Switching Interaction Topologies Research Articles

Adaptive neural network‐based practical fixed‐time consensus tracking for second‐order nonlinear multi‐agent systems with switching topologies

AbstractThe current study concerns the practical fixed‐time consensus tracking problem of second‐order nonlinear multi‐agent systems (MASs) with switching topologies. The neural network (NN) and adaptive technique are adopted to compensate the unknown nonlinearities of the followers. Then, an adaptive NN‐based fixed‐time controller is designed under switching interaction topologies. In order to give the rigorous proof of the practical fixed‐time consensus tracking, a novel lemma for analyzing the practical fixed‐time stability of the switched error system is firstly established, then by constructing appropriate topology‐dependent multiple Lyapunov functions, we theoretically show that the practical fixed‐time consensus tracking of the closed‐loop MASs can be ensured provided that the dwell time of the switching topologies is larger than a predefined threshold and further the involved control parameters are suitably selected. Moreover, the settling time estimation is explicitly given, which is regardless of the system's initial values. The theoretical results are finally verified via a numerical simulation.

Cooperative Guidance of a Multi-quadrotors System with Switching and Reduced Network Information Exchange: Application to Uncooperative Target Entrapping

In this paper, we investigate the leader–followers Time-Varying Formation Tracking (TVFT) problem of a networked Multi-Agent Systems (MASs) based output feedback. The agents’ behavior is featured by linear dynamics. The interaction topology among the agents is switching over time, directed and only assumed to contain a directed spanning tree. This latter is rooted by a leader-agent whose control input is unknown and bounded. A novel fully distributed TVFT controller is proposed that exhibits a reduced network information exchange property among the agents, thus less communicating-resources are utilized. The proposed controlled design is based on an adaptive observer and disturbance rejection technique, where the unknown leader-input is viewed as an external disturbance. The key feature lies in introducing a local observer in each agent-controller design to observe all the relative neighboring output-measurements and the relative neighboring distributed observer-outputs, all gathered in one signal that we denote the agent’s network information signal. The Lyapunov theory is used to prove that the closed-loop MASs tracking error is stable. An analysis of the effect of the interaction topology structure on the tracking-error convergence rate is further provided, showing the validity of the proposed formation control for switching interaction topologies. Finally, to verify the effectiveness of the obtained results, the proposed controller is extended to a cooperative guidance of a networked quadrotors to track and entrap an uncooperative aerial target that plays the role of a passive leader.

Cooperative Target Tracking of Multiple Autonomous Surface Vehicles Under Switching Interaction Topologies

This paper is concerned with the cooperative target tracking of multiple autonomous surface vehicles (ASVs) under switching interaction topologies. For the target to be tracked, only its position can be measured/received by some of the ASVs, and its velocity is unavailable to all the ASVs. A distributed extended state observer taking into consideration switching topologies is designed to integrally estimate unknown target dynamics and neighboring ASVs' dynamics. Accordingly, a novel kinematic controller is designed, which takes full advantage of known information and avoids the approximation of some virtual control vectors. Moreover, a disturbance observer is presented to estimate unknown time-varying environmental disturbance. Furthermore, a distributed dynamic controller is designed to regulate the involved ASVs to cooperatively track the target. It enables each ASV to adjust its forces and moments according to the received information from its neighbors. The effectiveness of the derived results is demonstrated through cooperative target tracking performance analysis for a tracking system composed of five interacting ASVs.

Fuzzy Adaptive Group Obstacle Avoidance Control for Second-Order Multi-Agent Systems Under Fixed and Switching Topologies

This paper investigates the multi-group formation obstacle avoidance control problem of second-order nonlinear leader-follower multi-agent systems (MASs) with unknown nonlinear function and uncertain input disturbance. To make multi-group MASs achieve global consensus, a distributed global fuzzy adaptive control method is presented. Then, navigation functions are employed to make agents bypass obstacles and reach the target positions. The adaptive method is applied to adjust parameters online which can substantially reduce computation burdens and make trajectories of agents smooth. Without loss of generality, both fixed and switching interaction topologies are all taken into account. After that, through Lyapunov stability theory and algebraic graph theory, the feasibility of the method proposed in this paper has been proved. Finally, simulation examples are given to validate the effectiveness of the method proposed in this paper.

