Double-integrator Multi-agent Systems Research Articles

Event-Based H ∞ Consensus of Double-Integrator Multi-Agent Systems: A Prescribed Performance Control Approach

Event-Based <i>H</i> _∞ Consensus of Double-Integrator Multi-Agent Systems: A Prescribed Performance Control Approach

Prescribed-time leader-following consensus and containment control for second-order multiagent systems with only position measurements

The problems of prescribed-time leader-following consensus and prescribed-time containment control for double-integrator multiagent systems (MASs) with only position measurements are investigated in this paper. An observer-based prescribed-time control protocol is proposed, in which the two groups of observers for estimating the consensus errors of each follower both converge to zero within a specified time. Furthermore, the proposed controller only relies on its own observers and does not need to obtain the data from observers embedded in its neighbor nodes. The sufficient conditions for the MASs to achieve the defined prescribed-time consensus and to fulfill the goal of prescribed-time containment control are, respectively, given. The effectiveness of the proposed control protocol is further verified by computer simulations.

Global Consensus of Double-Integrator Multi-Agent Systems with Input Saturation by Fully Distributed Event-Triggered and Self-Triggered Controls

Global Consensus of Double-Integrator Multi-Agent Systems with Input Saturation by Fully Distributed Event-Triggered and Self-Triggered Controls

Privacy-Preserving Consensus of Double-Integrator Multi-Agent Systems With Input Constraints

Privacy-Preserving Consensus of Double-Integrator Multi-Agent Systems With Input Constraints

Prescribed Time Fault-Tolerant Affine Formation Control for Multi-Agent Systems with Double-Integrator Dynamics

There is an increasing interest in the affine formation control of multi-agent systems, because it can change the centroid, orientation and scale of the formation by controlling only a few leaders. In this paper, the fault-tolerant affine formation control problem is addressed for double-integrator multi-agent systems with partial loss of efficiency and bias faults. Firstly, in order to track the leaders with dynamically changing accelerations, an acceleration observer with prescribed time convergence is proposed, which can estimate the ideal acceleration for each follower. Then, based on the acceleration observer, a fault-tolerant control algorithm is given. A new Lyapunov function candidate is constructed, based on which a sufficient condition to achieve the control objective is derived. Theoretical analysis shows that the formation tracking error can converge to zero within a prescribed time, and remain in a small neighborhood of zero after that time. Finally, numerical simulations are given to show the effectiveness of the proposed algorithm and compare it with existing results.

Rendezvous Control Design for the Generalized Cucker–Smale Model on Riemannian Manifolds

In this paper, we consider a rendezvous problem for the generalized Cucker-Smale model, which is a double-integrator multi-agent system, on complete Riemannian manifolds. With the help of the covariant derivative, parallel transport and logarithm map on the Riemannian manifold, we design a rendezvous feedback law that enables all agents to converge at a given target in the Riemannian manifold, under some a priori conditions. Furthermore, we consider three concrete complete Riemannian manifolds, such as the unit circle, unit sphere, and hyperboloid, and present the explicit feedback laws for rendezvous on them by calculating the corresponding covariant derivatives, parallel transports, and logarithm maps. Meanwhile, numerical examples are given for the manifolds as mentioned above to verify and illustrate the theoretical results.

Consensus of double-integrator multi-agent systems with asymmetric input saturation

Consensus of double-integrator multi-agent systems with asymmetric input saturation

Consensus of double integrator multiagent systems under nonuniform sampling and changing topology

&lt;abstract&gt;&lt;p&gt;This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.&lt;/p&gt;&lt;/abstract&gt;

Distributed optimization for consensus performance of delayed fractional-order double-integrator multi-agent systems

This paper addresses distributed optimization problems concerning consensus in delayed fractional-order double-integrator multi-agent systems (FDMSs). To start with, an optimized distributed protocol with state-fractional-order-derivative feedback (SF) is presented for delayed FDMSs. Then, the consensus problems are studied for the two kinds of delayed FDMSs with SF in the presence of symmetric time-delays over undirected network topology and asymmetric time-delays over directed network topology. Next, by the means of graph theory, matrix theory and frequency-domain analysis method, the sufficient conditions to guarantee consensus of delayed FDMSs with SF are derived. Compared to the traditional distributed protocol without SF, the proposed distributed optimization protocol with SF are taken into account to enable better consensus performance in delayed FDMSs with SF. Finally, numerical experiments are carried out to verify the feasibility of our theoretical results.

