Stability of a Class of Multiagent Tracking Systems With Unstable Subsystems

Sampled-data exponential consensus of multi-agent systems with Lipschitz nonlinearities

In this paper, the exponential consensus of leaderless and leader-following multi-agent systems with Lipschitz nonlinear dynamics is illustrated with aperiodic sampled-data control using a two-sided loop-based Lyapunov functional (LBLF). Firstly, applying input delay approach to reformulate the resulting sampled-data system as a continuous system with time-varying delay in the control input. A two-sided LBLF which captures the information on sampled-data pattern is constructed and the symmetry of the Laplacian matrix together with Newton-Leibniz formula have been employed to obtain reduced number of decision variables and decreased LMI dimensions for the exponential sampled-data consensus problem. Subsequently, an aperiodic sampled-data controller was designed to simplify and enhance stability conditions for computation and optimization purposes in the proposed approach. Finally, based on the controller design, simulation examples including the power system are proposed to illustrate the theoretical analysis, moreover, a larger sampled-data interval can be acquired by this method than other literature, thereby conserving bandwidth and reducing communication resources.

Multi-Agent Distributed Deep Deterministic Policy Gradient for Partially Observable Tracking

In many existing multi-agent reinforcement learning tasks, each agent observes all the other agents from its own perspective. In addition, the training process is centralized, namely the critic of each agent can access the policies of all the agents. This scheme has certain limitations since every single agent can only obtain the information of its neighbor agents due to the communication range in practical applications. Therefore, in this paper, a multi-agent distributed deep deterministic policy gradient (MAD3PG) approach is presented with decentralized actors and distributed critics to realize multi-agent distributed tracking. The distinguishing feature of the proposed framework is that we adopted the multi-agent distributed training with decentralized execution, where each critic only takes the agent’s and the neighbor agents’ policies into account. Experiments were conducted in the distributed tracking tasks based on multi-agent particle environments where N(N=3,N=5) agents track a target agent with partial observation. The results showed that the proposed method achieves a higher reward with a shorter training time compared to other methods, including MADDPG, DDPG, PPO, and DQN. The proposed novel method leads to a more efficient and effective multi-agent tracking.

Stability analysis of switched systems with all subsystems unstable: A matrix polynomial approach

This paper concentrates on the problem of continuous-time switched linear systems with all subsystems unstable under average dwell time (ADT) criteria. Inspired by the matrix polynomial approach, a new method is proposed to further lessen conservativeness and improve system performance. The new method is based on a matrix polynomial and the discretized Lyapunov function (DLF) technique. Using the matrix polynomial, the DLF is successfully established and applied to switched systems. Based on this function, convex sufficient conditions are derived, thereby ensuring the global uniform exponential stability of the system. In addition, the method can be expanded to uncertain systems. Finally, a numerical example is presented to illustrate the potential of the proposed approach.

Stability Analysis of Multi-Agent Tracking Systems with Quasi-Cyclic Switching Topologies

In this paper, the stability problem of a class of multi-agent tracking systems with quasi-cyclic switching topologies is investigated. The existing results of systems with switching topologies are usually achieved based on the assumption that the piecewise constant communication topologies are connected and the switchings are cyclic. The communication topologies are possible to be unconnected and it is difficult to guarantee the topologies switch circularly. The piecewise unconnected topology makes the interactive multi-agent tracking system to be an unstable subsystem over this time interval. In order to relax the assumption constraint, a quasi-cyclic method is proposed, which allows the topologies of multi-agent systems to switch in a less conservative way. Moreover, the stability of the tracking system with the existence of unstable subsystems is analyzed based on switched control theory. It is obtained that the convergence rate is affected by the maximum dwell time of unstable subsystems. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.

A class of cooperative relay analysis of multi-agent systems with tracking number switching and time delays

This paper investigates a complicated class of cooperative tracking problems with time-varying number of tracking agents and communication time delays. During the entire tracking process, tracking agents are dynamically changing and the number is not fixed. This results in jumping of tracking errors and dynamic dimensions of the corresponding Laplacian matrices. Consequently, the stability analysis turns to be difficult especially when the effect of communication time delays is taken into consideration. In order to solve this issue, a new type of average Lyapunov function is constructed to compensate the unmatched dimensions of communication topologies over different time intervals. Generalized reciprocally convex Lemma and a more relaxed switched technique are employed to achieve a less conservative switched stability condition for the multi-agent system with variable tracking number and time delays. Finally, through a series of numerical simulations, the effectiveness and feasibility of derived results are verified. The relationship between maximum allowable communication time delays and various control parameters is obtained in a quantitative way.

Tracking Control of a Class of Cyber-Physical Systems via a FlexRay Communication Network

Due to properties of flexibility, adaptiveness, error tolerance, and time-determinism performance, the FlexRay communication protocol has been widely used to investigate robot systems and new generation of automobiles. In this paper, with the FlexRay communication protocol, the tracking problem of a class of cyber-physical systems are investigated by developing a general hybrid model, in which an emulation controller is utilized. Based on the proposed hybrid model, some sufficient conditions are established to guarantee the convergence of tracking errors. Then, the maximum allowable transmission interval (MATI) of the static/dynamic segment is obtained with a more general formula than the ones in some the previous works. The obtained MATI over the FlexRay communication network can be adjusted via the appropriate length of the static/dynamic segment, which reflects the flexibility of FlexRay. Finally, the results are verified by considering the tracking problem of a single-link robot arm system as well as the stabilization of a batch reactor system.