Stability Of Multi-agent Systems Research Articles

Optimal Formation Control for Second-Order Multi-Agent Systems With Obstacle Avoidance

Dear Editor, The optimal formation control design problem is studied for a class of second-order multi-agent systems (MASs) with obstacle avoidance. Based on the actor-critic framework, an optimized formation controller is proposed by constructing a novel performance index function. Furthermore, the stability of MAS is proved by constructing the Lyapunov function. The simulation results are provided to depict the effectiveness of the proposed strategies.

Upper solution bound of the CCARE and its application in multi-agent systems with time-delay in the state

Stability is important for control systems. In this paper, using the transformation of the matrix equations and some significant properties of the matrix inequality, we derived new upper solution bounds of the continuous coupled algebraic Riccati equation (CCARE). The new bounds are more precise than those proposed in some existing works on this topic numerically. Next, a condition for the stability of multi-agent systems with time-delay in the state is presented according to the upper solution bound of the CCARE. Finally, corresponding numerical examples are provided to illustrate the superior and effectiveness of the derived results.

Stabilizability and Bipartite Containment Control of Multi-Agent Systems Over Signed Directed Graphs

This paper investigates the stabilizability and bipartite containment control problem of general linear multi-agent systems over signed directed graphs, where the negative edges indicate the antagonistic interactions between agents. By employing the proposed bipartite containment control protocols over signed directed graphs, and combining the linear system stabilization theory and the signed Laplacian matrix, the necessary condition for the stabilization of multi-agent systems with multiple leaders is discussed. According to this necessary condition, a leader-follower matching method is presented to establish leader-follower multi-agent system networks. Based on the leader-follower topology established above and the designed state feedback gain, the stability of multi-agent systems is proved by using the system error and the algebraic Riccati equation. It is shown that the followers can gradually converge into the convex hull spanned by the states and the sign-inverted states of leaders, and the bipartite containment control of multi-agent systems can be realized. The simulation results verify the feasibility of the theoretical analysis.

Prescribed performance global stable adaptive neural dynamic surface consensus tracking control of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics

ABSTRACTThis paper focuses on the leader-following consensus control problem of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics. A leader-following consensus scheme is presented for stochastic multi-agent systems directions under directed graphs, which can achieve predefined synchronisation error bounds. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded tracking stability of multi-agent systems recently. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronise with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and all the follower agents can keep consensus with the leader. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.

On the optimal parameter of the composite Laplacian quadratics function

Recently, the composite quadratic Lyapunov function has been extended to study of multi-agent systems, leading to the so-called composite Laplacian quadratics (CLQs) function. Compared with quadratic Lyapunov functions, the CLQs function can yield a larger convergence region and is particularly useful in stabilization of multi-agent systems with complex dynamics, such as differential inclusions. In the definition of the CLQs function, an optimal vector parameter plays a critical role in determining the value of the CLQs function and in constructing stabilization laws derived from the CLQs function. This paper focuses on the properties of the optimal parameter of the CLQs function. The uniqueness of the optimal parameter is established. A distributed computation approach is further proposed, which is useful in computing the optimal parameter. The robustness issue of the optimal parameter is also investigated for a multi-agent system described by linear differential inclusions. Finally, a numerical example is provided to validate the proposed theoretical results.

Multi-target consensus circle pursuit for multi-agent systems via a distributed multi-flocking method

ABSTRACTThis paper studies the multi-target consensus pursuit problem of multi-agent systems. For solving the problem, a distributed multi-flocking method is designed based on the partial information exchange, which is employed to realise the pursuit of multi-target and the uniform distribution of the number of pursuing agents with the dynamic target. Combining with the proposed circle formation control strategy, agents can adaptively choose the target to form the different circle formation groups accomplishing a multi-target pursuit. The speed state of pursuing agents in each group converges to the same value. A Lyapunov approach is utilised to analyse the stability of multi-agent systems. In addition, a sufficient condition is given for achieving the dynamic target consensus pursuit, and which is then analysed. Finally, simulation results verify the effectiveness of the proposed approaches.

Input-to-State Stability of Multi-Agent Systems

In this paper, we mainly study input-to-state-stability (ISS) for the multi-agent systems with directed graph and the communication noise under switching interaction topologies, using the method of input-to-state-stability, input-to-state-stability -Lyapunov function. We point out the results of [5] is correct, but the proof of its main theorem has a small mistake, we give the proof by quite a different method.

Event-Triggered Average Consensus for Multiagent Systems with Time-Varying Delay

The paper investigates average consensus for multiagent systems with time-varying delay. A reducing dimension multiagent systems model is presented firstly. Using event-triggered mechanism to reduce network load, a comprehensive model is then proposed, which considers communication delay and triggered issue. Furthermore, the event-triggered average consensus stability of multiagent systems with fixed directed/undirected graph is analyzed, and sufficient conditions are provided. Moreover, the upper bound of time-varying delay can be obtained conveniently. Finally, simulation results confirm the feasibility and effectiveness of the proposed method.

Passivity-based decentralized stabilization of multi-agent systems with uncertainty and mixed delays

In this paper, we investigate a decentralized stabilization problem of uncertain multi-agent systems with mixed delays including discrete and distributed time-varying delays based on passivity stability. We design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent passivity stability for each subsystem. Then, by employing a new Lyapunov-Krasovskii function, a linear matrix inequality (LMI) approach is developed to establish the delay-dependent criteria for the passivity stability of multi-agent systems. The sufficient condition is given for checking the passivity stability. The proposed LMI result is computationally efficient. An example is given to show the effectiveness of the method.

Cooperative control of discrete-time linear multi-agent systems with fixed information structure

In this paper, a cooperative control problem was investigated for discrete-time linear multi-agent systems with fixed information structure and without communication delays. Based on the bilinear matrix inequality (BMI), the sufficient condition was obtained for the stabilization of multi-agent systems composed of N agents. Then, the design problems of cooperative controllers were converted into the optimization problems with BMI constraints. To solve these problems, an optimization algorithm was proposed. Finally, numerical examples were provided to demonstrate the reduced conservatism of the proposed condition.

2124 Formation Stability of Multi-Agent Systems with State-Dependent Stochastic Communication Loss

2124 Formation Stability of Multi-Agent Systems with State-Dependent Stochastic Communication Loss

Stability of multiagent systems with time-dependent communication links

We study a simple but compelling model of network of agents interacting via time-dependent communication links. The model finds application in a variety of fields including synchronization, swarming and distributed decision making. In the model, each agent updates his current state based upon the current information received from neighboring agents. Necessary and/or sufficient conditions for the convergence of the individual agents' states to a common value are presented, thereby extending recent results reported in the literature. The stability analysis is based upon a blend of graph-theoretic and system-theoretic tools with the notion of convexity playing a central role. The analysis is integrated within a formal framework of set-valued Lyapunov theory, which may be of independent interest. Among others, it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.