Global Leader-Following Consensus of Double-Integrator Multiagent Systems by Fully Distributed Bounded Linear Protocols

This article is concerned with the global leader-following consensus problem of the input-constrained double-integrator multiagent systems. By utilizing a Lyapunov-like function consisting of a positive semidefinite term and an integral term, a class of bounded static linear protocols are proposed to ensure that the global leader-following consensus problem for homogeneous multiagent systems is solved in a fully distributed manner for all undirected communication graphs. As a further result, the global consensus problem for heterogeneous multiagent systems under directed communication graphs is also considered and two different distributed observer-based bounded linear protocols are proposed to solve such a problem also in a fully distributed manner. The most significant advantages of this article are that the system under consideration is more general, the designed protocols are linear, and the global consensus in a fully distributed manner can be guaranteed. A numerical example shows the effectiveness of the proposed approaches.

Distributed output agreement of PWM‐controlled double‐integrator multi‐agent systems with switching topologies

This paper studies the distributed pulse-width-modulation (PWM) control problem for double-integrator multi-agent systems with switching topologies. Usually, a PWM control signal updates only on discrete-time sample instants and only takes three constant values. This means that the methods based on linear and continuous designs are not directly applicable. The major contribution of this paper is that a new class of distributed PWM controllers, which feature nested saturated loops, is proposed. With the new design, the outputs of the controlled agents asymptotically converge to each other, as long as a mild connectivity condition is satisfied. The validity of the proposed PWM controller is proved based on a new invariant-set-like method. This work first shows that the state of each PWM-controlled agent stays within an appropriately chosen closed set if the interactions are bounded. Then, under a mild connectivity condition, the state boundedness and convergence of the closed-loop multi-agent system by analyzing the boundedness of the interactions are proved. A numerical example is employed to verify the effectiveness of the proposed design.

Fault-tolerant finite-time dynamical consensus of double-integrator multi-agent systems with partial agents subject to synchronous self-sensing function failure

This paper investigates fault-tolerant finite-time dynamical consensus problems of double-integrator multi-agent systems (MASs) with partial agents subject to synchronous self-sensing function failure (SSFF). A strategy of recovering the connectivity of network topology among normal agents based on multi-hop communication and a fault-tolerant finite-time dynamical consensus protocol with time-varying gains are proposed to resist synchronous SSFF. It is proved that double-integrator MASs with partial agents subject to synchronous SSFF using the proposed strategy of network topology connectivity recovery and fault-tolerant finite-time dynamical consensus protocol with the proper time-varying gains can achieve finite-time dynamical consensus. Numerical simulations are given to illustrate the effectiveness of the theoretical results.

Distributed Optimization of Multiagent Systems Against Unmatched Disturbances: A Hierarchical Integral Control Framework

This article investigates a distributed optimization problem of double-integrator multiagent systems with unmatched constant disturbances. Instead of involving an internal model or a disturbance observer to deal with the disturbances as in existing works, a two-layer control framework is presented based on state-integral feedback control (SIFC) and adaptive control techniques. The upper layer uses a virtual system to generate a global optimal consensus trajectory which is shared by the agents via a communication network. The lower layer includes an SIFC controller to guarantee asymptotic tracking of the given trajectory. Also in this layer, a model reference adaptive controller is introduced to enhance the dynamic tracking performance of the SIFC controller. This framework enables distributed optimization with time-triggered communication and mild requirements on the team objective. The method yields an interesting co-design algorithm of the control parameters and the communication intervals, which is proved to be convergent using Lyapunov stability theory. The effectiveness and advantages of the method are illustrated by numerical simulations.

