Research On Tracking Control Of Second-order Multi-agent Systems

As a critical topic of distributed control of multi-agent systems, trackingcontrol issue has drawn much attention of many researchers from mathematics,biology, sociology, computer science, control science, etc. This dissertation mainlystudies consensus tracking problems and bounded consensus tracking issues ofsecond-order multi-agent systems. Our main results and contributions are asfollows:1. For second-order sampled control multi-agent systems, by applying alge-braic graph theory, matrix theory and stability theory, consensus tracking criterionis established and the approach of how to choose the parameters is given.2. The consensus tracking control issues of continuous-time and discrete-timesecond-order multi-agent systems with time delays are studied, respectively. It isassumed that only a portion of agents can have the access to the virtual leaderand obtain the leader’s state information directly. For continuous-time case, byLyapunov-Razumikhin theory and Hopf bifurcation theory, respectively, the up-per bound of time delays is established and the corresponding consensus trackingcriteria are established as well. For discrete-time case, by iterative method, aug-mented system method and stability theory, necessary and sufcient conditionsare proposed to ensure that the multi-agent system can achieve the consensustracking.3. The bounded consensus tracking problem of second-order multi-agentsystems with fixed and Markovian switching topology in a sampling setting isstudied. All the agents are further assumed to only obtain the approximative valueof the leader’s acceleration instead of the actual value. By virtue of matrix analysisand perturbation theory, the necessary and sufcient conditions for boundednessof tracking error system are established and the ultimate bound of tracking errorsis given under fixed and Markovian switching topology, respectively.4. The observer-based bounded tracking control problem of second-ordermulti-agent systems in both sampling and disturbance environments is studied. The sampled-data protocol is introduced and distributed observers are designedto estimate the velocity of the active leader. For the fixed communication topol-ogy case, necessary and sufcient conditions of bounded consensus tracking areobtained by using the matrix analysis method. For the switching communica-tion topology case, by applying the common Lyapunov function and perturbationtheory, the sufcient condition is proposed to ensure that system can reach thebounded consensus tracking.