Class Of Nonlinear Multi-agent Systems Research Articles

Adaptive backstepping for distributed optimization

This paper presents an adaptive backstepping approach to distributed optimization for a class of nonlinear multi-agent systems with each agent represented by the parametric strict-feedback form. In particular, this paper does not assume known gradient functions of the local objective functions, and uses the measured gradient values depending on the agents’ real-time outputs instead. A stepwise method is presented to derive novel distributed adaptive optimization algorithms that steer the outputs of all the agents to the optimal solution of the total objective function. First, a novel distributed adaptive optimization algorithm is developed for first-order nonlinear uncertain multi-agent systems, supported by stability analysis and convergence proofs using Lyapunov arguments. Second, by means of Lyapunov arguments in the spirit of backstepping, a distributed adaptive optimization algorithm is presented for high-order strict-feedback systems with parametric uncertainty. Interesting extensions of the main result to practically important classes of systems with unknown virtual control coefficients, output feedback, and relative-measurement feedback are also discussed.

Inverse Optimal Control of a Class of Nonlinear Multi-Agent Systems With Applications to Ship Slew Rate Control

Abstract This paper deals with the inverse optimal leader-following consensus problem of a class of high-order nonlinear multi-agent systems in strict-feedback form under directed communication topology. By employing the backstepping methodology and introducing an integral type Lyapunov function, a nonlinear distributed control law is constructed using the relative information between neighboring agents. The proposed control law solves the inverse optimal leader-following consensus problem under directed communication graph that contains a spanning tree with the root node being the leader agent. A practical example of ship slew rate control system is given to verify the effectiveness of the theoretical results.

Adaptive consensus control for output-constrained nonlinear multi-agent systems with actuator faults

This paper addresses the problem of leader-follower consensus fault-tolerant control for a class of nonlinear multi-agent systems with output constraints. Specifically, a new nonlinear state transformation function is proposed to deal with the asymmetric constraint on output. Moreover, by integrating backstepping and radial basis function neural network approaches, an adaptive consensus control framework is developed with a single parameter estimator, which mitigates the computation of control algorithm in comparison with conventional adaptive approximation based control techniques. Then an adaptive compensation method is proposed to eliminate the effect of actuator failure. Under the proposed control scheme, all the closed-loop signals of the systems are bounded and the consensus tracking error converges to an adjustable small neighborhood of zero. To evaluate the developed control algorithm, a group of four networked two-stage chemical reactors is used to illustrate the effectiveness of the theoretic results obtained.

Predictor-Based Neural Dynamic Surface Control for Bipartite Tracking of a Class of Nonlinear Multiagent Systems.

This article is concerned with bipartite tracking for a class of nonlinear multiagent systems under a signed directed graph, where the followers are with unknown virtual control gains. In the predictor-based neural dynamic surface control (NDSC) framework, a bipartite tracking control strategy is proposed by the introduction of predictors and the minimal number of learning parameters (MNLPs) technology along with the graph theory. Different from the traditional NDSC, the predictor-based NDSC utilizes prediction errors to update the neural network for improving system transient performance. The MNLPs technology is employed to avoid the problem of "explosion of learning parameters". It is proved that all closed-loop signals steered by the proposed control strategy are bounded, and the system achieves bipartite consensus. Simulation results verify the efficiency and effectiveness of the strategy.

Bipartite consensus for a class of nonlinear multi-agent systems under switching topologies: A disturbance observer-based approach

This paper considers the leader-following bipartite consensus for a class of nonlinear multi-agent systems (MASs) subject to exogenous disturbances under directed fixed and switching topologies, respectively. Firstly, two new output feedback control protocols involving signs of link weights are introduced based on relative output measurements of neighboring agents. In order to estimate the disturbances produced by an exogenous system, a disturbance observer-based approach is developed. Then, sufficient conditions for leader-following bipartite consensus with directed fixed topologies are derived. Furthermore, by assuming that each switching topology contains a directed spanning tree, it is proved that the leader-following bipartite consensus can be realized with the designed output feedback control protocol if the dwell time is larger than a non-negative threshold. Finally, numerical simulations inspired by a real-world DC motors are provided to illustrate the effectiveness of the proposed controllers.

