Second-order Nonlinear Multi-agent Systems Research Articles

Observer-based time-varying group formation tracking for one-sided Lipschitz nonlinear second-order multi-agent systems

This paper discusses the observer-based time-varying group formation tracking (TVGFT) control problem for one-sided Lipschitz nonlinear second-order multi-agent systems (MASs). The followers in the MASs are divided into multiple groups, where only one follower in each group knows the leaders information, and a control protocol is designed through the interactions among the followers. Based on the one-sided Lipschitz definition and the properties of Laplacian matrices, sufficient conditions are provided to achieve the TVGFT for one-sided Lipschitz nonlinear MASs. By solving the linear matrix inequality (LMI), sufficient criteria for achieving TVGFT can be obtained. Finally, it is demonstrated from simulations that the designed control protocol can achieve TVGFT effectively.

Prescribed-Time Consensus Tracking of Multiagent Systems With Nonlinear Dynamics Satisfying Time-Varying Lipschitz Growth Rates.

Prescribed-time consensus tracking for second-order nonlinear multiagent systems (MASs) with the unknown nonlinear dynamics satisfying a time-varying Lipschitz growth rate is investigated in this article. A time-varying function is introduced as a part of the controller gains, and it plays an important role in overcoming the rapid growth of nonlinear terms and in ensuring that the consensus can be achieved in a preassigned time. An integral sliding-mode control protocol, which forces the system trajectory to move on to the defined sliding manifold at the initial moment, is proposed for solving the prescribed-time consensus tracking problem of leader-following MASs with disturbances. Furthermore, we propose a slightly different control law based on terminal sliding-mode control, and under such a controller, the trajectories of each follower reach the sliding manifold in an arbitrary assigned time T1 , and then in a specified time T2 , the position and velocity tracking errors for all followers converge to 0 at the same time instant. Based on the graph theory, state transformations, and Lyapunov theorem, we prove that the proposed solutions are feasible and, finally, three simulation examples are provided to verify the theoretical results.

Exponential Convergence of Distributed Optimal Coordination for Nonlinear Multiagent Systems Under Directed Graphs

In this article, the distributed optimal coordination problem of second-order uncertain nonlinear multiagent systems, which aims to satisfy a global constrained optimal objective, is formulated and investigated. To solve this problem, a couple of novel proportional–integral (PI)-type control laws are explored. Specifically, a gradient-descent-based PI control law is developed for the weight-balanced graph. Furthermore, by introducing the estimator of the left eigenvector of the Laplacian matrix, the proposed method is extended to the case of an unbalanced graph. Compared with the existing optimal coordination algorithms over nonlinear multiagent systems, our algorithm exhibits the favorable exponential convergence property, albeit employing relaxed balanced/unbalanced directed communication topologies. Two numerical simulations are provided to demonstrate the theoretical results.

Fully Distributed Optimal Consensus for a Class of Second-Order Nonlinear Multiagent Systems With Switching Topologies

This article proposes a novel optimal consensus protocol for a class of leaderless multiagent systems, where each agent is described by a second-order nonlinear system and agents interact with each other on switching networks. Any global information, including the eigenvalues of the Laplacian matrix, is unavailable in the control scheme development. The reference trajectory is designed for each agent, and the corresponding performance function, which reflects the off-track error evolution and control cost, is proposed. The sufficient condition for the synchronization of reference trajectories, which does not rely on the topology dwell time, is established by constructing an appropriate current topology-independent Lyapunov function. Due to the fact that the nonlinear function in the system dynamical equation of each agent is unknown, an equation termed integral reinforcement learning (IRL) equation is provided, and it is strictly proven that the provided IRL equation is equivalent to the given Hamilton–Jacobi–Bellman equation. The model-free optimal feedback control law is then derived based on the IRL technique. In the implementation of the developed control scheme, the neural network approximation tool is adopted, and the scheme is applied to a numerical system to show its effectiveness.

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.