Distributed Time-Varying Group Formation Tracking for Multiagent Systems With Switching Interaction Topologies via Adaptive Control Protocols

In this article, time-varying group formation (TVGF) tracking problems for general linear multiagent systems (GLMASs) with switching interaction topologies are investigated. Different from previous studies, a novel TVGF tracking approach is proposed, where all agents are divided into three types: the virtual leader, the group leader, and the follower. The virtual leader is designed to assign the trajectory of GLMASs. Subgroups can be interacted with each other by cooperation among group leaders such that the relative configuration between different groups can be adjusted simultaneously. The followers in each group can achieve time-varying subformations. Moreover, under the influence of external disturbances and switching topologies, based on the distributed observer, two different distributed adaptive control protocols are constructed without using any global information such as the eigenvalue of the Laplacian matrix related to the communication topologies, the upper boundness of the leader’s input, and so on. The algorithms to determine parameters of control protocols are also presented. Furthermore, the closed-loop stability of GLMASs is proven by the Lyapunov theory. Finally, numerical simulations are given to verify the effectiveness of theoretical results.

Consensus of nonlinear multiagent systems with uncertain disturbance under stochastic switching topologies

In this paper, we investigate the mean square consensus problem of leader‐following nonlinear multiagent systems which suffer from white noise disturbance under randomly switching interaction topologies. The control protocol of each agent is designed based on its local information from its neighbors and the leader. Using matrix inequality theory and stochastic stability theory, a sufficient condition is presented to guarantee the mean square consensus. Moreover, two special cases: balanced topologies switching randomly and random connection failures are considered. Finally, two corresponding numerical simulations are provided to demonstrate the theoretical results.

Bearing-based Formation Tracking of Multi-UAV System under Time-varying Directed Interaction

A problem of bearing-based formation control of a group of Unmanned Aerial Vehicles (UAVs) with directed and time-varying communication topology is considered. A subset of vehicles called “leaders” are remotely controlled to perform formation manoeuvres. The remaining vehicles, called “followers” use autonomous bearing-based control law for achieving the desired formation and maintaining it during the manoeuvres. Sufficient conditions for uniqueness of the formation in leader-follower configuration are analysed. For the time-varying manoeuvres of the leaders, the proposed control is shown to exponentially stabilize the formation. A switching time bound is presented that ensures the stability of the system with the proposed control under switching interaction topology. The results are validated with numerical simulations on a multi-vehicle system with directed and time-varying communication topologies.

Predefined formation‐containment control of high‐order multi‐agent systems under communication delays and switching topologies

This paper concerns the problem of formation-containment control for general-linear multi-agent systems (MASs) with both communication delays and switching interaction topologies. On the one hand, the leaders can communicate with each other to form the desired formation and on the other, the followers need to enter the convex envelope spanned by the multiple leaders. Firstly, by using the neighbouring relative information, formation-containment protocols are designed for each leader and follower, where an edge-based state observer is incorporated into the formation-containment controller to evaluate the whole leaders' state. Secondly, according to the linear matrix inequality technology, an algorithm is given to determine the unknown feedback matrixes in the protocol. Then, based on Lyapunov theory, the formation-containment error is proved to be convergent and formation feasibility conditions are also presented for the MASs to achieve formation-containment. Finally, a simulation on several MASs is provided to demonstrate the theoretical results.

Adaptive Bipartite Event-Triggered Output Consensus of Heterogeneous Linear Multiagent Systems Under Fixed and Switching Topologies.

This article addresses the adaptive bipartite event-triggered output consensus issue for heterogeneous linear multiagent systems. We consider both cooperative interaction and antagonistic interaction between neighbor agents in both fixed and switching topologies. An adaptive bipartite compensator consisting of time-varying coupling weights and dynamic event-triggered mechanism is first proposed to estimate the leader's state in a fully distributed manner. Different from the existing methods, the proposed compensator has three advantages: 1) it does not depend on any global information of the network graph; 2) it avoids the continuous communication between neighbor agents; and 3) it is applicable for the signed communication topology. Assume that the system states are unmeasurable, and we thus design the state observer. Based on the devised compensator and observer, the distributed control law is developed such that the bipartite event-triggered output consensus problem can be achieved. Moreover, we extend the results in fixed topology to switching topology, which is more challenging in that state estimation is updated in two cases: 1) the interaction graph is switched or 2) the event-triggered mechanism is satisfied. It is proven that no agent exhibits Zeno behavior in both fixed and switching interaction topologies. Finally, two examples are provided to illustrate the feasibility of the theoretical results.

