Interval Observer-Based Robust Control Of Harmonic Oscillator Systems

Harmonic oscillator systems,because of their important physical significance,are widely used in various fields.Harmonic oscillator systems have been one of the most important research topics in the control theory community in recent decades.However,the internal state information of the actual system model is usually not available,and the external disturbance or noise makes the measurement value unreliable,which will reduce the robustness of the system.High-gain observers,because they can cancel disturbances and guarantee arbitrarily fast error trajectory decay rates,are widely considered to be effective tools for enhancing robustness.On the other hand,by considering replacing a single measurement with an appropriate estimation interval,related scholars have proposed new observer design methods,namely interval observer.The interval observer only needs to design two Luenberger-like observers,and only needs to design the error dynamic system matrix as Metzler matrix to ensure the non-negativity of the error dynamic system.However,some systems cannot directly obtain the observer gain matrix so that the error system matrix satisfies the Metzler property.And for uncertain systems,the interval estimates the width,depending on the uncertainty of the boundary information.Therefore,how to tighten the interval width is an important topic for uncertain systems.At the same time,in the current research of coupled harmonic oscillator system,the information interaction is real-time communication,which makes redundant information generated when the system is stable.Event-triggered mechanism is used in various fields because it can effectively reduce the frequency of communication and save the cost of limited computing resources.In summary,how to use the interval observer to achieve robust control of the harmonic oscillator system,how to reduce the interval estimation width of the interval observer and enhance the robustness of the system,and how to reduce the energy consumption of the coupled harmonic oscillator system based on interval observation have become the important research directions of this paper.Therefore,the main research works of this paper are as follows:1.For the harmonic oscillator system and the coupled oscillator system with unknown additive disturbances and unknown initial states,the interval observer based event-triggered control strategies are designed by using the output feedback,respectively,so that the system can achieve Lyapunov stability and ultimate bounded consensus.Finally,the analysis results exclude Zeno behavior.A corollary is given for the case where there is no event-triggered controller,and its stability is also analyzed.2.For the harmonic oscillator system with uncertain disturbance and observation noise,we design a high-gain interval observer to eliminate the uncertainty and enhance the robustness of the system.However,for the influence of the existence of observation noise on the high-gain observer,we use the method of switched high-gain to solve it.The proposed scheme is able to quickly recover the system state during large estimation errors,reducing the effect of measurement noise.3.Due to the particularity of designing interval observer for harmonic oscillator system,in order to ensure that the error dynamic system matrix is Metzler matrix,we use time-invariant coordinate transformation to design interval observer for harmonic oscillator system and coupled oscillator system respectively.According to the existing theorem,we can solve the numerical solution of the observer gain matrix.For the design of high-gain interval observer of harmonic oscillator system,the time-invariant coordinate transformation cannot be applied due to the OSD decomposition of the system.In this paper,the time-varying coordinate transformation is adopted to solve the Metzler problem.4.At present,the research on cooperative control of multi-agent system is mainly based on theoretical research and simulation verification.This paper uses MATLAB platform to simulate and verify the robust control results of harmonic oscillator system and coupled oscillator system,and confirms the reliability of the research in this paper.