Event-triggered bipartite consensus control algorithm design for nonlinear second-order multi-agent systems

Bipartite consensus of nonlinear second-order multi-agent systems with directed communication topology is investigated in this article. A kind of novel event-triggered control protocol is proposed, which based on relative information sensing. Different from some conventional event-triggered control for second-order multi-agent systems, the event-triggered control in distributed way for second-order multi-agent systems is studied in this article, which imply that the controller of each follower only needs to collect the local information. To eliminate too large control gain, the control gain of control protocol is further designed based on adaptive way. Moreover, these control algorithms prove that Zeno behavior can be avoided. Finally, the performance of the proposed control protocols is presented by virtue of two simulation examples.

Aperiodically intermittent output feedback consensus control for second-order leader-following multi-agent systems based on observer

This study examines the leader-following consensus problem of a class of second-order nonlinear multi-agent systems, where the velocity information is supposed to be unmeasurable. Under the setting, this paper presents a novel aperiodically intermittent output feedback control protocol such that all followers reach consensus with the leader, in which a distributed state observer is built for each follower to observe the velocity state. Based on the Lyapunov stability theory and some matrix analysis techniques, a couple of sufficient conditions for the leader-following consensus of the nonlinear multi-agent system under study are obtained even though the velocity state is unavailable. Finally, the effectiveness of the theoretical results is verified by numerical simulation.

Finite-Time Containment Control for Nonlinear Multi-Agent Systems Based on High Order Sliding Mode

Several finite-time containment control issues under stationary and dynamic leadership are the main emphasis of this thesis, which is concerned with a typical class of second-order nonlinear multi-agent systems susceptible to outside intervention. According to a given network topology, the second-order super-twisting sliding mode control is a technique for distributed control that has been developed. In this paper, we mainly consider the situation that the leader moves at a uniform speed. With the proposed method, the followers update status in real time via communication with each other such that all of them are able to eventually converge to the convex hulls consisting of stationary leaders and dynamic leaders in finite time. It leads to make the followers remain stationary or keep moving within the designed region. Eventually, according to the matrix theory and finite-time stability theorem, the paper proves the stability of the finite-time on the proposed control protocol and validates its effectiveness and correctness through simulation.

Time Cost for Consensus of Stochastic Multiagent Systems With Pinning Control

In this article, the estimation of time cost for stochastic consensus of second-order nonlinear multiagent systems (MASs) is investigated. Compared with previous studies, the effect of noise and nonlinear inherent dynamics of agents are considered. In order to achieve the finite/fixed-time stochastic consensus while minimizing energy consumption, the pinning protocols are designed, which only need to control a small fraction of agents. Sufficient conditions for the stochastic consensus are established by employing the stability theory of stochastic differential equations and the algebra graph theory. Finally, the proposed protocols are verified through numerical simulation on the consensus of unmanned aerial vehicles (UAVs) system.

Consensus Control of Mixed-Order Nonlinear Multiagent Systems: Framework and Case Study.

This article investigates the consensus problem of mixed-order nonlinear multiagent systems (MASs). First, a new research framework of consensus control for MASs with hybrid-order dynamics is established. In this framework, the order of low-order dynamic subsystems is increased to higher-order dynamic subsystems by means of increasing order technology, so that the mixed-order MASs can be changed into the same-order MASs. Thus, the distributed controller of hybrid-order MASs can be designed by using the consensus control method of the same-order MASs. Second, through a case study of a stochastic mixed first- and second-order nonlinear MASs, this article further expounds the design idea of the framework structure and gives the concrete design form of the distributed controller and the stability analysis of the closed-loop system. Finally, simulations are given to verify the effectiveness of the distributed control protocol in this case.

Leader-Following Consensus of Discrete-Time Stochastic Nonlinear Multiagent Systems Under Fixed and Switching Topologies via Impulsive Control

In this article, the leader-following consensus of discrete-time second-order stochastic nonlinear multiagent systems with Markovian switching topology is investigated. Assume that the switching rule between the communication topologies is subject to the average dwell time (ADT) constraint. By taking advantage of the impulsive control strategy, the leader-following consensus issue is transformed into the stability problem of the impulsive error systems. Several sufficient conditions respecting the exponential mean-square stability for impulsive error system under fixed and switching topologies are derived by utilizing the Lyapunov function and the notions of average impulsive interval and ADT. Intriguingly, this article considers that impulsive instant and switching instant are independent of each other. Four potential cases of system evolution under Markovian switching topology are discussed. Finally, simulation results are reported to illustrate the effectiveness of our developed results.

