Second-order Multi-agent Systems Research Articles

Pinning Group Consensus of Multi-agent Systems Under DoS Attacks

In this paper, group consensus is investigated for a class of nonlinear multi-agent systems suffered from the DoS attacks. Firstly, a first-order nonlinear multi-agent system is constructed, which is divided into M subsystems and each subsystem has an unique leader. Then a protocol is proposed and a Lyapunov function candidate is chosen. By means of the stability theory, a sufficient criterion, which involves the duration of DoS attacks, coupling strength and control gain, is obtained for achieving group consensus in first-order system. That is, the nodes in each subsystem can track the leader of that group. Furthermore, the result is extended to nonlinear second-order multi-agent systems and the controller is also improved to obtain sufficient conditions for group consensus. Additionally, the lower bounds of the coupling strength and average interval of DoS attacks can be determined from the obtained sufficient conditions. Finally, several numerical simulations are presented to explain the effectiveness of the proposed controllers and the derived theoretical results.

Fast finite-time formation control with obstacle avoidance of second-order multi-agent systems with input saturation

This paper proposes a leader-follower formation control protocol using fast finite-time (FFT) theory, based on second-order nonlinear multi-agent systems (MASs) with input saturation constraints. The artificial potential field method is addressed to implement the formation control with obstacle avoidance of the MASs. An adaptive FFT strategy is constructed that all the agents follow required formation performance. Neural networks are considered to approximate uncertain functions, which improved convergence and ensuring safety of distributed formation control. Finally, the validity of the theoretical approach is demonstrated by FFT stability theory validated by simulation examples.

Fixed-time cooperative output regulation for second-order nonlinear multiagent systems with an unknown exosystem

This paper investigates the fixed-time cooperative output regulation (FTCOR) problem with unknown exosystem of second-order nonlinear multiagent systems. To solve this problem, it is necessary to ensure that each agent can obtain the reference trajectory originating from an unknown exosystem and reconstruct the solution of the regulator equation containing the exogenous signal and unknown parameter vectors within a fixed time, and the unknown exosystem makes it difficult to solve these two problems with existing tools. By using auxiliary filtering variables, we propose a fixed-time adaptive distributed observer (FTADO) and design a fixed-time distributed internal model (FTDIM) based on this FTADO. These two new tools ensure the solvability of the two problems just mentioned. Then, based on these two tools, we transform the problem into a fixed-time stabilization problem of a so-called augmented system. Through the backstepping technique, we propose a distributed controller that solves this fixed-time stabilization problem while relaxing the assumptions of similar references.

Fast finite-time time-varying formation tracking control of multi-agent systems with external disturbance and region constraints

In this paper, fast finite-time time-varying formation tracking control for second-order multi-agent systems with external disturbance and region constraints is investigated. The ubiquitous control input response delay is considered. A predictor-based state transformation is employed to obtain the ideal equivalent systems without control input response delay. Considering the difficulty of measuring external disturbance, a fast finite-time observer with the sliding mode technique is proposed to estimate the disturbance, which positively compensates the system. By adopting the sliding mode control strategy, a novel fast finite-time formation tracking controller is proposed. Sufficient conditions for the formation tracking control with region constraints are obtained. Numerical simulations are employed to validate the feasibility and effectiveness of the theoretical results.

Finite-time consensus control of second-order multi-agent systems with input saturation constraint

A novel finite-time consensus technique is derived for second-order linear multi-agent systems with input saturation constraints. The hyperbolic tangent–based saturation function is presented for achieving input saturation while reducing the chattering issue of classical saturation functions. The leader-following consensus controller with a single saturation function is constructed to address the issue of saturation level partition between position feedback and velocity feedback. Theoretically, the property of finite-time consensus, bounded input, and smoothness of a closed-form system are proved by the Lyapunov theory in detail. Numerical simulations are conducted to exhibit the effectiveness of the proposed method fully.

Parameter variational based adaptive bipartite formation control of second-order multi-agent systems with antagonistic interactions

This article mainly concentrates on researching the leader-following bipartite formation of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions and time-varying delay. A novel distributed feedback control and impulsive control strategy is proposed for realizing the bipartite formation. By establishing an error system, the bipartite formation issue of the MASs is transformed into the stability issue of the error systems. Sufficient conditions for achieving the bipartite formation of second-order nonlinear MASs are obtained by jointly employing the extended parameters variation formula, the comparison principle and the definition of average impulsive interval. In addition, in order to obtain the optimal control gains and control effects, an adaptive control strategy is taken into account by designing the adaptive updating laws. Ultimately, the effectiveness of the theoretical results is demonstrated by two numerical simulations.

