Control of multi-agent systems by nonlinear techniques

Over the past decade, the coordinated control problems for multi-agent systems have attracted extensive attention. Both centralized and distributed control protocols have been developed to study such multi-agent coordinated control problems as consensus, formation, swarming, flocking, rendezvous and so on. However, most papers employ standard linear control techniques. The results are mainly limited to linear multi-agent systems. In this thesis, we will study some coordinated control problems of both linear and nonlinear multi-agent systems by some advanced nonlinear techniques. This thesis has mainly studied two problems. i) The leader-following rendezvous with connectivity preservation. We have studied this problem for both single integrator and double integrator multi-agent systems by nonlinear control laws utilizing bounded potential function. Although the model of multi-agent system is linear, the closed-loop system is nonlinear due to the employment of nonlinear control laws. We have developed a Lyapunov-based method to analyze the performance of the closed-loop system, and conducted extensive simulations to evaluate the effectiveness of our control schemes. The specific results are summarized as follows. · We have studied the case where the leader system is a linear autonomous system and the follower system is a multiple single-integrator system. The existing results can only handle the case where the leader signal is a constant signal or ramp signal and the control law is discontinuous. By introducing an exosystem, we have proposed a distributed state feedback smooth control law. For a class of reference signals such as step, ramp, and sinusoidal signals, our control law is able to maintain the connectivity of the system and, at the same time, achieve asymptotic tracking of all followers to the output of the leader system. · We have also studied a leader-following rendezvous problem for a double integrator multi-agent system subject to external disturbances. Both the leader signal and disturbance signal can be a combination of step signal, ramp signal and sinusoidal signal with arbitrary amplitudes and initial phases. Motivated by some techniques in output regulation theory, we have developed both distributed state feedback control protocol and distributed output feedback control protocol which utilizes a distributed observer. Both of our control laws are able to maintain the connectivity of an initially connected communication network, and, at the same time, achieve the objective of the asymptotic tracking of all followers to the leader regardless of external disturbances. It is noted that even though we have only studied the rendezvous problem, the techniques of this thesis can also be used to handle other similar problems such as formation, flocking, swarming, etc. ii) Cooperative output regulation problem of nonlinear multi-agent systems. We have formulated the cooperative output regulation problem for nonlinear multi-agent systems. The problem can be viewed as a generalization of the leader-following consensus/synchronization problem in that the leader signals are a class of signals generated by an exosystem, each follower subsystem can be subject to a class of external disturbances, and individual follower subsystems and the leader system have different dynamics. We first show that the problem can be converted into the global stabilization problem of a class of multi-input, multi-output nonlinear systems called augmented system via a set of distributed internal models. Then we further show that, under a set of standard assumptions, the augmented system can be globally stabilized by a distributed output feedback control law. We have solved the cooperative output regulation problem of uncertain nonlinear multi-agent systems in output feedback form. The main result can be summarized as follows: assuming the communication graph is connected, then the problem can be solved by a distributed output feedback control law if the global robust output regulation problem for each subsystem can be solved by an output feedback control law. We have also applied our approach to solve a leader-following synchronization problem for a group of Lorenz multi-agent systems.