Cooperative Control Of Distributed Parameter Systems Based On Sensor/Actuator Networks

Distributed parameter systems are dynamical systems in which the states depend on not only time but also spatial variables,which makes the system infinite dimensional.Distributed parameter systems are widely used in engineering,society,ecology,environment and other fields.It is of great theoretical significance and application value to study the control problem of distributed parameter systems based on sensor/actuator networks.In this dissertation,for the n-dimensional diffusion systems under a sensor/actuator networks environment,mobile agents are used to control the distributed parameter system inorder to improve the control performance.For the n-dimensional coupled fractional-order reaction-diffusion systems,the backstepping method of boundary control of the systems using sensor/actuator networks is studied.The main contributions are as follows:1.For the control problem of n-dimensional diffusion systems,a system architecture of sensor/actuator networks is proposed based on mobile agents.With a new coverage metric,a mobile strategy of the agents based on coverage optimization is proposed to improve the con-trol performance of the close-loop system.Each agent in the system moves in the direction of its local spatially optimal gradient,which can be formulated as an(n-1)-dimensional sur-face integration.The spatial distributions of the agents'sensor and actuator are formulated as indicator functions in the n-dimensional space,so that the main results have a uniform and con-cise expression in the n-dimensional space,and the sensing(actuating)regions only need to have piecewise smooth surfaces without geometric constraints.With the help of Dirac surface delta function,the stability of the closed-loop system is proved by the Lyapunov method and the theory of infinite-dimensional operators.On this basis,the case of continuous time-varying interaction between agents is further considered,and the centralized and decentralized mobile control strategies for first-order and second-order agents are designed respectively.2.For a class of time-fractional reaction-diffusion systems with spatially varying cou-pling coefficients,a Robin boundary controller with state feedback is designed by backstepping method.The well-posedness of the solution of the control gain kernel function matrix partial differential equation is proved by the successive approximation and mathematical induction method.An analytical solution of the control gain kernel function partial differential equation is given under certain conditions,and a numerical solution of the control gain kernel function matrix is given.This numerical solution can simplify the selection algorithm of design param-eter matrix.The Mittag-Leffler stability of the coupled time-fractional system on L~2and H~1spaces is proved by the fractional Lyapunov method.Numerical simulations verify the theoret-ical results.3.For the time-fractional reaction-diffusion system with space-dependent coupling coeffi-cients,the observer design and observer-based boundary output feedback control are proposed by backstepping method.The well-posedness of the kernel function matrix partial differential equations of the observer gain and control gain with coupling coefficients.For the error system and close-loop system of output feedback,the Mittag-Leffler stability of the system is proved by the fractional Lyapunov method.By using the Wirtinger's inequality,the lower bound of the design parameter under stable conditions of the coupled system is improved,and the re-sults are less conservative.The analytical solution of the observer gain and control gain kernel function matrix partial differential equations are given under certain conditions,and the numer-ical solutions are given.The numerical solution can greatly simplify the selection algorithm of the design parameters of observer and controller.Numerical simulations verify the theoretical results.