Differentially Private Consensus for Second-Order Multiagent Systems With Quantized Communication.

This article considers the differentially private consensus problem of discrete-time second-order multiagent systems with partially measurable states and limited communication channel capacity, where only the integer-value information of agents can be transmitted. To reduce the potential risk of state information disclosure in digital communication, a differentially private consensus algorithm via dynamic encoding-decoding is proposed for the second-order multiagent system to make agents achieve mean-square consensus by transmitting quantized integer values with privacy protection. To deal with the uncertainty of the quantizer saturation, the statistical analysis is given for the boundedness of the input of quantizers. It is shown that the expectation of the minimum memory capacity of quantizers is 2 bits. Finally, some simulation results are given to visualize our conclusions.

Optimal Formation Control of Second-Order Heterogeneous Multiagent Systems Using Adaptive Predefined-Time Strategy

Optimal Formation Control of Second-Order Heterogeneous Multiagent Systems Using Adaptive Predefined-Time Strategy

Behaviors of matrix-weighted networks with antagonistic interactions

This essay considers the bipartite consensus of matrix-weighted second-order multi-agent systems with structurally unbalanced antagonistic interactions networks. Owing to the influence of matrix-weights, bipartite consensus and cluster bipartite consensus can also be reached, which is different from the existing works on signed networks. With the assistance of Lyapunov stability and matrix-valued Gauge transformation, a condition to achieve bipartite consensus is established. Moreover, a relatively straightforward algebraic graph condition for reaching cluster bipartite consensus is attained. Finally, simulation examples are supplied to illustrate the obtained results.

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

Containment control for second-order multi-agent systems with time-varying delays via variable-augmented-based free-weighting matrices

This paper investigates the containment control problem for multi-agent systems (MASs), where the time-varying communication delays are considered. The aim of this paper is to introduce new methods for the containment control research of MASs with time-varying delays. To obtain better results on maximum admissible upper bounds (MAUBs) of the delays to ensure the containment control, the variable-augmented-based free-weighting matrices (VABFWMs) method is introduced to avoid the higher-order terms of time-varying delays in estimating the derivative of the Lyapunov-Krasovskii functionals (LKFs). So our method no longer requires the quadratic function negative-determination lemma. In addition, by utilizing the proposed method, we design a containment controller to ensure that all followers are included into the convex hull formed by leaders. Finally, a numerical example is presented to illustrate the feasibility and superiority of our method.

Adaptive neural network finite-time prescribed performance consensus control for a class of second-order multi-agent systems

Adaptive neural network finite-time prescribed performance consensus control for a class of second-order multi-agent systems

Finite-Time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems with Non-Strict Feedback Based on a Neural Network Observer

Finite-Time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems with Non-Strict Feedback Based on a Neural Network Observer

Optimal time-invariant distributed formation tracking for second-order multi-agent systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton’s method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

Fixed-time leader–follower consensus for second-order multi-agent systems: Variable exponent sliding mode control approach

This paper investigates the fixed-time leader–follower consensus (LFC) problem of second-order multi-agent systems (MASs) with bounded disturbance under directed interaction topology. First, a sliding mode manifold (SMM) with consensus errors–dependent variable exponential coefficient is given. Then, two sliding mode control (SMC) protocols are proposed. The proposed control protocols can eliminate the singularity, while guaranteeing the fixed-time reachability of the consensus errors to the sliding mode surface (SMS) and the fixed-time convergence of the consensus errors toward the origin along the SMS. Finally, the validity of the obtained methodology is confirmed by two simulation examples.

Practical fixed-time event-triggered output feedback containment control for second-order nonlinear multi-agent systems with switching topologies

This paper studies the fixed-time containment of the second-order nonlinear multi-agent system (MAS) accompanied by switching topologies and event-triggered communication. The agent is subjected to unknown nonlinear dynamics. A fixed-time RBF observer was constructed based on information obtained from neural networks and event-triggered communication. By combining the controller with the identification information from the observer, it is demonstrated that the system can achieve practical fixed-time output feedback containment and exclude Zeno behavior during the control process. The effectiveness of the proposed event-triggered control method for fixed-time output feedback containment control of the second-order nonlinear MAS is verified by simulation examples.

