Research On The Consensus Control Of Networked Partial Differential Systems

Consensus,as an important and basic research direction in cooperative control of networked systems,has been widely investigated by scholars in different fields.At present,many theoretical research results are focused on the consensus control problem of networked ordinary differential systems.But in real life,the movement of matter exists a certain spatio-temporal environment.Because of the uneven distribution between individuals in space,the diffusion phenomenon is universal.At this point,the dynamic equations of the system depend on both time and space variables and are represented by partial differential equations.Therefore,it is significant to investigate the consensus control problem of networked partial differential systems.Based on graph theory,matrix theory and partial differential theory,this thesis designs different control algorithms,namely,sampling-based event-triggered control,output feedback control,adaptive output feedback control,intermittent boundary control,to study the consensus issue of networked partial differential systems.The specific works are as follows:The study on exponential consensus control of reaction-diffusion neural networks.Combining sampling control and event-triggered control,the sampling-based event-triggered mechanism is designed.The existence problem of the diffusion term in the model is overcome and Zeno behavior is effectively excluded.A new Lyapunov-Krasovskii functional is considered,and sufficient conditions for exponential consensus are obtained by using some important inequality scaling techniques and related partial differential theory.Compared with the traditional continuous consensus control method,the control method in this chapter does not need continuous communication and only needs to know the state information of neighbors at the triggered instant,which greatly reduces the communication transmission times and energy loss.Finally,a numerical example is presented to verify the effectiveness of the algorithm.The study on finite-time output consensus control of multiple weighted reaction-diffusion neural networks with adaptive output couplings under undirected topology.The effects of coupling delays,external disturbances and multiple coupling weights on system performance are considered respectively.The adaptive law is adopted to adjust the coupling weights,and different output feedback controllers are designed to ensure the finite-time output consensus of the multi-weight reaction-diffusion neural networks without coupling delays and with coupling delays.At the same time,in the presence of external disturbances,the above algorithms can realize finite-time H_∞output consensus.Different from research works on state feedback and state consensus,this chapter considers the fact that the state of nodes is immeasurable and the lives of machine and human are limited,and solves the finite-time output consensus issue through output feedback.Finally,relevant numerical simulation results are shown to demonstrate the feasibility of algorithms.The study on finite-time output consensus control for reaction-diffusion neural networks with output couplings under directed topology.Based on the output information,different output feedback control laws are proposed.By using the key inequality scaling technique and the finite-time consensus theory,the finite-time output consensus criteria of reaction-diffusion neural networks with fixed coupling weights and adaptive coupling weights are obtained.Different from the control algorithms designed under undirected topology,this chapter overcomes the asymmetry problem of the Laplacian matrix associated with directed topology,designs new algorithms,constructs a new Lyapunov function,and introduces new symmetric matrixes in the theoretical proof,to solve the finite-time output consensus issue of output-coupled reaction-diffusion neural networks.Finally,the effectiveness of algorithms is verified by numerical simulation results.The study on consensus control of linear parabolic partial differential multi-agent systems.Under undirected fixed topology,based on the relative output information of the node and its neighbors,vertex-based distributed adaptive observer-type control algorithms are respectively designed to solve the leaderless and leader-following with one leader consensus problems of linear parabolic partial differential multi-agent systems.Under undirected switching topology,a new edge-based adaptive observer-type control law is proposed,which relies on the relative output information of an agent and its neighbors rather than the relative state information.By constructing appropriate the Lyapunov function and adopting scaling techniques of related inequalities,sufficient conditions for consensus are obtained.Different from state feedback,distributed adaptive output feedback control is mainly used in this chapter to solve the problem of immeasurable node’s state information in practice and achieve the system’s state consensus.At the same time,these control algorithms do not depend on the global information of the network.Finally,the feasibility of algorithms is demonstrated by numerical simulation results.The study on exponential consensus control of nonlinear parabolic partial differential multi-agent systems.When the system’s state information is fully available,an intermittent boundary controller is designed based on the transmission information generated by the communication between the agent and its neighbors and the coupling information at the boundary,and a sufficient condition of leader-following exponential consensus is obtained.When the state information of the system cannot be obtained completely,an observer is designed to estimate the agent’s state,and then an observer-based intermittent boundary controller is proposed to realize the leader-following exponential consensus of nonlinear parabolic partial differential multi-agent systems.Unlike distributed control and continuous control,the intermittent boundary control designed in this chapter only requires the actuator to be placed on the boundary and is not continuous,not only reducing the time cost but also reducing the space cost,which is easier to operate in practical engineering applications.Finally,two numerical simulation examples are provided to demonstrate the effectiveness of algorithms.