Energy-Constraint Formation for Multiagent Systems With Switching Interaction Topologies

The current paper investigates energy-constraint formation design and analysis problems for multiagent systems with two types of switching interaction topologies; that is, leaderless ones and leader-following ones. Firstly, a new formation control protocol with switching interaction topologies is shown, where the whole energy supply is limited previously. Then, by constructing the relationship of the whole energy supply and the matrix variable, sufficient conditions for leaderless energy-constraint formation design and analysis are respectively presented by the linear matrix inequality tool. Furthermore, an approach is proposed to determine an explicit expression of the formation center function, which determines the macroscopic motion of a multiagent system as a whole and consists of two parts: the initial state term and the formation function term. Moreover, main conclusions of leaderless energy-constraint formation are extended into leader-following multiagent systems by a new two-step transformation approach, where the asymmetric structure feature of leader-following switching interaction topologies is well dealt with. Finally, two numerical examples are provided to demonstrate the effectiveness of main conclusions.

Improved Consensus Conditions for Multi-Agent Systems With Uncertain Topology: The Generalized Transition Rates Case

This paper is dedicated to addressing the consensus issues for a class of multi-agent systems (MASs) subjected to Markovian switching interaction topology and time-varying input delay. In line with this consideration, we first propose a modified reciprocally convex inequality, named as delay-dependent reciprocally convex inequality to obtain a tighter upper bound about the time-derivative of Lyapunov-Krasovskii functional. As a result, an improved condition with less conservatism stated elegantly in terms of linear matrix inequalities is established such that the MASs with Markovian switching topology and time varying input delay can approach the unified state. Further, the general cases of Markovian switching topology where each transition rate is completely unknown or just its estimate value is known are systematically investigated as well. Moreover, to make our results more meaningful, several comparison results concerning the admissible input delay against other related ones are also presented, which yield that our consensus conditions significantly improve the existing ones advocated thus far. Finally, we verify the validity, the effectiveness, and the practical applicability of our results in the simulation examples.

Stability of General Linear Dynamic Multi-Agent Systems under Switching Topologies with Positive Real Eigenvalues

Abstract The time-varying network topology can significantly affect the stability of multi-agent systems. This paper examines the stability of leader–follower multi-agent systems with general linear dynamics and switching network topologies, which have applications in the platooning of connected vehicles. The switching interaction topology is modeled as a class of directed graphs in order to describe the information exchange between multi-agent systems, where the eigenvalues of every associated matrix are required to be positive real. The Hurwitz criterion and the Riccati inequality are used to design a distributed control law and estimate the convergence speed of the closed-loop system. A sufficient condition is provided for the stability of multi-agent systems under switching topologies. A common Lyapunov function is formulated to prove closed-loop stability for the directed network with switching topologies. The result is applied to a typical cyber–physical system—that is, a connected vehicle platoon—which illustrates the effectiveness of the proposed method.

Sampled-time containment control of high-order continuous-time MASs under heterogenuous time-varying delays and switching topologies: A scrambling matrix approach

This paper studies the containment control problem for high-order continuous-time multi-agent systems (MASs) under switching topologies and time-varying delays. We propose a distributed sampled-time containment protocol in which the restriction of choosing weights of the communication links from a finite set is eliminated. Under such a protocol, the states of the followers will asymptotically converge to the convex hull spanned by those of the leaders. Based on the properties of scrambling matrices, necessary and sufficient containment criteria are obtained for the network of agents with arbitrary bounded communication delays and switching interaction topologies. The proposed condition does not need the communication graph has a united spanning tree at each time instant and only requires that the union of communication graphs has a united spanning tree over a bounded period of time. In addition, the appropriate feedback gains are computed via given mathematical relations. Some numerical examples are given to demonstrate the effectiveness of the new protocols.

Predefined containment control for general linear multiagent systems with time‐varying delays and switching topologies

AbstractContainment control problems for general linear multiagent systems with switching interaction topologies and time‐varying delays are studied. Firstly, state observers are constructed to estimate the multiple leaders under the influence of switching graphs and time‐varying delays. Secondly, a predefined containment protocol is presented based on the distributed state observer, where the expected convex combination of multiple leaders is predefined by several given weights. Moreover, an algorithm with two steps to confirm the gain matrices of the containment protocol and state observer is given. Based on linear matrix inequality technique and common Lyapunov‐Krasovskii stability theory, the convergence of this control strategy for multiagent systems with switching topologies and time‐varying delays to achieve state containment is proved. Finally, a numerical simulation is given to verify the validity of the theoretical results.

