Consensus Tracking Problem Research Articles

Bounded consensus tracking of second-order multi-agent systems with sampling delay under directed networks

The bounded consensus tracking problems of second-order multi-agent systems under directed networks with sampling delay are addressed in this paper. When the sampling delay is more than a sampling period, new protocols based on sampled-data control are proposed so that each agent can track the time-varying reference state of the virtual leader. By using the delay decomposition approach, the augmented matrix method, and the frequency domain analysis, necessary and sufficient conditions are obtained, which guarantee that the bounded consensus tracking is realized. Furthermore, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Consensus tracking for higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs

This paper studies the distributed consensus tracking problem of linear higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs. In this framework, the underlying topology of dynamic agents may switch among several directed graphs, each having a directed spanning tree rooted at the leader. Furthermore, the control inputs to the followers may be temporally missed due to actuator failures and network-induced packet loss. To guarantee asymptotic consensus tracking in such a multi-agent system, several distributed controllers are constructed based only on the relative state information of neighboring agents. By appropriately constructing a switching Lyapunov function and using tools from the M-matrix theory, some sufficient conditions for achieving distributed consensus tracking are provided. Finally, some numerical simulations are given to illustrate the theoretical analysis.

Bounded consensus tracking for sampled‐data second‐order multi‐agent systems with fixed and Markovian switching topology

SUMMARYThis paper studies the bounded consensus tracking problems of second‐order multi‐agent systems with fixed and Markovian switching topology in a sampling setting. It is assumed that all the agents can only obtain the approximative value of the leader's acceleration instead of the actual value. Moreover, only a portion of agents can have the access to the leader and obtain the leader's position and velocity directly. By virtue of matrix analysis and perturbation theory, we present necessary and sufficient conditions for boundedness of tracking error system and show the ultimate bound of tracking errors under fixed and Markovian switching topology, respectively. Finally, a simulation example is given to illustrate the effectiveness of the results. Copyright © 2013 John Wiley & Sons, Ltd.

Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader

This paper investigates the distributed consensus tracking problem for multi-agent systems with Lipschitz-type dynamics under a reference leader. It is assumed that the leader state information is only available to a subset of followers, while the bounded reference input of the leader’s is unavailable to any follower. To achieve consensus tracking, a class of discontinuous protocols based on the relative information between the neighbouring agents are proposed. Furthermore, as extensions of the former result, the robust and adaptive consensus tracking problems are studied for the case where there exist parameter uncertainties and external disturbances in the network. Finally, the effectiveness of the theoretical result is demonstrated through a network of single-link manipulators.

Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM

The finite-time consensus tracking problem for second-order multi-agent system is investigated in this paper. The multi-agent system here is composed of a leader with bounded input signal and n followers with bounded disturbances. A new continuous nonlinear distributed consensus tracking protocol is constructed via nonsingular terminal sliding mode (TSM) scheme. It is proved that the overall system will reach consensus in finite time via Lyapunov theory when appropriately choosing the parameters under directed connected topology. Finally, simulations are performed, and results show that the method is robust and efficient.

Robust consensus tracking of multi‐agent systems with uncertain Lur'e‐type non‐linear dynamics

This study addresses the robust consensus tracking problem of multi-agent systems with uncertain Lur'e-type non-linear dynamics under a fixed topology. To achieve consensus tracking, a class of discontinuous control protocols are first proposed, which rely on the relative information among the neighbouring agents. Theoretical analysis indicates that the robust consensus tracking of uncertain Lur'e network can be achieved if the coupling strength and the control gain are both larger than the thresholds depending on some global information of the network. Then, an adaptive consensus tracking protocol is further designed to solve the robust consensus tracking problem as a modification of a fully distributed version without the need of any global information of the multi-agent systems. Furthermore, as an expansion of the discontinuous protocols, a new class of continuous control laws are developed based on the boundary layer concept. Finally, a couple of examples are given to illustrate the effectiveness of the theoretical results.

