Tracking Problems Of Multi-Agent Systems With General Dynamics Under Dynamic Topologies

In the last decade, the distributed control of MASs(multi-agent systems)has received increasing attention. The distributed control is to design protocol to achieve control objectives by using local information from its neighbors. The convergence of the whole system, such as consensus, is the critical issue of distributed control of multi-agent systems. The existence of leaders in the MASs can lead the whole system to achieve control objectives fast and efficiently. One order and two-order integrator systems, which have simpler forms, have been studied extensively. This paper devotes itself to the study of multi-agent systems with general dynamics. Compared with one or two-order integrator systems, the dynamics of each agent of multi-agent systems with general dynamics is linear or nonlinear system, so it has more general form and can model more complicated systems. Based on Lyapunov or trajectory analysis, tracking problems of general linear multi-agent systems are consider by using matrix theory, algebraic graph theory and linear system theory. The main results of this paper are proposed as follow.For MASs with directed stochastic switching topologies and multiple leaders,the containment control problem is considered. The directed stochastic switching topologies are Markov switching, and the dynamics associated with each agent is not merely confined to be linear. The control protocol that only based on the neighbor’s states is designed, then the algorithm on choosing control parameters in the protocol is given. In the case that general linear dynamics with uncertainty, sufficient conditions are given to ensure containment tracking in the sense asymptotic unbiased mean square sense; in the case that general linear dynamics with nonlinear leaders, containment result is obtained with bounded error in mean square sense. It’s worth pointing out that convergence analysis is provided under any initial distribution instead of under the assumption that the Markov process starts from the stationary distribution. Simulations are also provided to demonstrate the effectiveness of the results.The containment control problem of MASs with directed deterministic switching topology is considered. The dynamics of each agent has general linear form.For general linear MASs with time-varying weight-unbalanced digraph(directed graph), the containment control problem is difficult and challenging, because the Lyapunov method is not an effective approach in this case. Different with previous works, the convergence analysis is based on trajectory analysis rather than the Lyapunov method. Nonnegative matrix theory, in particular the row-stochastic matrix properties, are explored to handle the containment control problem. Under the assumption that the graph topology uniformly and jointly has a directed spanning forest, it’s shown that when the exponentially unstable mode associated with each agent’s self-dynamics is weak enough, the followers can asymptotically tend to the dynamical convex hull spanned by the leaders, i.e. the containment can be achieved. Moreover, the least convergence rate is explicitly specified.Simulations are also provided to demonstrate the effectiveness of the result.The distributed containment control problem of discrete-time generl linear MASs is studied. The graph topology of MASs has general form, i.e. it’s timevarying and directed. As the Lyapunov method relies heavily on the symmetric property of the associated Laplacian matrix, the trajectory analysis method is applied. Based on a technical lemma concerning norm estimation of infinite product of row-stochastic matrices, it’s shown that the containment can be achieved under the very relaxed conditions: strictly instability of the individual-system of each agent(without interactions with other agents) is allowable and the graph topology is only required to be jointly having directed spanning forest frequently enough. Moreover, the least convergence rate is explicitly specified. Simulation is also provided to demonstrate the effectiveness of the result.The leader-following tracking control problem of general linear MASs with noise interference. Two kind of noises are considered: one is the communication noise, which comes from the information transmission; the other is the model noise, which can also be called modeling noise. By constructing Lyapunov function and using tools like It?o integral, it’s proven that the leader-following consensus can be achieved in the two cases under some conditions. Simulation is also provided to demonstrate the effectiveness of the result.