Control Of Formation And Consensus For Networked Swarm Agents

Recent years have seen the emergence of formations of swarm agents as a topic ofsignificant interest to the control community. Swarm agents systems have appeared widely inmany applications including formation flight of Unmanned Air Vehicles (UAVs), automatedhighway systems, and sensor networks. One common feature for these systems is thatcomplicated coordinated behaviors are exhibited by interactions among agents whereinformation exchange is local. In this work, three relevant issues are investigated in detail:robust stability of networked swarm agents systems with time delays and model uncertainties,analysis on convergence and robusmess for consensus of networked swarm agents, robustcontroller for consensus of swarm systems with extemal noises or disturbances.Formation control of multi-agent systems involves harmony among local controller design,interaction topology analysis, and common tasks among networked agents. Usually, due tolimited bandwidth and congestion, time delays always exist in communication networkcomposed of agents. Otherwise, since most engineering systems designs are based onmathematical model, the models and realities they represent are always different. To be practical,model uncertainties must be considered. This study provides a theoretical analysis for stabilityof continuous-time formation system with time delays in fixed, undirected and directed graphbased on two methods. One method is in terms of linear matrix inequlity, and the other is basedon frequency domain theory like Nyquist Criterion. Firstly, time delay is time invariant, and thePD controller is used in formation, Two cases of delay-independent and delay-dependentvehicles formations are considered. Then delay-independent and delay-dependent robuststability conditions with model and feedback uncertainties are presented. The sufficientconditions are given to guarantee that with time delays and uncertainties the vehicles formationcan asymptotically converge to predeflned formation. Furthermore, a way based on free weightsmatrix and linear matrix inequlity is used to reduce conservativeness and extend these results oncase of time invariant delays to the case of time varying delays. Then the stability and robuststability conditions are given for swarm formation system with time varying delays on cases ofwithout model uncertainty and with model uncertainty, respectively. Simulations are provided toverify the feasibility and efficiency of these results. Secondly, a more general linear controller isdesigned. The method based on frequency domain theory is suitable to both cases of undirected and directed graph. It is proved that stability of N Vehicles formations is equivalentto the stability of N-1 subsystems which are related to eigenvalues of graph Laplacian.Convergence speed and robustnee to delays are very important in coordination of swarmagents. In most engineering systems, a fast convergence speed and robustness are necessary.This dissertation proposes solutions to consensus of one order swarm system and high ordermulti-agent system. Aimed at one order system, a way to design the optimal weights associatedwith edges of undirected graph composed of multi-agent systems is presented. The optimalweights are designed to make the states of multi-agent systems converge to consensus with afast speed as well as the maximum communication time-delay can be tolerated. Theconvergence speed which is determined by the second-smallest eigenvalue of graph Laplacianmatrix is assumed to be a given value, at the same time the maximum communication timedelaywhich is decided by the maximum eigenvalue of Laplacian can be got. In order to getrequired second-smallest eigenvalue and optimal maximum eigenvalues, the order of Laplacianis reduced by variable decomposition. Moreover, designing the optimal weights is equivalent tominimizing condition number of a positive-definite matrix. This is a convex optimizationproblem. Simulation results are coincidental with theoretical analysis. Aimed at second andhigher order system, simulations are provided to show the effects of controller paremeters onstability of formation control. The optimal parameters of controller are decided. In order toimprove the robusmess, fractional PD^μcontroller is presented to control formation system.How optimal parameterμaffects robusmess to delays also is analized by simulations. Thenthe optimal value is got. Simulations show that the fractional PD^μcontroller can improverobustness significantly.It is very obvious that there are always disturbances and noises in swarm systems,especially in practical engineering systems. With disturbances the system will be not stable anymore. So the controller for the system in case of no noise will do not work again. It is veryimportant and necessary to design a robust controller to make the states of swarm agents reachconsensus with some performance under various of external and internal disturbances. Thisdissertation proposes a way to design robust controller for consensus of the system so as tomake the closed-loop system reach consensus with non-consensus part be Lyapunov stablemeeting certain performance for disturbances attenuation. Two cases are considered. The firstone is that the agents in the swarm can interact with every other agent when each agent can receive information from every other. The other one is that the topology structure composedby the agents is fixed when each agent in the swarm can only exchange information with someagents but not all other agents. The methods to design H_{∞}H₂/H_{∞}controllers for consensusof networked continuous-time swarm system are given with white noises and persistant noises.Then how to design H₂,H_{∞},H₂/H_{∞}controller for consensus of discrete-time systems arealso stated. Simulation results demonstrate that designed controller for the system can make theclosed-loop system reach consensus with non-consensus part be Lyapunov stable meetingcorossponding performance for disturbances attenuation.Finally, a summary has been done for all discussions in the dissertation. The researchworks in further study are presented.