Consensusability of multi-agent systems with time-varying communication delay

This paper investigates an observer-based control strategy for networked multi-agent systems with general linear dynamics and time-varying communication delays in a sampling setting. The communication topology is assumed to be directed fixed. Different from a traditional observer-based controller for a single system, the objects that need to be observed here are the state differences between an agent and its neighbours. Using a system transformation method, some equivalent conditions concerning the consensus of multi-agent systems are established. Moreover, we prove that both the connection weights and the communication topology play an important role in the study of multi-agent systems, and establish a linear matrix inequality based observer design method.

In this paper, we discuss average consensus problem in directed networks of dynamic agents with fixed, switching, or dynamically changing topologies as well as time-varying communication delays. The main contribution of this paper is that we prove average consensus of all the nodes in the network will be preserved for a suitable upper bound of the time-varying communication delay if the network topology is strongly connected and balanced. Particularly, the maximal admissible upper bound of the time-varying communication delay can be easily obtained by solving several simple and feasible linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of our theoretical results.

In this paper, time-varying formation tracking problem for second-order nonlinear multi-agent systems with time-varying communication delays has been investigated, where the followers maintain a predefined time-varying formation while tracking the moving leader. Based on a distributed observer, a formation tracking protocol with time-varying delay is developed using the relative neighboring information. By constructing the Lyapunov-Krasovskii (L-K) function, sufficient conditions have been obtained to guarantee the stability of time-varying formation tracking. In addition, the unknown gain matrix in the proposed protocol is computed out through the technique of variable substitution. Numerical simulation results are presented to validate the effectiveness of our theoretical analysis.

Nonfragile robust [formula omitted] containment control for multi-agent systems with a time-varying delay

Stable Teleoperation with Time Domain Passivity Approach

The Consensus control of second-order multi-agent system with stochastic time-varying communication delay is discussed in detail. It is assumed that there exists the stochastic time-varying delay following the Markov distribution in the communication network between agents, then to guide the action of agents keeping consensus. In this paper, consensus control problem is transformed into a stability problem of the error system where the error is the state of agents in network to reference state according to the consensus protocol. The sufficient conditions for stabilizing the error system are derived by stochastic analysis and Lyapunov stability theory. The upper bound of the allowable random time-varying delay to lead to consensus control is obtained. The simulation results verify the correctness of the conclusion.

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper dwells upon the synchronization phenomena in Hindmarsh-Rose (HR) neuron model of N number of neurons with time-varying communication delays between them. By considering a suitable Lyapunov-Krasovskii (L-K) functional, the synchronization criteria is obtained in terms of linear matrix inequality (LMI) for asymptotically stabilizing the error dynamics between the master-slave neuron configuration. The effectiveness of the proposed method is established through the numerical simulations of the neuron model.

Finite-time coordinated formation control of discrete-time multi-AUV with input saturation under alterable weighted topology and time-varying delay

In this paper, two novel adaptive finite-time control schemes are proposed for position tracking of nonlinear teleoperation system, which dynamic uncertainties, actuator saturation, and time-varying communication delays are considered. First, a novel auxiliary variable is designed to provide more stable performance. The radial basis function (RBF) neural network is introduced to estimate dynamic uncertainties. Second, two adaptive finite-time control schemes are investigated. In control scheme I, the RBF neural network and the gain switching strategy are applied to compensate the actuator saturation. In control scheme II, an auxiliary compensation filter and the compensation adaptive update laws, which contain the finite-time structure, are developed for dealing with saturation. Third, the finite-time adaptive controller is designed in each of these two control schemes. Based on the multiple Lyapunov function method, the closed-loop teleoperation system with these two control methods is proved to be bounded and finite-time stability. Finally, the simulation experiments are performed and the comparisons with other control methods are shown. The effectiveness of the proposed control schemes is demonstrated.

Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay

We address the stability problem for a class of nonpassive teleoperators in the presence of the symmetrical and unsymmetrical time varying transmission delay. The design combines local velocity and nonlinear adaptive terms with the delayed position signals. Nonlinear adaptive terms for master and slave devices are used to cope with the unknown uncertainties that appeared into closed-loop systems. The LyapunovKrasovskii-like functionals are used to derive stability condition for the closed-loop systems under time varying communication delay. These condition allows the designer to estimate the control gains in order to achieve bounded position and velocity of the master and slave systems. Finally, simulation is conducted to demonstrate the validity of the proposed design for real-time teleoperation.

Nonlinear Multi-Agent System Consensus with Time-Varying Delays

Many marine missions demand a single remotely operated underwater vehicle (ROV) or multiple ROVs to achieve position tracking. However, the time-varying communication delay in water makes it challenging to achieve the tracking task. This paper is concerned with single-vehicle tracking and multi-vehicle tracking problems. With the consideration of time-varying communication delay, two model-free proportional-derivative (PD) tracking controllers are designed. For the proposed controllers, Lyapunov–Krasovskii functions are constructed to analyze the stability, and then sufficient conditions for asymptotic stability are presented. In particular, the relationship between controller gains and time delay is established by using linear matrix inequality (LMI), such that the allowable upper bound of time delay can be calculated. Finally, simulation and experiment results are performed to validate the effectiveness.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.