Point-to-point consensus tracking control for unknown nonlinear multi-agent systems using data-driven iterative learning

This paper considers the point-to-point consensus tracking control for a class of nonlinear multi-agent systems with completely unknown dynamics, where the consensus is concerned with some given desired points instead of the entire desired trajectory. It is assumed that the multi-agent system executes repetitive coordination tasks in a finite time interval and the iterative learning control is also utilized to design a consensus protocol with learning ability. To deal with the unknown nonlinear agent’s dynamic, the relationship between agent’s output at these given points and agent’s control input is first derived and then a data-based model referring to the agent’s dynamic is established by utilizing the iteration-domain dynamical linearization technique. Then, a data-driven iterative learning protocol is developed by optimizing two performance indexes, which contains a control input updated algorithm, a parameter estimation algorithm and a reset algorithm. The results show that the proposed design can achieve the point-to-point consensus tracking task only by using the I/O data of the agent. Finally, simulation examples are provided to verify the effectiveness of the proposed protocol.

Event‐triggered leader‐following consensus for a class of nonlinear multiagent systems with time‐varying delay

AbstractThis article studies the consensus problem for discrete‐time nonlinear multiagent systems with time delay. Based on an asynchronous event‐triggered mechanism where local information of a communication graph is involved, a distributed consensus protocol is proposed to reduce the network communication congestion for achieving state consensus for multiagent systems with nonlinear perturbations. To avoid complications involving data fusion, this distributed consensus protocol allows every agent to broadcast its state at its own triggering condition instead of using continuous updates and without continuous monitoring of the triggering condition. To save the energy consumption involved in a consensus protocol, the proposed event‐triggering guaranteed cost is investigated in this article for multiagent systems. We select an agent as a leader that is constrained by its neighbors and controlled by the proposed protocol as other agents. It has been theoretically demonstrated that the consensus problem of multiagent systems with nonlinear perturbation and time delays can be achieved if the control gains and the triggering parameters are appropriately selected. Sufficient conditions are given to guarantee that the agents achieve consensus. Moreover, the gain matrix and triggering parameters of the proposed protocol are cast into matrix inequalities conditions. A simulation example is given to illustrate the effectiveness of the theoretical results.

Adaptive consensus control for a class of nonlinear multi-agent systems with unknown time delays and external disturbances

This paper investigates a class of unknown nonlinear multi-agent systems with unknown time delays and external disturbances. The external disturbance considered in this paper is completely unknown, and the accurate mathematical expression cannot be obtained. To eliminate the external disturbance, a disturbance observer is constructed by the Disturbance-Observer-Based-Control (DOBC) method. By utilizing Young’s inequality scaling technique, the problem of time delay is solved. By assuming that the communication graph among the agents is directed and connected, a novel distributed adaptive consensus control protocol is established based on the relative output information to achieve the goal of consensus control. Furthermore, the stability of the multi-agent system is analyzed by selecting an appropriate Lyapunov function; it is certified that with the proposed control protocol, all signals are guaranteed to be globally uniformly bounded, and the considered multi-agent systems can reach consensus even in the presence of time delay and external disturbance. Finally, two simulation examples are given to support the proposed control strategy.

Observer-based event-triggered adaptive containment control for multiagent systems with prescribed performance

This paper focuses on the problem of the event-triggered adaptive containment control for a class of nonlinear multiagent systems (MASs) with prescribed performance and immeasurable states. First, the radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain smooth nonlinear function, and the neural network-based state observer is designed to estimate the unmeasurable state. Besides, to reduce the control resource consumption and get a better balance between the system performance and network constraints, the switching threshold-based event-triggered control strategy is introduced. Based on this, the novel distributed containment controller is designed by utilizing the adaptive backstepping technique and the dynamic surface control (DSC) technique to guarantee that the output of each follower converges to the convex hull formed by multileader. Moreover, the containment errors can be converged to the prescribed boundary and all signals in closed-loop system are semi-global uniformly ultimately bounded (SGUUB) as well. Finally, the simulation examples are carried out to illustrate the efficiency of the proposed controller.

Sampled-based bipartite tracking consensus of nonlinear multiagents subject to input saturation

This paper is concerned with the sampled-data bipartite tracking consensus problem for a class of nonlinear multiagent systems (MASs) with input saturation. Both competitive and cooperative interactions coexist among agents in the concerned network. By resorting to Lyapunov stable theory and linear matrix inequality (LMI) technique, several criteria are obtained to ensure that the considered MASs can achieve the bipartite tracking consensus. Besides, with the help of the decoupled method, the dimensions of LMIs are reduced for mitigation of the computation complexity so that the obtained results can be applied to large-scaled MASs. Furthermore, the controller gain matrix is explicitly expressed in terms of solutions to a set of LMIs. We also provide with an estimate of elliptical attraction domain of bipartite tracking consensus. Finally, numerical simulation is exploited to support our theoretical analysis.