Containment Control of Double-Integrator Multi-Agent Systems With Time-Varying Delays

This article mainly considers the containment control problem of multi-agent systems (MASs), where the time-varying communication delays are taken into consideration and the multiple leaders are stationary or dynamic. Specially, when leaders are stationary, the communication delays among agents are nonuniform, which is rarely considered in existing papers. Furthermore, when leaders are dynamic, we derive the sufficient conditions for the case with uniform time-varying communication delays. In both cases, all followers are included into the convex hull spanned by leaders with proposed control protocol, in which we get the sufficient conditions by using Lyapunov-Krasovskii functional. At last, the effectiveness is verified by simulations.

Bounded Consensus of Discrete Stochastic Double-Integrator Multi-Agent Systems Over Switching Topologies

Bounded Consensus of Discrete Stochastic Double-Integrator Multi-Agent Systems Over Switching Topologies

Rotating consensus for double-integrator multi-agent systems with communication delay

In this paper, the rotating consensus problem for the multi-agent systems of double-integrator dynamic is mainly considered with and without communication delay. A fully distributed control strategy is given on the more general complex plane. For the case without communication delay, we design a distributed control protocol with the help of local relative information and obtain the sufficient and necessary condition with the lower bounded control parameter for the directed communication topology. Furthermore, with taking communication delay into consideration, the sufficient and necessary condition with the upper bounded communication delay is obtained with the help of frequency domain analysis method. Compared with some existing results, the communication topology considered is a more general directed graph. Finally, some simulation examples are presented to clarify the correctness of our results.

Reset control for consensus of double-integrator multi-agent systems

In this paper, we address the consensus problem for double-integrator multi-agent systems integrated with a novel reset control protocol. It reveals the conditions under which consensus is achieved and the reset function is in action. The proposed reset control essentially provides a dynamically generated higher gain for better transient consensus performance, including faster convergence with less control effort. Compared with a static high gain controller, this dynamic high gain mechanism is more efficient and sophisticated especially in regularly resetting the additional gain to zero during the dynamic evolution.

Distributed Optimal Consensus for Euler–Lagrange Systems Based on Event-Triggered Control

The distributed optimal consensus based on an event-triggered scheme for Euler-Lagrange (EL) multiagent systems is investigated in this article. The objective is to minimize the global cost function in a distributed manner while achieving consensus, where the local cost function of each agent is only known by itself. First, the distributed optimization algorithms based on the event-triggered scheme are proposed to achieve optimal consensus as well as reduce communication costs for the EL multiagent systems when the model parameters are available. Second, when the model parameters are unavailable, the tracking controllers are developed to solve the optimization problem for the EL multiagent systems. Then, the distributed optimization problem for EL systems can be transformed into the tracking problem for double-integrator multiagent systems. With the proposed algorithms, global optimization can be achieved with the exponential convergence rate. Finally, a simulation example is presented to illustrate the effectiveness of the proposed method.

Distributed Model Predictive Control for Linear-Quadratic Performance and Consensus State Optimization of Multiagent Systems.

The optimal consensus problem of asynchronous sampling single-integrator and double-integrator multiagent systems is solved by distributed model predictive control (MPC) algorithms proposed in this article. In each predictive horizon, the finite-time linear-quadratic performance is minimized distributively by the control input with consensus state optimization. The MPC technique is then utilized to extend the optimal control sequence to the case of an infinite horizon. Conditions depending only on each agent's weighting scalar and sampling step are derived to guarantee the stability of the closed-loop system. Numerical examples of rendezvous control of multirobot systems illustrate the efficiency of the proposed algorithm.

Distributed Formation Maneuver Control of Multiagent Systems Over Directed Graphs.

To steer a team of multiple mobile agents to desired collective maneuvers so that the geometric pattern, translation, orientation, and scale of formation can be changed continuously, this article studies the formation maneuver control of single-integrator and double-integrator multiagent systems by a leader-follower strategy. Unlike most existing results requiring generic configurations or convex configurations, the proposed control algorithms can be applied to either nongeneric or nonconvex configurations. Distributed control algorithms are designed for the leaders and followers over directed graphs, respectively, where the formation's maneuver parameters, such as geometric pattern, translation, orientation, and scale of formation are decided by the first leader. It is worth noting that the closed-loop tracking errors converge to zero globally. Some numerical simulations are given to illustrate the theoretical results.