Second-order Agents Research Articles

Scaled consensus of heterogeneous multi-agent systems under asynchronous DoS attacks

This paper addresses the issue of scaled consensus in heterogeneous multi-agent systems (HMASs) under asynchronous Denial-of-Service (DoS) attacks. In the system structure, our exploration centers on the challenge of achieving scaled consensus in HMASs. The aim is to guarantee that the states of both first-order and second-order agents within the system reach predetermined scalar values, aligning with diverse real-world scenarios. Subsequently, the security of the system in directed communication topology under asynchronous DoS attack is also taken into account. To achieve above research objectives, an impulsive control scheme based on topology switching is proposed and a corresponding algorithm for determining the pulse moments based on the Floyd algorithm is devised. This scheme utilizes the topology switching caused by asynchronous DoS attacks as the driving force for impulsive control. Furthermore, leveraging the correlation property of random matrices, we derive the sufficient conditions for the system to achieve secure control. Finally, a numerical simulation is provided to validate the effectiveness of the protocol and the accuracy of conclusions.

Distributed Strategies for Constrained Nonsmooth Resource Allocation Problems With Autonomous Second-Order Agents

Distributed Strategies for Constrained Nonsmooth Resource Allocation Problems With Autonomous Second-Order Agents

Couple-group consensus of heterogeneous nonlinear multi-agent systems with cooperative–competitive interactions and input saturation

Couple-group consensus of multi-agent systems with cooperative–competitive interactions and input saturation is studied under fixed and switching topologies based on pinning control and event-triggered control. First, for heterogeneous multi-agent systems consisting of first- and second-order agents, we propose two new distributed event-triggered control protocols, and the control protocols both enable the groups of agents to achieve the desired consensus state, which can effectively reduce the number of controller updates and save communication resources. Second, based on the Lyapunov stability theory, the sufficient conditions are established for the couple-group consensus of multi-agent systems. Meanwhile, Zeno behavior is excluded. Third, the effectiveness and feasibility of the control methods proposed in this paper are verified via some simulation examples.

$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control

<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.</p></abstract>

Robust Adaptive Leader-Following Formation Control of Nonlinear Multiagents Using Three-Layer Neural Networks.

This article studies a formation control problem for a group of heterogeneous, nonlinear, uncertain, input-affine, second-order agents modeled by a directed graph. A tunable neural network (NN) is presented, with three layers (input, two hidden, and output) that can approximate an unknown nonlinearity. Unlike one- or two-layer NNs, this design has the advantage of being able to set the number of neurons in each layer ahead of time rather than relying on trial and error. The NN weights tuning law is rigorously derived using the Lyapunov theory. The formation control problem is tackled using a robust integral of the sign of the error feedback and NNs-based control. The robust integral of the sign of the error feedback compensates for the unknown dynamics of the leader and disturbances in the agent errors, while the NN-based controller accounts for the unknown nonlinearity in the multiagent system. The stability and semi-global asymptotic tracking of the results are proven using the Lyapunov stability theory. The study compares its results with two others to assess the effectiveness and efficiency of the proposed method.

Comparison of Formation Algorithms with Collision Avoidance for Second-Order Agents

This work compares two novel strategies that address formation control with collision avoidance for a group of second-order agents. The first control strategy is based on the Backstepping approach (B), while the second is based on the Nested Saturation methodology (NS). Both approaches utilize the Repulsive Vector Fields (RVFs) approach for avoiding collisions. Two numerical simulations are carried out to compare the performance of both approaches. For the first numerical simulation, the simplest case of collision avoidance is considered, that is, the interchange of the position of two agents. On the other hand, for the second numerical simulation, the formation with collision avoidance for a group of nine agents is considered.

Saturated formation containment control for a heterogeneous multi-agent system with unknown perturbations

This work addresses formation containment control for a heterogeneous multi-agent system composed of first-order (FO) and second-order (SO) agents that can be either leader or follower agents. It is assumed that unknown but bounded disturbances perturb its dynamical model. An error-based version of a generalized proportional–integral observer (GPIO) is proposed to estimate these perturbations, and saturation functions, based on position measurement and estimated velocity errors, are designed to achieve the control objective. Specifically, it is shown that the leader agents converge to a desired geometric pattern following a desired trajectory simultaneously. Furthermore, the follower agents converge to the convex hull spanned by the leaders. The result applies to a group of robots in which a directed spanning tree gives the communication topology among the leaders with a root in the main leader. At the same time, each follower receives information from at least one leader agent, and the communication is directed. Real-time experiments and a comparison with a robust control technique exhibit the excellent performance of the proposed GPIO and control strategy in achieving formation containment control.

