This paper considers the collective dynamics of a group of mobile autonomous agents moving in Euclidean space with a virtual leader. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control laws are a combination of attractive/repulsive and alignment forces, and the control law acting on each agent relies on the state information of its flockmates and the external reference signal (or "virtual leader"). Using the control laws, all agent velocities asymptotically approach the desired velocity, collisions can be avoided between the agents, and the final tight formation minimizes all agent global potentials. Moreover, we show that the velocity of the center of mass either is equal to the desired velocity or exponentially converges to it. Furthermore, when the velocity damping is taken into account, we can appropriately modify the control laws to generate the same stable flocking motion. Subsequently, for the case where not all agents know the desired common velocity, we show that the desired flocking motion can still be guaranteed. Numerical simulations are worked out to illustrate our theoretical results. Additionally, we consider the effect of white noise on the collective dynamics of the group, and demonstrate numerically that the desired flocking motion can be kept for weak noise and, as the noise intensity increases, the flocking motion can be destroyed.

A new approach to robust stabilisation of a class of sampled-data systems with nonlinear uncertainties is proposed. The case that the plant and the controller are connected via a network channel, which may be subjected to data packet dropout and communication delays is of particular interest. Such systems as continuous-time nonlinear systems with delayed input are modelled. Sufficient conditions on the existence of stabilising state feedback controllers are established in terms of linear matrix inequalities (LMIs). One advantage of the present method is that the maximum bound on the nonlinearity can be computed by solving a constrained convex optimisation problem; another is that the upper bound on the delayed input can be obtained by solving a quasiconvex optimisation problem. Finally, a simulation example is worked out to illustrate the efficiency and feasibility of our proposed approach.

Quadratic stabilisation via state and output feedback for continuous-time switched linear systems is studied with the use of a linear matrix inequality (LMI) approach. LMI-based conditions are established for both a state feedback case and an observer-based output feedback case. Under these conditions, the switched linear systems are quadratically stabilisable via either a state-based or a measurable output-based switching strategy. A sufficient and necessary LMI-based condition is also obtained for the state feedback case when there are only two subsystems in the switched linear systems. These results are extended to uncertain switched systems.

We study the collective dynamics of a group of motile particles with a leader. The leader is unaffected by the particle members whereas each member is influenced by the leader and the other members. By using coupled oscillators theory and Lyapunov function method, we show how the group dynamics depends on the motion of the leader and the coupling weights among all particles. Generally speaking, two types of collective motions will occur, depending on different ranges of the coupling weights among the member particles. One is that all the member particles will move in the same direction and the other is that all the member particles move in such a way that the weighted centroid of the group approaches a fixed position. In each case, all the member particles eventually move in the same manner except for the directions of the motion in certain cases. Numerical simulations are worked out to demonstrate the theoretical results. The study suggests potential approaches to control a group motion by steering the motion of the leader and adjusting coupling patterns. This is of practical interest in applications of multiagent systems

Different from the existing mathematical models for switched systems, where the switching from one subsystem to another subsystem is finished instantly, in this paper it is assumed that the switching is a transfer process. Moreover, there exists a basic transfer subsystem such that in the transfer process, the transfer subsystem is active. Based on the model of switched systems under constrained switching, this paper studies the controllability of such systems with time delay in the control function. A necessary and sufficient condition for controllability of such systems is established. Finally, an example is given to illustrate the utility of our results.