Sampled-data Control For Multi-agent Systems Based On Relative State Measurements

In recent years,multi-agent coordination control has emerged as an important topic in the field of control theory.The main concern is that how to coordinate all individuals to achieve control objectives under information interaction.As one of the central problems in multi-agent coordination,the distributed sampled-data control of multi-agent systems has attracted a great deal of attention from researchers.The key technical point is to focus on how the sensors assembled on each individual are sampled to update the controller for coordinated control.We mainly study distributed sampled-data control theory based on relative state measurements,in which time-triggered,event-triggered and self-triggered control approaches are proposed for multi-agent systems.We explore the dynamic behavior of all agents under the proposed sampling mechanisms.The main contents and innovations are listed as follows:Based on the control protocol with arbitrary sampling intervals and relative position sampling,we study the dynamic behavior of double-integrator networks under leader-following topologies,in which the consensus problem and containment problem are solved in a unified framework.Under different network structures,consensus analysis is provided in the single leader-subgroup case and containment control analysis is provided in the multiple leader-subgroup case,respectively.Furthermore,based on the Hermite-Biehler Theorem,these theoretical results are generalized to any weakly connected digraph.Rigorous mathematical arguments guarantee that all agents in doubleintegrator networks achieve different control objectives in different topologies under the proposed control strategy,in which the sampling periods can be set to be of an arbitrary time-varying length;that is,the proposed protocol can be employed in constrained communication networks,such as packet loss and sampling jitter.Based on the event-and self-triggered control protocols and algorithms with combined relative state measurements,we propose new strategies with lower system resource consumption to schedule controllers and sensors to solve the consensus problems of single-and double-integrator networks,respectively.In the proposed event-triggered control protocols and algorithms,all relative states incident to each agent are processed together,and all agent check the corresponding triggering conditions periodically to determine whether or not to update control inputs.In comparison with the traditional periodic sampling control,the proposed event-triggered control strategies can greatly decrease the number of controller updates,which can save system resources.The proposed selftriggered control algorithms can further reduce the numbers of relative state sampling,which can avoid the periodic work of all active sensors required in event-triggered control.In self-triggered control strategies,each sensor only performs sampling operations at each event instant,and there exists a trade-off between relative-state-sampling costs and computation costs.These scheduling methods for sensors and controllers can cope with the scenarios with different levels of sensor and computation resource supports.Based on the edge-event-and edge-self-triggered control protocols and algorithms with separate relative state measurements,we propose new strategies to schedule controllers and sensors to solve the synchronization problem of coupled harmonic oscillators,which are different from the above combined relative state measurement strategies.In the proposed edge-event-triggered control algorithms,all edges check the triggering conditions asynchronously,and the information exchanges of each edge are independent of those of others.In comparison with the previous combinational measurement schemes,the proposed algorithms in this chapter are different scheduling ways for sensors and controllers,which can suitable for the scenarios with different levels of sensor resource supports.First,an asynchronous edge-event-triggered control strategy is proposed for coupled harmonic oscillators,in which the edge events of each edge are asynchronous with respect to each pair of adjacent oscillators.Then,we further consider the influence of transmission time delays,and propose a synchronous edge-event-triggered control strategy,in which if the corresponding sampling edge states satisfy the triggering conditions,the controllers of these two oscillators are updated synchronously.Compared with the asynchronous triggering,the parameter selections in the synchronous triggering scheme are more relaxed.To reduce the numbers of edge-state-sampling,we propose two edge-self-triggered control algorithms for all oscillators,which are different scheduling methods for all sensors and controllers,and both of them can reduce the numbers of edge-state-sampling.Based on the integral-type edge-event-and self-triggered control protocol and algorithm with relative state measurements,we propose new strategies with more relaxed triggering conditions to schedule controllers and sensors to solve the synchronization problem of a class of nonlinear multi-agent systems.In the proposed event-triggered condition,only the integral of measurement errors needs to be less than a designed function in some time intervals.This is a more relaxed mechanism,in which the triggering frequency of each edge is less than the nonintegral-type event condition;that is,this solution can further save system resources.The triggering condition has a hybrid form,which contains the state-dependent item and time-dependent item.This design can avoid Zeno behavior.To relieve the pressure of sensor load,we propose an integral-type edge-selftriggered control algorithm.This algorithm with intermittent relative-state-sampling and controller updates can further reduce the resource consumption of sensor sampling.