Delayed and Switched Deployment of Second-Order Agents on a Line Segment: Delays and Switches Do Not Matter

The problem of the equidistant deployment of mobile agents on a line segment is studied. It is assumed that agent dynamics are modeled by linear second-order models. Two types of control protocols are studied: with and without relative velocity measurements. For any positive damping coefficient of agents we propose a control protocol that ensures the achievement of the control goal and possesses robustness for any communication delays and any switching topology. The designed multi-agent system behavior is illustrated by numerical simulation. The proofs of the results are based on the theory of positive systems.

Cooperative circumnavigation by multiple second-order agents with prescribed formations

This paper studies the target circumnavigation problem by multiple second-order agents under directed topology. All agents need to surround the target with prescribed formation and circular velocity. Firstly, according to the control objectives, the cooperative circumnavigation problem is converted into the stability problem of the corresponding error system. Then, the error system is divided into two second-order subsystems, and a distributed controller comprised of two parts is delivered. The stability analysis of the whole system is given by the employing cascaded control theory. One key merit of the proposed controller is that the prescribed formation is an extensive case and unlimited, including different tracking radii and angular spacing. Another merit is that the communication topology among agents only needs to have a directed spanning tree. Furthermore, the controller can be implemented by each agent in its local frame so that only local information is utilised without knowing global information. These all extend the scope of practical application, the controller is more universal. Finally, the simulations validate the effectiveness of the proposed controllers.

Finite-time cooperative circumnavigation control of multiple second-order agents with desired formations

This paper investigates the finite-time cooperative circumnavigation control of multiple second-order agents, in which the agents should surround a moving target with desired formation and circular velocity based on local information. Firstly, the controller design is transformed into design control parameters such that the error system, including distance error, speed error and angle error, is finite-time consensus. The error system is viewed as a cascaded system containing two second-order subsystems, and then a distributed finite-time controller composed of two parts is delivered. The finite-time stability of the entire system is given by employing cascaded control theory. One significant advantage of the proposed controller is that it allows the agents to converge to desired trajectory in a finite time instead of asymptotically. Another merit is that the desired formation is an extensive case and unlimited, including different tracking radii and angular spacing. Furthermore, the proposed controller can be implemented by each agent in its local frame, utilizing only local information. These properties significantly extend the application scope of cooperative circumnavigation. Finally, simulations are carried out to validate the effectiveness of the proposed method.

Distributed consensus of heterogeneous switched nonlinear multiagent systems with input quantization and DoS attacks

In this paper, the consensus tracking control problem is investigated for a class of heterogeneous switched nonlinear multiagent systems (MASs) with input quantization under denial-of-service (DoS) attacks, where first-order agents and second-order agents exist simultaneously, and each agent shows the switching characteristic. Due to the prevalence of DoS attacks in communication channels, a DoS attack model is constructed in this study, and the upper bounds on the duration and frequency of DoS attacks are given. Meanwhile, taking the chattering phenomena of control inputs into account, a hysteresis quantizer is introduced to overcome the issue of the undesirable input chattering. Hence, a new anti-attack distributed consensus protocol is developed such that MASs with input quantization can effectively resist the impact of DoS attacks. Based on the Lyapunov stability theory, the boundedness of all signals in the closed-loop system is verified and the consensus target can be achieved. Finally, the effectiveness of the proposed control scheme is demonstrated by two simulation examples.

On fast queue consensus of discrete-time second-order multi-agent networks over directed topologies

Queue consensus, which aims to drive a set of agents to form a prescribed queue while moving with a common reference velocity, has attracted much attention due to its wide applications. This paper investigates the problem of fast queue consensus for a class of directed multi-agent networks with discrete-time second-order agent dynamics. First, a discrete-time consensus-based control protocol is constructed, and the necessary and sufficient condition to achieve queue consensus is presented. Then, the explicit formulas for the control parameters to achieve the fastest convergence are derived. It is found that the convergence rate of the reference velocity dominates the convergence performance of the overall network. To further accelerate the convergence rate, the agents' node memory is introduced to redesign the update rule of the reference velocity. Furthermore, the analytic formulas of the improved optimal convergence rate and control parameters are established. Finally, numerical examples are given to validate the effectiveness of the proposed theoretical results.

Sampling-Position-Based Event-Triggering Consensus of Nonlinear Second-Order Agents

In this brief, we study the consensus seeking problems for second-order nonlinear multi-agent systems with unavailable velocity measurements. An event-triggered control strategy is developed based on causally sampled position data only, which can reduce the controller update frequencies significantly and avoid continuous communications effectively. Some sufficient conditions for achieving consensus are obtained in light of Lyapunov-Krasovskii stability theory and linear matrix inequality technique.