Passivity-Based Output Consensus for Second-Order Nonlinear Multiagent Systems

The output consensus for a second-order nonlinear multiagent system (MAS) with mismatched input and output vectors is investigated by exploiting the output strict passivity (OSP). By resorting to the Lyapunov functional approach and the state feedback control method, an OSP criterion for the MAS is derived. Based on the OSP and the relationship between output consensus and the OSP, a sufficient condition to ensure the output consensus of the MAS is obtained. At last, a numerical simulation is given to substantiate the merits of the obtained theoretical results.

Fully distributed adaptive finite-time consensus over uncertain network topology

ABSTRACT Communication network could suffer uncertainties originating from link faults and network attacks. This situation, in multi-agent systems, can be featured by unknown weights of network topology. To impair the influence of the uncertain topology, typical compensation should be taken into account in distributed protocols to the workability of multi-agent systems. This paper, in the context of uncertain topology, addresses finite-time leader-following consensus for second-order uncertain nonlinear multi-agent systems. In addition to uncertainties in topology, the systems also allow unknown control coefficients, which together with the unknown weights renders the realisation of finite-time leader-following consensus nontrivial. Specifically, a fully distributed protocol based on distributed finite-time observer is designed via integrating the adaptive compensation scheme. Notably, in the designed protocol, dynamic high gains are introduced for the compensations of the network uncertainties and agents uncertainties. It turns out that the designed fully distributed protocol guarantees the global finite-time leader-following consensus. Simulation examples are provided to illustrate the validity of the proposed approach.

Adaptive consensus control of second-order nonlinear multi-agent systems with event-dependent intermittent communications

This article deals with the adaptive consensus control problem for second-order nonlinear multi-agent systems under intermittent communications. The main contribution is that a novel event-dependent intermittent communication scheme is proposed, where the work time and the rest time can be changed according to the current states. This event-dependent intermittent communication is named Sun’s intermittent communication scheme. In this communication scheme, by dividing the nonnegative real region into three subregions, the work time and the rest time are decided by the events, which are produced by the pre-given subregions and a Lyapunov function. Then by developing a distributed adaptive protocol based on state estimates of neighboring agents, the overall consensus is achieved under the event-dependent intermittent communication. Compared with the existing related schemes, the proposed scheme can tolerate a larger intermittent rate. Finally, a simulation example is developed to verify the proposed approach.

Distributed Model-Free Sliding-Mode Predictive Control of Discrete-Time Second-Order Nonlinear Multiagent Systems With Delays.

In this article, the tracking problem of networked discrete-time second-order nonlinear multiagent systems (MASs) is studied. First, for the MASs without communication delay, a novel method, called distributed model-free sliding-mode control algorithm is proposed, which can make the system converge quickly without the accurate model. Furthermore, for the MASs with delay, in order to eliminate the influence of time delay on the system, a distributed model-free sliding-mode predictive control strategy based on time-delay compensation technology is proposed, which can actively compensate for time delay while ensuring system stability and consensus tracking performance requirements. Both the simulation and experiment results reveal the superiority of the proposed methods.

Finite-time and fixed-time sliding mode control for second-order nonlinear multiagent systems with external disturbances

In this paper, the leader-following consensus of second-order nonlinear multiagent systems (SONMASs) with external disturbances is studied. Firstly, based on terminal sliding model control method, a distributed control protocol is proposed over undirected networks, which can not only suppress the external disturbances, but also make the SONMASs achieve consensus in finite time. Secondly, to make the settling time independent of the initial values of systems, we improve the protocol and ensure that the SONMASs can reach the sliding surface and achieve consensus in fixed time if the control parameters satisfy some conditions. Moreover, for general directed networks, we design a new fixed-time control protocol and prove that both the sliding mode surface and consensus for SONMASs can be reached in fixed time. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.