Formula omitted] consensus of stochastic delayed multi-agent systems with ADT switching interaction topologies

This paper investigates the L2−L∞ consensus for a class of stochastic delayed multi-agent systems subject to switching interaction topologies via utilizing an observer-based control protocol. The switching between the interaction topologies is assumed to have the average dwell time (ADT) constraint. With the aid of a simple model transformation, the L2−L∞ consensus issue is transformed into the problem of weighted stochastic L2−L∞ control. Analysis results on the weighted stochastic L2−L∞ control are proposed by constructing Lyapunov-Krasovskii functional and employing stochastic analysis methods. Then, an approach is developed to determine the desired observer-based consensus protocol. Finally, an illustrative numerical example is given to show the usefulness of our design method.

Hierarchical Controller-Estimator for Coordination of Networked Euler-Lagrange Systems.

This paper proposes several hierarchical controller-estimator algorithms (HCEAs) to solve the coordination problem of networked Euler-Lagrange systems (NELSs) with sampled-data interactions and switching interaction topologies, where the cases with both discontinuous and continuous signals are successfully addressed in a unified framework. The HCEAs comprise two main layers (i.e., a control layer and an estimator layer) and one optional layer (i.e., a filter layer), in which the coordination problem is tackled in the main layers and the transient response can be optionally smoothed in the filter layer. For stabilizing the corresponding cascade closed-loop systems, several sufficient conditions on the upper bound of the aperiodic sampling intervals and the lower bound of the control parameters are established. In addition, the HCEAs are extended to address the task-space coordination problem of networked heterogeneous robotic systems, which shows the versatility of the HCEAs. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented algorithms.

Time-Varying Formation Control for Time-Delayed Multi-Agent Systems with General Linear Dynamics and Switching Topologies

Time-varying formation analysis and design problems for general linear multi-agent systems with switching interaction topologies and time-varying delays are studied. Firstly, a consensus-based formation control protocol is constructed using local information of the neighboring agents. An algorithm with three steps is presented to design the proposed formation control protocol. Then, based on linear matrix inequality technique and common Lyapunove–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with switching topologies and time-varying delays to achieve time-varying formation are given together with a time-varying formation feasibility condition. Finally, a numerical simulation is given to demonstrate the effectiveness of the obtained theoretical results.

Distributed LQR Consensus Control for Heterogeneous Multiagent Systems: Theory and Experiments

Controlling heterogeneous multiagent systems (MASs) to cooperatively accomplish tasks is currently an emerging topic in the application-oriented research of robotics. This paper investigates the consensus problem of a MAS consisting of quadrotors and two-wheeled mobile robots (2WMRs). Directed and switching interaction topologies over the network are considered. We propose a distributed linear quadratic regulation (LQR) consensus protocol for the quadrotors and design an LQR-based Rotate&Run Consensus Scheme for the 2WMRs to update the states. We use the algebraic graph theory and stochastic matrix analysis to conduct the convergence analysis of consensus. The underactuation characteristic of the 2WMR dynamics is considered in the controller design. The effectiveness of the control methods is verified by simulations and experiments.

Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying

Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, where the states of the followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed based on the relative information of the neighboring agents. Necessary and sufficient conditions for Multi-Agent systems with switching interaction topologies to achieve time-varying formation tracking are proposed together with the formation tracking feasibility constraint based on the graph theory. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proved using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a multiquadrotor unmanned aerial vehicle (UAV) system consisting of one leader (target) quadrotor UAV and three follower quadrotor UAVs. A numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.

Robust consensus tracking control of multiple mechanical systems under fixed and switching interaction topologies.

Consensus tracking problems for multiple mechanical systems are considered in this paper, where information communications are limited between individuals and the desired trajectory is available to only a subset of the mechanical systems. A distributed tracking algorithm based on computed torque approach is proposed in the fixed interaction topology case, in which a robust feedback term is developed for each agent to estimate the external disturbances and the unknown agent dynamics. Then the result is extended to address the case under switching interaction topologies by using Lyapunov approaches and sufficient conditions are given. Two examples and numerical simulations are presented to validate the effectiveness of the proposed robust tracking method.