Mobile Control And Estimation For Distributed Parameter Systems With Moving Boundaries

Distributed parameter systems with moving boundaries are a class of infinite dimen-sional systems with wide application background,where the time-varying characteristics of the boundaries may affect the performance of the systems.On the other hand,the mobile controls which are equivalent to adding another control dimension to the systems can effectively improve the system's performance.Therefore,it is of great theoretical and practical significance to study the mobile control and estimation of the distributed parameter systems with moving boundaries.The main contents are as follows:1.Considering the distributions of sensors and actuators in space,the problem of mobile control for a diffusion system with moving boundary is discussed by using col-located and non-collocated mobile sensor/actuator networks.Based on the theory of operator semigroup,appropriate operator Lyapunov functionals are chosen by consider-ing the time-varying characteristics of the spatial diffusion operator.Several sufficient conditions for the asymptotic stability of the diffusion system with moving boundary are obtained.Meanwhile,based on the dynamic systems of the sensors/actuators,the control forces exerted on the sensors/actuators are obtained,and the collision avoidance strategies among them when they travel in the spatial domain are discussed.The proposed strate-gies show that mobile control of the system based on mobile sensor/actuator networks can effectively eliminate the influence of time-varying boundary and can also improve the control performance of the system.2.The problems of state estimation for a convection-diffusion system with moving boundary are studied.In view of the non-symmetry characteristic of the time varying spatial diffusion operator caused by the moving boundary,a Lyapunov functional with symmetry characteristic is proposed for the first time in the stability analysis of the error system.A centralized estimator for convection-diffusion system with moving boundary is designed,and several sufficient conditions for the asymptotic stability of the error system are obtained.Considering the problem of missing measurements in mobile sensor net-works,consensus-based distributed state estimators are designed,and several sufficient conditions for the global asymptotic stability of the error system in the mean square sense are gotten.Simulation examples and comparative analysis show that the mobile estima-tion can make the state error system stable much faster,both the moving boundary of the system and the missing measurement in the network will affect the sensors'trajectories when travelling throughout the spatial domain.3.Based on the mobile sensor/actuator network,the robust H_?control and filtering are firstly studied for a reaction-advection-diffusion system with moving boundary and moving source.For the disturbance of the unmeasured moving source to the system s-tate,a class of robust controllers and filters which satisfy the H_?performance criteria are designed,respectively.The problem of delayed measurements in sensor networks is considered when designing the robust H_?filters,and the influence of the delayed mea-surements on system performance is eliminated by using mobile sensors.The conclusions show that the designed controllers and filters have strong robustness on the disturbance caused by the moving source,as well as the change of system state caused by the moving boundary and the delayed measurements in the network.4.The problems of mobile control for a class of It?o stochastic distributed parameter systems are studied.Based on the theory of stochastic analysis,the system state defined in a complete probability space is regarded as a solution random field of the stochastic distributed parameter system.The mobile control strategies which make the system stochastically stable are obtained by using the It?o differential formula,as well as the full differential formula and the Lyapunov stability argument.The effectiveness of the proposed mobile control strategies are simulated thereafter.