Optimized Leader-Follower Consensus Control Using Reinforcement Learning for a Class of Second-Order Nonlinear Multiagent Systems

In this article, an optimized leader-follower consensus control is proposed for a class of second-order unknown nonlinear dynamical multiagent system. Different with the first-order multiagent consensus, the second-order case needs to achieve the agreement not only on position but also on velocity, therefore this optimized control is more challenging and interesting. To derive the control, reinforcement learning (RL) can be a natural consideration because it can overcome the difficulty of solving the Hamilton–Jacobi–Bellman (HJB) equation. To implement RL, it needs to iterate both adaptive critic and actor networks each other. However, if this optimized control learns RL from most existing optimal methods that derives the critic and actor adaptive laws from the negative gradient of square of the approximating function of the HJB equation, this control algorithm will be very intricate, because the HJB equation correlated to a second-order nonlinear multiagent system will become very complex due to strong state coupling and nonlinearity. In this work, since the two RL adaptive laws are derived via implementing the gradient descent method to a simple positive function, which is obtained on the basis of a partial derivative of the HJB equation, this optimized control is significantly simple. Meanwhile, it not merely can avoid the requirement of known dynamic acknowledge, but also can release the condition of persistent excitation, which is demanded in most RL optimization methods for training the adaptive parameter more sufficiently. Finally, the proposed control is demonstrated by both theory and computer simulation.

Distributed Fuzzy Consensus Control of Uncertain Nonlinear Multiagent Systems With Actuator and Sensor Failures

In this article, an adaptive fuzzy consensus-tracking control scheme is developed for a class of second-order nonlinear multiagent systems with unmodeled dynamics and external disturbance under unknown faults on sensors and actuators. Based on the approximation characteristics of fuzzy logic systems, an adaptive fuzzy estimator is designed to estimate the nonlinear functions, and then a dynamic signal is utilized to deal with the unmodeled dynamics. Meanwhile, by using the backstepping technique and Lyapunov stability theory, a distributed adaptive fuzzy controller is proposed to guarantee that all the consensus-tracking errors between followers and leader converge to an adjustable neighborhood of the origin in the presence of the sensor and actuator failures, unmodeled dynamics, and disturbance. Finally, one demonstrative example of multiple mechanical systems is presented to illustrate the effectiveness of the theoretical results.

Event-triggered finite-time formation control for second-order leader-following multi-agent systems with nonlinear term time delay

ABSTRACT Event-triggered finite-time formation control is considered for second-order leader-following multi-agent systems with nonlinear term time delay in this study. Collision avoidance radius is designed for a class of second-order nonlinear multiagent systems to avoid collisions between agents. Collision avoidance control is realised by detecting the flight radius. Control cost is economised, and communication volume is reduced by controlling key nodes and designing an event-triggered control strategy. The system can realise formation control in finite time by designing an FTC function. Some sufficient conditions for the formation of the second-order multi-agent system in finite time are obtained by using Lyapunov stability theory and analysis. The integral sliding mode control algorithm and finite-time stability theory are used to enhance the robustness of the system, and the upper bound of finite time is given. At the same time, the ability of the designed event-triggered function to avoid Zeno behaviour is proven. Finally, the feasibility of the results is verified through a numerical simulation.

Cooperative output feedback consensus control of second-order nonlinear multi-agent systems under Markovian switching topologies

This paper deals with the leader-following consensus problem for a class of second-order nonlinear multi-agent systems by output feedback. The communication topology is characterized by a Markovian switching graph. Firstly, an input-driven observer is introduced to estimate the consensus error of each follower agent. Then, a cooperative nonlinear control law is constructed using the relative output information between neighboring agents by employing the backstepping methodology, which achieves leader-following consensus in mean square sense. Compared with the existing results, the nonlinear functions are required to satisfy polynomial growth condition rather than globally Lipschitz growth or Lipschitz-like growth condition. A numerical example is given to illustrate the theoretical results.