but also has energy generation and energy exchange with the external environment,and its Hamiltonian represents the total energy of the energy storage element,which can be used as the candidate Lyapunov function of the system to bring great convenience to the analysis and synthesis of the system.However,there are still some problems that have not been solved.This paper considers theH_?control problem of two types of time-delay Hamiltonian systems.Under the framework of the Hamiltonian system,a suitable controller is designed to ensure that the original system has a robust performance criterion.The specific content of this paper is as follows:1)H_?control for singular Hamiltonian systems with time delay and saturation.For a class of singular Hamiltonian systems with time-varying delay and input satu-ration,a global asymptotic stabilization controller is proposed based on output feedback.Then,considering the influence of external disturbance on the system,a robust stabiliza-tion controller is designed to make the system in question haveH_?control performance.According to the structural characteristics of nonlinear singular Hamiltonian system,the closed-loop system with output feedback controller is converted into slow subsystem and fast subsystem.Using the Lyapunov-Krasoviskii functional method,different sufficient con-ditions are proposed to ensure that the closed-loop system is asymptotically stable,and the-dissipation inequality holds in the presence of disturbances.Finally,a numerical example is given to verify the effectiveness of the proposed results.2)H_?control for event-triggered Hamiltonian systems with time delay.For a class of Hamiltonian systems with networked communication delay,the observer-based event-triggeredH_?control design problem is studied.Firstly,a discrete event trig-gering scheme based on Hamiltonian function is proposed,which determines whether the sampling time is triggered or not.In addition,the event trigger receives the sampling mo-ment from the sensor at a fixed period,which can avoid Zeno phenomenon.Under the event trigger condition,the stabilization controller is designed to make the closed-loop system re-alize globally asymptotically stable.When the state is difficult to measure,a state observer is designed to reconstruct the unknown state.According to the structural characteristics of the Hamiltonian system,some sufficient conditions are proposed based on the observer and the event triggering mechanism to ensure that the-dissipation inequality with external disturbance is established.Finally,a multi-machine power system is taken as a simulation example to verify the validity of the results.