Dynamic Analysis Of Hybrid Systems And Its Application To Attitude Control

From the perspective of engineering and control,the hybrid system is a unified dynamic system composed of continuous variable dynamic system and discrete variable dynamic system mixing and interacting with each other.With the rapid development of computer technology,the hybrid systems have been widely concerned by scholars in related fields,and many interesting results on the dynamic analysis have been also reported.Particularly,the impulsive systems,sampled-data control systems,switched systems and so on all belong to the category of theoretical research on hybrid systems.So far,the theory of hybrid systems has been widely applied in many practical systems with both continuous and discrete dynamics,such as intelligent transportation networks,attitude control systems,and epidemic model with impulse vaccination.This paper mainly investigates the impulsive systems and sampled-data control systems in the hybrid systems and carries out the corresponding dynamic analyses,e.g.,Lyapunov stability,synchronization and(integral-)input/output-to-state stability.Further,the obtained results are applied to the attitude control of the rigid spacecraft,and the effectiveness of the theoretical research in this paper is demonstrated by combining with some numerical simulations.To begin with,the first chapter mainly introduces the basic definition and current situation analysis of the hybrid systems.The research status of impulsive systems and sampled-data control systems as well as the bottleneck problems to be solved are introduced;the application of theory of hybrid systems to spacecraft attitude control is introduced,and the improvement ideas of the controller under the event-triggered strategy are proposed.The main research content of this paper(Chapters 2-8)can be simply sorted and summarized as follows:based on the average impulsive interval method,this paper reveals the potential impact of the time delay term in the continuous variable dynamic system(Chapter 2)and the discrete variable dynamic system,i.e.,the delayed impulses(Chapter 3)on globally exponential stability of the impulsive systems,respectively.Considering the effects of input and output on the stability of impulsive systems,a robust impulsive controller is designed(Chapter 5),and the(integral)input/output-to-state stability of impulsive systems is studied(Chapter 6).In this paper,the theoretical results of Chapter 3 and Chapter 5 are further generalized and applied to the investigation on synchronization problem of impulsive dynamic networks(Chapter 7)and the attitude stabilization problem(Chapter 9)respectively.In addition,this paper studies the stability of sampled-data control systems with average sampling interval inspired by the average impulsive interval method(Chapter 4).By designing a novel periodic event-triggered strategy,the theoretical results are also applied to the sampling stabilization problem of attitude control systems(Chapter 8).Finally,Chapter 10 briefly summarizes all the results introduced above,discusses some issues that may be studied in the future,and makes a simple plan for the future work.Particularly,the main research results of this paper can be summarized as follows:(1)It is shown that some unstable impulsive time-delay systems can be stabilized by increasing the delay in continuous dynamics.More interestingly,it is also shown that within a certain range,as the delay increases,the corresponding convergence rate also increases.Furthermore,a strict comparison principle is established for impulsive control systems with time delay.Then,it is verified that for some impulsive control systems with time delay,under certain conditions,the stability is robust with respect to arbitrary finite time delay.(2)In order to break through the bottleneck that the delays in impulses need a strict upper bound in previous studies,the concept of average impulsive delay is proposed.With the help of the idea of the average impulsive interval,it is proved that the delay in the impulse has a dual effect,that is,the appearance of the delay may make the originally stable system unstable,and it may also make the originally unstable system stable.(3)The concept of average sampling interval is proposed,which further broadens the research ideas of seeking the maximum sampling interval in the previous literature.A novel truncated sampled-data controller is designed,and the concept of average truncated length is also introduced,which effectively generalizes the classical sampled-data control method.(4)The robust practical stability of linear time-invariant systems with external disturbances under event-triggered impulsive control is investigated.Based on the event-triggered condition of the sliding variable,a robust impulsive controller is designed,which realizes the ultimate boundedness of system states and effectively avoids the Zeno phenomenon.It is also demonstrated that the obtained results can handle the problem of unknown bounded external disturbances well,which usually requires adaptive control strategies to be solved in previous results.(5)The theoretical research results are extended and applied to the position tracking problem of motor servo systems,the synchronization problem of complex dynamic networks and the robust stabilization problem of attitude control systems.Finally,the validity of the theoretical results is verified by corresponding numerical simulations.