Time-varying formation control for general linear multi-agent systems with switching directed topologies

In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in noncooperative games, the players considered in this paper cannot directly observe the actions of the players who are not their neighbors. Instead, the players are supposed to be capable of communicating with each other via an undirected and connected communication graph. By a synthesis of a leader-following consensus protocol and the gradient play, a distributed Nash equilibrium seeking strategy is proposed for the noncooperative games. Analytical analysis on the convergence of the players’ actions to the Nash equilibrium is conducted via Lyapunov stability analysis. For games with nonquadratic payoffs, where multiple isolated Nash equilibria may coexist in the game, a local convergence result is derived under certain conditions. Then, a stronger condition is provided to derive a nonlocal convergence result for the nonquadratic games. For quadratic games, it is shown that the proposed seeking strategy enables the players’ actions to converge to the Nash equilibrium globally under the given conditions. Numerical examples are provided to verify the effectiveness of the proposed seeking strategy.

Distributed Nash Equilibrium Seeking by a Consensus Based Approach

Leader-follower consensus of time-varying nonlinear multi-agent systems

In this paper, a cooperative time-varying formation maneuvering problem with connectivity preservation and collision avoidance is investigated for a fleet of autonomous surface vehicles (ASVs) with position–heading measurements. Each vehicle is subject to unknown kinetics induced by internal model uncertainty and external disturbances. At first, a nonlinear state observer is used to recover the unmeasured linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based cooperative time-varying formation maneuvering control laws are designed based on artificial potential functions, nonlinear tracking differentiators, and a backstepping technique. The stability of closed-loop distributed formation control system is analyzed based on input-to-state stability and cascade stability. The salient features of the proposed method are as follows. First, cooperative time-varying formation maneuvering with the capability of connectivity preservation and collision avoidance can be achieved in the absence of velocity measurements. Second, the complexity of the cooperative time-varying formation maneuvering control laws is reduced without resorting to dynamic surface control. Third, the uncertainty and disturbance are actively rejected in the presence of position–heading measurements. Simulation results are given to substantiate the proposed output feedback control method for cooperative time-varying formation maneuvering of ASVs with connectivity preservation and collision avoidance.

Output-Feedback Cooperative Formation Maneuvering of Autonomous Surface Vehicles With Connectivity Preservation and Collision Avoidance

This paper studies a distributed secure consensus tracking control problem for multiagent systems subject to strategic cyber attacks modeled by a random Markov process. A hybrid stochastic secure control framework is established for designing a distributed secure control law such that mean-square exponential consensus tracking is achieved. A connectivity restoration mechanism is considered and the properties on attack frequency and attack length rate are investigated, respectively. Based on the solutions of an algebraic Riccati equation and an algebraic Riccati inequality, a procedure to select the control gains is provided and stability analysis is studied by using Lyapunov’s method.. The effect of strategic attacks on discrete-time systems is also investigated. Finally, numerical examples are provided to illustrate the effectiveness of theoretical analysis.

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Distributed Secure Coordinated Control for Multiagent Systems Under Strategic Attacks

A leader-following rendezvous problem of double integrator multi-agent systems

Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law

Recently, we investigated the problem of leader-following rendezvous with connectivity preservation for a double integrator multi-agent system subject to external disturbances by a full information feedback controller. In this technical note, we further study a generalized problem via the position feedback control. Thus, the result of this technical note is more practical than that of the previous paper.

Leader-Following Connectivity Preservation Rendezvous of Multiple Double Integrator Systems Based on Position Measurement Only

In this technical note, we consider the cooperative global robust output regulation problem for nonlinear multi-agent systems in output feedback form by distributed output feedback control. The main result can be summarized as follows: if the information of the leader can reach every follower through a path and the communication flows among the followers are bidirectional, 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.

Cooperative Global Output Regulation for a Class of Nonlinear Multi-Agent Systems

In this paper, we consider the global robust output regulation problem for a class of nonlinear multi-agent systems by distributed output feedback control. 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. 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. Finally, we apply our approach to solve a leader-following synchronization problem for a group of Lorenz multi-agent systems.

Yi Dong

Papers

A leader-following rendezvous problem of double integrator multi-agent systems

Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law

Leader-Following Connectivity Preservation Rendezvous of Multiple Double Integrator Systems Based on Position Measurement Only

Cooperative Global Output Regulation for a Class of Nonlinear Multi-Agent Systems

Cooperative Global Robust Output Regulation for Nonlinear Multi-Agent Systems in Output Feedback Form