Finite-time guarantee-cost [formula omitted] consensus control of second-order multi-agent systems based on sampled-data event-triggered mechanisms

This study presents a solution to the challenges of tracking consensus and guarantee-cost H∞ control in a specific set of second-order multi-agent systems with external disturbances. A proposed event-triggered control method based on periodic sampling data is presented for second-order multi-agent systems that include external disturbances. In contrast to the real-time monitoring of system state information used in the previous event-triggered mechanism, this approach collects system state information through periodic sampling. This ensures that the interval between two consecutive triggering moments is at least one sampling cycle, thereby preventing the controller from triggering infinitely within a finite time frame. A finite-time controller based on the sampled-data event-triggered mechanism is designed, and sufficient conditions to ensure the finite-time stability of the closed-loop system at a specified attenuation level are established using theoretical methods such as matrix analysis. For the given sampled-data event-triggered control protocol with a finite-time controller, a quadratic guarantee-cost function is introduced, and by designing control inputs and determining the parameters such as the finite-time upper bound T∗ and the H∞ performance index γ , the exact value of the upper bound of the system’s guarantee-cost function under the action of the designed controller is derived. Finally, the feasibility of the proposed control scheme is verified through numerical simulation.

Safe Region Multi-Agent Formation Control With Velocity Tracking

This paper provides a solution to the problem of safe region formation control with reference velocity tracking for a second-order multi-agent system without velocity measurements. Safe region formation control is a control problem where the agents are expected to attain the desired formation while reaching the target region and simultaneously ensuring collision and obstacle avoidance. To tackle this control problem, we break it down into two distinct objectives: safety and region formation control, to provide a completely distributed algorithm. Region formation control is modeled as a high-level abstract objective, whereas safety and actuator saturation are modeled as a low-level objective designed independently, without any knowledge of the former, and being minimally invasive. Our approach incorporates connectivity preservation, actuator saturation, safety considerations, and absence of velocity measurement from other agents with second-order system dynamics which are important constraints in practical applications. Both internal safety for collision avoidance among agents and external safety for avoiding unsafe regions are ensured using exponential control barrier functions. We provide theoretical results for asymptotic convergence and numerical simulation to show the approach’s effectiveness.

Design and comprehensive analysis of improved Proportional-Integral-Retarded protocol for second-order multi-agent systems

BackgroundThe attractive characteristics of an innovative delay-based controller called Proportional-Integral-Retarded (PIR) controller are reported in many fields. However, a detailed investigation of the merits of the PIR controller for multi-agent systems (MASs) is still missing. MethodsTo bridge this gap, we propose an improved PIR protocol for a general class of second-order MASs. This protocol, using multiple intentional delays and heterogeneous gains as tunable parameters, realizes the optimal spectrum assignment of each subsystem in a completely independent way without affecting the stability of other subsystems. We then present a systematic and flexible parameter tuning strategy for the PIR protocol such that the desired exponential decay rate of the consensus system can be achieved. Specifically, this strategy achieves an arbitrary dominant root assignment in the domain of non-negative real numbers and enables enhanced control flexibility by adjusting an additionally introduced free variable in the analytical parameter formulae. To unveil the superiority of our proposed PIR protocol, we develop a comprehensive comparison of the PIR protocol with the Proportional-Integral-Derivative (PID) scheme and the Proportional-Retarded (PR) protocol. Significant findingsThe numerical simulations show that our PIR protocol outperforms the PID scheme regarding the noise attenuation property. Besides, this protocol can attain faster consensus, stronger robustness against parameter uncertainties, and superior disturbance resistance than the PR protocol. Our paper provides a valuable reference for the design of an effective and implementable multi-agent consensus protocol.

Impulsive consensus algorithms for vector second-order Lipschitz nonlinear multi-agent systems using only velocity regulation

The existing impulsive consensus algorithms for second-order Lipschitz nonlinear multi-agent systems require to apply the impulsive control to both position and velocity vectors at the same time. Such a requirement cannot be met in most of the real-world applications. To overcome the limitations of these impulsive algorithms, two kinds of new second-order impulsive consensus algorithms using only velocity regulation are proposed. Through developing a weighted discontinuous Lyapunov function-based approach that is able to leverage the spectral property of Laplacian matrix, impulse-dwell-time-dependent sufficient conditions for solving second-order impulsive consensus are derived in the form of linear matrix inequalities. Further, it is shown that if the impulsively controlled velocity subsystems are globally exponentially stable, the impulsive static consensus algorithm is able to ensure that all agents tend to an agreed position. Based on the consensus conditions, two convex optimization problems are formulated, by which the impulsive gain matrices for ensuring a prescribed exponential convergence rate can be designed. Finally, the effectiveness of the proposed distributed impulsive consensus algorithms is certified through numerical simulations.