Passivity-based Boundary Control For Two Classes Of Delay Reaction-diffusion Systems

Passivity,as a special case of dissipativity,has wide applications in physics,applied mathematics and mechanics fields.Based on the energy input and output,the theory of passivity gives the methods of analysis and design for system control,which largely contributes to the development of system control theory.The theory of passivity plays an important role not only in system control but also in practical application systems,such as thermodynamic systems,biological population systems and some systems in chemical engineering.Taking into account the inevitable diffusion effects,the reaction-diffusion systems can be used to describe the state changes of these systems.On the other hand,due to the wide existence of time delay,and it may reduce or damage the performance of systems.It is necessary to study the passivity of delay reaction-diffusion systems.In Chapter 2,the passivity-based boundary control is studied for delay reactiondiffusion systems with boundary input and output.Firstly,the delay reaction-diffusion system is considered.By employing Lyapunov functional method and inequality techniques,sufficient conditions of the strict passivity are obtained.Secondly,the delay reaction-diffusion system with uncertain parameters is studied,since the fluctuation of the parameters is universal.Using Lyapunov-Krasovskii functional method and Wirtinger inequality,sufficient conditions of robust strict passivity are obtained.Finally,the obtained results are applied to investigate the synchronization of coupled delay reactiondiffusion systems,and the relationship between the output strict passivity and the synchronization is revealed through further analysis.Owing to the ubiquitous stochastic disturbance in practical applications,Chapter 3studies the stochastic passivity of stochastic delay reaction-diffusion systems with the boundary input and output.In addition,stochastic delay reaction-diffusion system with uncertain parameters is considered.In light of Lyapunov-Krasovskii functional method and It(?) formula,delay-dependent sufficient conditions are derived for the system to achieve the stochastic strict passivity and stochastic robust strict passivity,respectively.These results show that the small delay and a slow change rate are beneficial to achieve the stochastic passivity.Finally,the relationship between stochastic passivity and the mean square asymptotic synchronization is also studied.At the end of each chapter,the validity of the theoretical results is verified by numerical simulations.In the end,the research contents are summarized and some new directions and suggestions are provided for the future study.