Stochastic bounded consensus tracking of second-order multi-agent systems with measurement noises based on sampled-data with general sampling delay

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbours or the virtual leader with a time-varying reference state, the measurements are corrupted by random noises and the signal sampling process induces the general sampling delay. First, the stochastic bounded consensus tracking protocol based on sampled-data with the general sampling delay is presented by using the delay decomposition technique. Second, the augmented matrix method, the probability limit theory and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. The theoretical results show that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampled period and the sampling delay, and that the static consensus tracking error depends on not only the above-mentioned factors, but also the noise intensity and the upper bound of the velocity and the acceleration of the virtual leader. The obtained results cover no sampling delay and the small sampling delay as two special cases. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications

SUMMARY Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi-agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi-agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low-dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi-step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi-agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Distributed adaptive consensus tracking of a class of networked non‐linear systems with parametric uncertainties

This study investigates a distributed adaptive consensus tracking problem for multiple non-linear strict-feedback systems with parametric uncertainties under a directed communication graph topology. It is assumed that the information of a leader is available for only a limited subset of followers. The distributed adaptive dynamic surface design approach is presented to design the local controller of each follower to guarantee that all networked followers with unmatched parametric uncertainties synchronise to the leader regardless of a lack of the shared information on the communication links. From the Lyapunov stability theorem, it is shown that the consensus tracking errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighbourhood of the origin.

Tracking Consensus for Second-Order Multi-Agent Systems with Nonlinear Dynamics in Noisy Environments

This paper investigates the leader-following tracking consensus problem for second-order multi-agent systems with time delays and nonlinear dynamics in noisy environments on the conditions of fixed and switching directed topologies. Based on a novel velocity decomposition technique and stochastic analysis, a measurement-based distributed tracking control protocol is proposed, under which all agents can track the leader in mean square. Simulation results are also given to illustrate the effectiveness of the proposed protocol.

Bounded consensus of leader-following multi-agent systems with sampling delay for double-integrator dynamics

The authors are concerned with the bounded consensus tracking problems of leader-following multi-agent systems with sampling delay for double-integrator dynamics. Based on the delay decomposition approach, the augmented matrix method and some other technologies, the necessary and sufficient conditions are obtained which guarantee that each agent can track the time-varying reference state of the virtual leader. Some numerical simulations are presented to illustrate the effectiveness of the theoretical results.

Stochastic bounded consensus tracking of leader—follower multi-agent systems with measurement noises and sampled-data

This paper is concerned with the stochastic bounded consensus tracking problems of leader—follower multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbours or the virtual leader with a time-varying reference state, and the measurements are corrupted by random noises. The probability limit theory and the algebra graph theory are employed to derive the necessary and sufficient conditions guaranteeing the mean square bounded consensus tracking. It is shown that the maximum allowable upper boundary of the sampling period simultaneously depends on the constant feedback gains and the network topology. Furthermore, the effects of the sampling period on the tracking performance are analysed. It turns out that from the view point of the sampling period, there is a trade-off between the tracking speed and the static tracking error. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Stochastic bounded consensus tracking of leader–follower multi-agent systems with measurement noises based on sampled-data with small sampling delay

This paper is concerned with the stochastic bounded consensus tracking problems of leader–follower multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighborhood agents or a virtual leader with a time-varying reference state, the measurements are corrupted by random noises, and the signal sampling process induces a small sampling delay. The augmented matrix method, probability limit theory and algebra graph theory are employed to derive the necessary and sufficient conditions guaranteeing mean square bounded consensus tracking. It turns out that the convergence of the proposed protocol simultaneously depends on the constant feedback gains, the network topology, the sampling period and the sampling delay, and that the static consensus tracking error depends on not only the above-mentioned factors, but also the noise intensity, the number of agents and the upper bound of the changing rate of the virtual leader’s state. The obtained results cover no sampling delay as a special case. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements

This Letter investigates the finite-time consensus problems of second-order multi-agent systems in the presence of one and multiple leaders under a directed graph. Specifically, we propose two bounded control laws, which are independent of velocity information, to deal with the finite-time consensus tracking problem with one leader and the finite-time containment control problem with multiple leaders, respectively. With the aid of homogeneous theory, some sufficient conditions are established for the achievement of the finite-time tracking control problem of second-order multi-agent systems. Numerical examples are finally provided to illustrate the theoretical results.

Finite‐Time Consensus Tracking for Second‐Order Multiagent Systems

AbstractIn this paper, the finite‐time consensus tracking problem is investigated for second‐order multi‐agent systems. A novel distributed consensus algorithm based on the sliding mode control (SMC) is designed, and the tracking time is estimated analytically.

Stochastic Bounded Consensus Tracking of Second-Order Multi-Agent Systems with Measurement Noises and Sampled-Data

This paper investigates the stochastic bounded consensus tracking problems of second-order multi-agent systems, where the control input of an agent can only use the information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state, and the measurements are corrupted by random noises. The probability limit theory, the algebra graph theory, and some other techniques are employed to derive the necessary and sufficient condition guaranteeing the mean square bounded consensus tracking. It turns out that the maximum allowable sampling period depends on not only the network topology but also the constant feedback gains. Furthermore, the effects of the sampling period on tracking performance, including the tracking speed and the static tracking error, are also analyzed. The results show that reducing the sampling period can accelerate the tracking speed and decrease the static tracking error. Simulations are provided to demonstrate the effectiveness of the theoretical results.