Dynamic event-based finite-horizon [formula omitted] secure consensus control of a class of nonlinear multi-agent systems

In this paper, we investigate the H∞ consensus control issue for nonlinear multi-agent systems (MASs) subject to multiple attacks over a finite time interval. A novel and comprehensive model to characterize the multiple attacks is presented that includes denial-of-service (DoS) attacks, scaling attacks and replay attacks. With the hope of easing the communication burdens, we implement a dynamic event-triggered scheme to schedule the process of data sharing among the individual subsystems, which helps judge if the collected data should be shared to neighboring agents for control input update. The aim of the proposed problem is to develop an output feedback strategy to meet the desired H∞ consensus performance despite the existence of multiple attacks. Some conditions are presented for the solvability of the investigated problem, and the feedback gains are obtained via certain convex optimization algorithms. The proposed theoretical result is finally demonstrated by virtue of two illustrative simulation examples.

Output-feedback distributed consensus for nonlinear multi-agent systems with quantization

In this paper, we investigate the distributed consensus problem for a class of nonlinear multi-agent systems. Firstly, the uniform quantizer with scaling function is considered in the communication channels to reduce the communication burden. Secondly, noting that the state’ information of each agent cannot be directly obtained, we design a suitable observer to rebuild the states of the nonlinear systems with the help of dynamic gain function. Since the information of communication quantization and state observation is coupled to each other, it is necessary to jointly design uniform quantizer with scaling function and the observer. Based on this, a distributed control protocol is proposed, which leads to a distributed asymptotic consensus of overall nonlinear systems with either known or unknown Lipschitz constant through ⌈log2(2R)⌉-bit information exchange between each pair of agents. Finally, to validity the feasibility of the control scheme, a simulation example is provided.

Consensus for clusters of agents with cooperative and antagonistic relationships

In this paper we address the consensus problem in the context of networked agents whose communication graph splits into clusters: interactions between agents in the same cluster are cooperative, while interactions between agents belonging to different clusters are antagonistic. This problem set-up arises in the context of social networks and opinion dynamics, where reaching a consensus means that the opinions of the agents in the same cluster converge to the same decision, that is typically different for the different clusters. Under the assumption that agents belonging to the same cluster have the same amount of trust (/distrust) to be distributed among their cooperators (/adversaries), we propose a modified version of DeGroot’s law. By simply constraining how much agents in each group should be conservative about their own opinions, it is possible to achieve a nontrivial solution by means of a distributed algorithm. The result is then particularized to unweighted complete communication graphs, and subsequently extended to a class of nonlinear multi-agent systems.

Event-triggered surrounding adaptive control of nonlinear multi-agent systems

This paper investigates an event-triggered control method for a class of nonlinear multi-agent systems, in which a group of followers surround a group of leaders. Dynamics of leaders and followers are assumed to be heterogeneous and to have unknown parameters. To deal with this problem, some adaptive laws and also controllers including event-triggered estimator of leaders’ geometric center are proposed. In order to reduce some dispensable data exchange among the follower agents and save the limited communication resources, event-triggered control protocols are used to attain better performance of resources. The proposed control scheme guarantees that all the closed loop signals are globally bounded and surrounding error converges toward a compact set, exponentially. Moreover, Zeno behavior is also excluded under certain conditions. Eventually, numerical simulations are provided to verify theoretical results and demonstrate that the triggering laws cause decrement of the number of controller updates and inter-agent communications.

Fuzzy fault-tolerant containment control for multi-agent systems with unknown nonlinear dynamics

This paper studies the containment control problem for a class of nonlinear multi-agent systems (MASs) with actuator faults (AFs) and external disturbance under switching communication topologies. To address this problem, a new fuzzy fault-tolerant containment control method is developed via utilizing adaptive mechanisms. Furthermore, a sufficient condition is obtained to guarantee the stability of the considered closed-loop system by the dwell time technique combined with Lyapunov stability theory. Unlike the traditional method to estimate the weight matrix, the fuzzy logic system is used to estimate the norm of weight vectors. Thus, the difficulty that the unknown nonlinear function cannot be compensated for when the actuator produces outage or stuck fault is solved. Compared with the existing controllers for nonlinear MASs, the proposed controller is more suitable for the considered problem under the influence of AFs that are detrimental to the operation of each agent system. Besides which, the closed-loop system is proven to be stable by using the developed controller, and all followers converge asymptotically to the convex hull formed by the leaders. Finally, an example based on a reduced-order aircraft model is presented to verify the effectiveness of the designed control scheme.