Formation Control for Second-Order Multi-Agent Systems with Collision Avoidance

This paper deals with the formation control problem without collisions for second-order multi-agent systems. We propose a control strategy which consists of a bounded attractive component to ensure convergence to a specific geometrical pattern and a complementary repulsive component to guarantee collision-free rearrangement. For convergence purposes, it is assumed that the communication graph contains at least a directed spanning tree. The avoidance complementary component is formed by applying repulsive vector fields with unstable focus structure. Using the well-known input-to-state stability property a control law for second-order agents is derived in a constructive manner starting from the first-order case. We consider that every agent is able to detect the presence of any other agent in the surrounding area and also can measure and share both position and velocity with his predefined set of neighbours. The resulting control law ensures the convergence to the desired geometrical pattern without collisions during the transient behaviour, as well as bounded velocities and accelerations. Numerical simulations are provided to show the performance and effectiveness of the proposed strategy.

Leader–Follower Formation of Second-Order Agents via Delayed Relative Displacement Feedback

This paper investigates a leader-follower formation of a group of second-order agents, considering an undirected and connected topology. It is assumed that no velocity information is available, and that a uniform delay affects the processing of the displacement information. To address these issues, a delayed relative displacement feedback is introduced. A necessary and sufficient condition for stability is derived in terms of a delay threshold, given that the delay-free controller is stable. Moreover, a stability region in the complex plane for the eigenvalues of the Laplacian interaction matrix is introduced. The results are illustrated through numerical examples.

Prescribed fixed-time consensus control of multiple second-order systems with communication connectivity assurance

The leader-following consensus tracking problem is investigated for multiple second-order agent systems subject to communication range constraints in this paper. First, a novel fixed-time convergent performance function is developed to quantitatively characterize the consensus tracking performance. Then, an auxiliary state variable is defined by integrating the position and velocity consensus tracking errors with the potential function for removing the communication range constraints. Based on this auxiliary state variable, a fixed-time leader-following consensus controller is devised to guarantee the preassigned consensus tracking performance and communication preservation simultaneously. Compared with the existing consensus control methods, the prominent advantage of the proposed one is that the fixed-time convergence rate of the position and velocity tracking errors can be guaranteed without applying discontinuous control techniques. And the communication connectivity among the multiple agents is assured simultaneously via adding a potential function into the auxiliary state. Finally, two groups of illustrative examples are organized to validate the effectiveness of the proposed consensus control method.

Spherical Formation Tracking Control of Nonlinear Second-Order Agents With Adaptive Neural Flow Estimate.

This article addresses the spherical formation tracking control problem of nonlinear second-order vehicles moving in flowfields under both undirected networks and directed, strongly connected networks. Different from the previous adaptive estimate of the time-invariant parameters of flowfields, the flowfields under our consideration are spatial and absolutely unknown dynamics. Adaptive neural networks (ANNs) with the novel cooperative adaptive algorithms are proposed to approximate the flowfield acting on the channel of each vehicle's velocity (i.e., the mismatched flowfield) and the flowfield pushing the acceleration (i.e., the matched flowfield), respectively. For the purpose of avoiding the complex derivation derived from backstepping, the novel first-order filters are generated by dynamic surface based on barrier functions and relative positions of neighbors. The proposed control algorithms and adaptive upgrade law are fully distributed without using any global information of the graph. The uniform boundedness is analyzed in the Lyapunov sense. Simulation results are given to verify the theoretical analysis.

Group consensus of heterogeneous multi-agent systems with packet loss and unknown speed of second-order agents in cooperative–competitive networks

Group consensus of heterogeneous multi-agent systems with packet loss and unknown speed of second-order agents in cooperative–competitive networks

Finite time consensus control for nonlinear heterogeneous multi-agent systems with disturbances

This paper discusses the finite time consensus (FTC) issue of nonlinear heterogeneous multi-agent systems (HMASs) by combining integral sliding-mode control (SMC), event-triggered control (ETC) and pinning control methods. The SMC is constructed separately for first-order and second-order agents to assure that the system is not interfered by the nonlinearities and disturbances when the state trajectory of the system moves on the sliding surface. To stimulate the FTC of system, the novel control protocols and the fully distributed ETCs with adjustable trigger frequency only rely on the local information are designed. Moreover, the Zeno behavior is eliminated and the range of pinning gain of each agent under directed weakly connected topology is determined. Meanwhile, we also give the conditional criteria for the system to achieve FTC. Eventually, the correctness of the obtained conclusion is illustrated by several simulation examples.

Numerically Efficient Agents-to-Group H∞ Analysis

This paper proposes a numerically efficient approach for computing the maximal/minimal impact a subset of agents has on the cooperative system. For instance, if one is able to disturb/bolster several agents so as to maximally disturb/bolster the entire team, which agents to choose and what kind of inputs to apply? We quantify the agents-to-team impacts in terms of H∞ norm whereas output synchronization is taken as the underlying cooperative control scheme. Sufficient conditions on agents’ parameters, synchronization gains and topology are provided such that the associated H∞ norm attains its maximum for constant agents’ disturbances. Linear second-order agent dynamics and weighted undirected topologies are considered. Our analyses also provide directions towards improving graph design and tuning/selecting cooperative control mechanisms. Lastly, numerical examples, some of which include forty thousand agents, are provided.