Robust consensus tracking of a class of second-order multi-agent dynamic systems

In this paper, we study the problem of robust consensus tracking for a class of second-order multi-agent dynamic systems with disturbances and unmodeled agent dynamics. Contrary to previous approaches, we design continuous distributed consensus protocols to enable global asymptotic consensus tracking. Our focus is on consensus protocol design and stability analysis which also leads to the derivation of sufficient conditions for consensus tracking. We first consider the case of undirected information exchange with a symmetric and positive definite information-exchange matrix. We develop an identifier for each agent to estimate the unknown disturbances and unmodeled agent dynamics. Based on the identifier, we develop a consensus tracking protocol to enable global asymptotic consensus tracking using local information obtained from neighboring agents. The closed-loop stability is proven using Lyapunov analysis theory and an invariance-like theorem. We then extend the approach to the case of directed information exchange, whose information-exchange matrix is only of full rank so that the approach for undirected graphs cannot be directly applied. We show that global asymptotic consensus tracking can still be enabled under the new derived sufficient conditions by designing a new identifier, which utilizes the estimated information exchanged from neighboring agents, and constructing a new Lyapunov function. Examples and numerical simulations are provided to validate the effectiveness of the proposed robust consensus tracking method.

Distributed Space Situational Awareness (D-SSA) with a Satellite-assisted Collaborative Space Surveillance Network

AbstractThis paper addresses the problem of tracking space-borne objects of interest (OoIs) with a satellite-assisted collaborative space surveillance network (SSN). It is formulated as a multiple moving-object tracking problem in a hybrid distributed wireless sensor network (WSN) made of both mobile and static nodes. The static nodes may be considered as ground-based sensors with fixed locations, while mobile sensor nodes can be satellites in space. At any given time, due to relative motion among nodes and OoI's, not all sensors are capable of observing a given target. The number of space OoI's (targets) of interest is several orders of magnitude larger than the number of nodes in the SSN, and each node can observe only a finite number of targets at a time. The challenge is to be able to schedule the nodes so that the best possible node-target assignments are made. A distributed approach is more desired in terms of scalability and robustness. However, for a distributed scheduling scheme to be efficient the distributed scheduling decisions need to be consistent across the network, which in turn requires the distributed local tracking estimates to be consistent across the network. As a result, the problem turns out to be a nonlinear consensus tracking problem on a time-varying graph with incomplete data and noisy communications links. We propose a distributed and collaborative framework in which each node in the network updates its tracking estimate of an object based on its own observations via an extended Kalman filter (EKF), followed by a consensus update stage in which nodes exchange their local estimates in order to arrive at a consensus on the distributed estimates leading to conflict-free node scheduling. Simulations of a two-dimensional hybrid SSN have been carried out in order to evaluate the performance of the proposed distributed tracking with consensus algorithm. The performance results show that the proposed algorithm indeed performs very well under conditions that can be expected in a realistic SSN, paving way for possible distributed scheduling.

Robust consensus tracking for an integrator-type multi-agent system with disturbances and unmodelled dynamics

In this article, a robust consensus tracking problem for a multi-agent system with integrator-type dynamics has been addressed in the presence of disturbances and unmodelled dynamics. The desired trajectory to be tracked is only provided to a small group of team members. An identifier is developed to estimate the unknown disturbances and unmodelled dynamics. A consensus controller is developed based on this identifier to achieve asymptotic consensus tracking using the local information obtained from neighbouring agents. The closed-loop stability is proved using the Lyapunov-based analysis and an invariance-like theorem. Numerical simulations are provided to demonstrate the effectiveness of the developed robust consensus controller.

Consensus Tracking Under Directed Interaction Topologies: Algorithms and Experiments

Consensus tracking problems with, respectively, bounded control effort and directed switching interaction topologies are considered when a time-varying consensus reference state is available to only a subgroup of a team and the team members have only local interaction. A consensus tracking algorithm explicitly accounting for bounded control effort is proposed and analyzed under a directed fixed interaction topology. Furthermore, convergence analysis for a consensus tracking algorithm is provided when the time-varying consensus reference state is available to a dynamically changing subgroup of the team under directed switching inter-vehicle interaction topologies. Experimental results of a formation control application are demonstrated on a multi-robot platform to validate one of the proposed consensus tracking algorithms.