The Cooperative Output Regulation Problem of Discrete-Time Linear Multi-Agent Systems by the Adaptive Distributed Observer

In this paper, we first present an adaptive distributed observer for a discrete-time leader system. This adaptive distributed observer will provide, to each follower, not only the estimation of the leader's signal, but also the estimation of the leader's system matrix. Then, based on the estimation of the matrix S, we devise a discrete adaptive algorithm to calculate the solution to the regulator equations associated with each follower, and obtain an estimated feedforward control gain. Finally, we solve the cooperative output regulation problem for discrete-time linear multi-agent systems by both state feedback and output feedback adaptive distributed control laws utilizing the adaptive distributed observer.Comment: 7 pages, 4 figure

Cooperative Global Robust Stabilization for a Class of Nonlinear Multi-Agent Systems and its Application

This paper studies the cooperative global robust stabilization problem for a class of nonlinear multi-agent systems. The problem is motivated from the study of the cooperative global robust output regulation problem for the class of nonlinear multi-agent systems in normal form with unity relative degree which was studied recently under the conditions that the switching network is undirected and some nonlinear functions satisfy certain growth condition. We first solve the stabilization problem by using the multiple Lyapunov functions approach and the average dwell time method. Then, we apply this result to the cooperative global robust output regulation problem for the class of nonlinear systems in normal form with unity relative degree under directed switching network, and have removed the conditions that the switching network is undirected and some nonlinear functions satisfy certain growth condition.Comment: 9 pages, 1 figure. This paper was submitted to the journal "Automatica

Event-Triggered Cooperative Robust Practical Output Regulation for a Class of Linear Multi-Agent Systems

In this paper, we consider the event-triggered cooperative robust practical output regulation problem for a class of linear minimum-phase multi-agent systems. We first convert our problem into the cooperative robust practical stabilization problem of a well defined augmented system Based on the distributed internal model approach. Then, we design a distributed event-triggered output feedback control law together with a distributed output-based event-triggered mechanism to stabilize the augmented system, which leads to the solvability of the cooperative robust practical output regulation problem of the original plant. Our distributed control law can be directly implemented in a digital platform provided that the distributed triggering mechanism can monitor the continuous-time output information from neighboring agents. Finally, we illustrate our design by an example.Comment: This paper has been accepted for publication in Automatica on May 21, 201

Cancellation and homotopy rigidity of classical functors

We first show that simply connected co-$H$-spaces and connected $H$-spaces can be uniquely decomposed into prime factors in the homotopy category of pointed $p$-local spaces of finite type, which is used to develop a $p$-local version of Gray's correspondence between homotopy types of prime co-$H$-spaces and homotopy types of prime $H$-spaces, and the split fibration which connects them as well. Further, we use the unique decomposition theorem to study the homotopy rigidity problem for classic functors. Among others, we prove that $\Sigma \Omega$ and $\Omega$ are homotopy rigid on simply connected $p$-local co-$H$-spaces of finite type, and $\Omega\Sigma$ and $\Sigma$ are homotopy rigid on connected $p$-local $H$-spaces of finite type

Analytical solution for Klein-Gordon equation and action function of the solution for Dirac equation in counter-propagating laser waves

Nonperturbative calculation of QED processes participated by a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the usage of analytical solutions of the particle dynamical equation, such as the Klein-Gordon equation and Dirac equation. However only for limited field configurations such as a plane-wave field could the equations be solved analytically. Studies have shown significant interests in QED processes in a strong field composed of two counter-propagating laser waves, but the exact solutions in such a field is out of reach. In this paper, inspired by the observation of the structure of the solutions in a plane-wave field, we develop a new method and obtain the analytical solution for the Klein-Gordon equation and equivalently the action function of the solution for the Dirac equation in this field, under a largest dynamical parameter condition that there exists an inertial frame in which the particle free momentum is far larger than the other field dynamical parameters. The applicable range of the new solution is demonstrated and its validity is proven clearly. The result has the advantage of Lorentz covariance, clear structure and close similarity to the solution in a plane-wave field, and thus favors convenient application.Comment:

Adaptive Leader-Following Consensus for Uncertain Euler-Lagrange Systems under Directed Switching Networks

The leader-following consensus problem for multiple Euler-Lagrange systems was studied recently by the adaptive distributed observer approach under the assumptions that the leader system is neurally stable and the communication network is jointly connected and undirected. In this paper, we will study the same problem without assuming that the leader system is neutrally stable, and the communication network is undirected. The effectiveness of this new result will be illustrated by an example

Cooperative Global Robust Output Regulation for a Class of Nonlinear Multi-Agent Systems by Distributed Event-Triggered Control

This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact sets. Second, the nonlinear functions in our system do not need to satisfy the global Lipchitz condition. Thus our systems are general enough to include some benchmark nonlinear systems that cannot be handled by existing approaches. Finally, our control law is a specific distributed output-based event-triggered control law, which lends itself to a direct digital implementation.Comment: This paper has been submitted to a journal on July 17, 201

Adaptive Leader-Following Consensus for a Class of Higher-Order Nonlinear Multi-Agent Systems with Directed Switching Networks

In this paper, we study the leader-following consensus problem for a class of uncertain nonlinear multi-agent systems under jointly connected directed switching networks. The uncertainty includes constant unbounded parameters and external disturbances. We first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence. Then, by integrating the conventional adaptive control technique with the adaptive distributed observer, we present our solution by a distributed adaptive state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of van der Pol oscillators.Comment: 21 pages, 5 figures. In this replacement version, the higher-order case is considered instead of the second-order case. Also, the main difference of this version from the reference [16] is that Appendix B is added to show the existence of the limit of the function V(t) defined in the equation (33) as t tends to infinit

Modified light cone condition via vacuum polarization in a time dependent field

The appearance of unconventional vacuum properties in intense fields has long been an active field of research. In this paper the vacuum polarization effect is investigated via a pump probe scheme of a probe light propagating in the vacuum excited by two counter-propagating laser beams. The modified light cone condition of the probe light is derived analytically for the situation that it passes through the electric/magnetic antinode plane of the pump field. The derivation does not follow the commonly adopted assumption of treating the pump field as a constant field. Differences from the conventional light cone conditions are identified. The implications of the result are discussed with a consideration of the vacuum birefringence measurement.Comment: 7 pages, 0 figure

Internal Model Approach to Cooperative Robust Output Regulation for Linear Uncertain Time-Delay Multi-Agent Systems

In this paper, we study the cooperative robust output regulation problem for linear uncertain multi-agent systems with both communication delay and input delay by the distributed internal model approach. The problem includes the leader-following consensus problem of linear multi-agent systems with time-delay as a special case. We first generalize the internal model design method to systems with both communication delay and input delay. Then, under a set of standard assumptions, we have obtained the solution of the problem via both the state feedback control and the output feedback control. In contrast with the existing results, our results apply to general uncertain linear multi-agent systems, accommodate a large class of leader signals, and achieve the asymptotic tracking and disturbance rejection at the same time.Comment: 15 pages, 3 figure