Fault-Tolerant Fuzzy Formation Control for a Class of Nonlinear Multiagent Systems Under Directed and Switching Topology

The fault-tolerant formation control problem of a class of nonlinear multiagent systems with actuator/sensor faults under directed and switching network topology is addressed in this article. The main contributions are as follows: 1) the developed controller is effective to compensate for actuator/sensor faults and unknown nonlinearity simultaneously and 2) in contrast to the existing fault-tolerant formation control results, the more general directed and switching network topology is considered. In particular, by using a fuzzy logic system to approximate unknown nonlinearity and by introducing fault estimators to estimate actuator/sensor faults, a novel distributed fuzzy formation controller is developed. By virtue of introducing a modification technique in adaptive law, the phenomenon of strictly increase in adaptive law caused by actuator/sensor faults and unknown nonlinearity can be avoided. In addition, the uniformly ultimately bounded of the formation errors can be shown by introducing a novel Lyapunov function and a new analysis method. The efficiency of the developed method can be shown by an illustrative example demonstrates.

Distributed control for output-constrained nonlinear multi-agent systems with completely unknown non-identical control directions

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol.

On designing a distributed event‐triggered output feedback consensus protocol for nonlinear multiagent systems

AbstractIn this article, the leader–follower consensus problem is considered for a class of nonlinear multiagent systems with event‐triggered inputs. A novel time‐varying gain compensator is designed for each follower by only utilizing the output information of the follower and its neighbors. Based on a time‐varying threshold strategy and a directed communication topology, a distributed event‐triggered output feedback controller is designed for each follower. It is proved by the Lyapunov theory that the leader–follower consensus of the multiagent systems is achieved and the Zeno‐behavior is avoided. Compared with the existing results, it is the first time that a time‐varying gain control algorithm is proposed for the multiagent systems subject to event‐triggered inputs. The effectiveness of the proposed consensus protocol is validated by the chemical reactor systems.

State consensus cooperative control for a class of nonlinear multi-agent systems with output constraints via ADP approach

A state consensus cooperative adaptive dynamic programming (ADP) control strategy is proposed for a nonlinear multi-agent system (MAS) with output constraints. On the basis of the transformation function, state models of leader and followers are transformed into affine ones. By using a monotonically increasing mapping function, the state-consensus cooperative control problem for an MAS with output constraints is equivalently transformed into a cooperative approximately optimal control one for an affine MAS. Then, a neural network observer is constructed for estimation of inner states, and, by graph theory and ADP method, the state consensus cooperative ADP control strategy is developed. The proposed strategy guarantees the performance index of the transformed system is approximately optimal. Furthermore, the stability analysis of whole closed-loop system is presented. Through the Lyapunov Theorem, we prove that the states of the MAS achieve consensus and the output signals of the followers satisfy the constraints. Also, all signals of the closed-loop MAS are bounded, and the trajectory of the leader node is cooperative bounded. The theoretical analysis and effectiveness of the strategy are verified by both a physical and a numerical example.

Consensus control for nonlinear multi-agent systems with event-triggered communications

This paper investigates the consensus problems for a class of nonlinear multi-agent systems (MASs) by distributed event-based control protocols. Firstly, we design the static distributed event-triggered control protocols to achieve leader-follower and leaderless consensus problems, respectively, and the systems exclude Zeno behavior under the proposed control schemes. In order to avoid utilizing the global information of the system networks, that is, the minimum eigenvalues of the correlation matrices. Then, the fully distributed event-based control schemes are designed by introducing the time-varying coupling weights to achieve the leader-follower and leaderless consensus problems, respectively. It has been shown that the Zeno behavior is ruled out in the MASs under the fully distributed event-based control protocols. All static and dynamic event-based control schemes are able to be constructed based on the solvability of linear matrix inequalities (LMIs). Finally, the rationality of the theoretical results is illustrated by the example.