High-order Nonlinear Multi-agent Systems Research Articles

Distributed robust event-triggered adaptive control for a class of uncertain nonlinear multi-agent systems with actuator saturation

This paper studies the event-triggered consensus control problem for high-order uncertain nonlinear multi-agent systems with actuator saturation. By using a smooth Lipschitz function to approximate the saturation nonlinearity, an augment system and the Nussbaum function are adopted to deal with the residual terms of saturation nonlinearity based on adaptive backstepping method. Since excessive energy and communication resources will be consumed during the procedure to handle actuator saturation, two event-triggered mechanisms are proposed to save the communication resources and reduce the controllers’ update frequency. Whenever the triggered conditions are satisfied, the control signals transmitted to the actuators are updated and broadcasted to the neighboring area. A ’disturbance-like’ term is integrated so that the event-triggered control problem with actuator saturation can be transformed into a robust problem while the unknown disturbances are tackled by adaptive update laws. Moreover, the requirement for global communication topology known by all the agents is relaxed by introducing new estimators. All the signals in the closed-loop system are uniformly bounded and the consensus tracking errors are exponentially converged to a bounded set. Meanwhile, the Zeno behavior is excluded. Simulation results are employed to validate the advantages of our proposed methods.

Distributed adaptive bipartite consensus tracking of high-order nonstrict-feedback nonlinear multi-agent systems

This paper is concerned with the problem of adaptive bipartite tracking problem for multi-agent systems (MASs) over signed directed graphs with unknown nonlinear functions. Each following agent is modelled by a higher-order nonlinear system in nonstrict-feedback form. The virtual and the actual control items of the considered system are the power functions with positive odd integers rather than linear items. A distributed neural-based adaptive backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by Neural networks. Under the proposed protocol, the bipartite output tracking errors converge to a small neighbourhood of the origin and all the signals of the closed-loop system remain semiglobally uniformly ultimately bounded. Since the considered high-order non-strict feedback nonlinear MASs in our paper include some existing nonlinear MASs as the special case, our result can be extended to control more general nonlinear MASs. Finally, the simulation results illustrate the validity of the proposed schemes by a numerical example and a practical example about a group of forced damped pendulums.

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.

A consensus protocol considering Lipschitz constant and communication topology condition of high-order nonlinear multi-agent systems

A new protocol is proposed for the consensus of multi-agent systems with the properties of high-order and nonlinearity for every single system. It is assumed that the nonlinear function of the sub-agent is restricted by the Lipschitz condition, and in addition, there are two kinds of communication topology structures among the members. The protocol combines the eigenvalues of the Laplace matrix and the Lipschitz constant of the multi-agent system. By reasonably designing the Lyapunov function, the convergence condition of the system is divided into two parts which are connected by an unknown quantity k. Except for quantity k, the connection of other parts of the protocol is loose, which makes the protocol more flexible.

Fixed-time consensus disturbance rejection for high-order nonlinear multi-agent systems with input saturation

This study is devoted to investigating the fixed-time consensus disturbance rejection problem for a class of high-order nonlinear multi-agent systems (MASs) with input saturation. A distributed fixed-time state observer (FTSO) is first proposed to reconstruct the leader’s states for each follower. Based on the estimated values, a fixed-time consensus protocol is designed via backstepping, where a fixed-time disturbance observer (FTDO) is used to provide the robustness against the external disturbances. The violation of the input saturation is prevented by introducing an auxiliary variable and the problem of “explosion of terms” suffered by the conventional backstepping design is also successfully avoided by a fixed-time differentiator. Detailed convergence results are presented by leveraging Lyapunov stability theory. Finally, the effectiveness of the proposed approach is numerically validated through simulation results.

Distributed Optimization of High-Order Nonlinear Systems: Saving Computation and Communication via Prefiltering

This brief investigates a distributed optimization problem for high-order strict-feedback nonlinear multiagent systems. A virtual system is built for each agent using a distributed proportional-integral (PI) optimization algorithm to estimate the global optimal solution online. The estimate is then input into a prefilter to generate an alternative estimate and its high-order derivatives. Based on these signals, a backstepping controller is used to make the actual system track the alternative estimate asymptotically, which thereby realizes exact global consensus optimization. Compared to the existing result, the proposed algorithm is fully distributed under undirected topologies with much weaker assumptions on local and global objective functions, lower computation and communication cost. Exact global optimal consensus can also be reached in the cases with directed topologies and intermittent communications. The effectiveness of the method is verified by simulations.

Event-Triggered Consensus Control for Nonlinear Multiagent Systems With Unmeasured State Variables

This article is concerned with event-triggered consensus control for nonlinear multi-agent systems with unknown nonlinear functions, unmatched disturbances, and unmeasured state variables. A novel distributed control algorithm is designed for high-order nonlinear multi-agent systems by using input-driven filters and defining dynamic feedback systems. In addition, the salient features of the proposed control algorithm are highlighted as follows: 1) our proposed control algorithm employs only local information from itself and its neighboring agents, 2) only a binary signal is transmitted to the actuator during the control process, and 3) the proposed control scheme avoids the use of approximate structures and lacks complex calculations. Finally, the simulation of the inverted pendulum verifies the validity of our theoretical findings.

Dynamic H∞ Consensus of Higher-Order Nonlinear Multi-Agent Systems With General Directed Topology

This paper investigates the leaderless <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem of multi-agent systems with higher-order Lipschitz dynamics and external disturbance. The topology is assumed to be directed. Distributed controllers using only relative outputs information of the adjacent agents are constructed. In order to deal with the non-symmetric property of the associated Laplacian matrix of directed topology, some properties of Laplacian matrix are introduced. By introducing an appropriate state transformation, the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem is converted to a low-dimensional system stability problem which is solved using Lyapunov stability analysis method. The effectiveness of the proposed control design is demonstrated through simulation examples.

Distributed Output Tracking Control of Nonlinear Multi-Agent Systems with Unknown Time-Varying Powers

In this paper, we investigate the distributed output tracking problem for high-order nonlinear multi-agent systems (MASs) with unknown time-varying powers. For one leader case, by using the algebra graph theory and adding a power integrator, the distributed tracking control law is successfully designed to achieve that the tracking errors can be adjusted to be arbitrarily small, while ensuring that all the signals of the closed-loop system are bounded. Then we extend this result to the case of multiple leaders and solve the containment tracking problem, the designed distributed nonlinear controller can guarantee that the followers' outputs of the systems eventually converge to a limit point in the convex hull spanned by the leaders' outputs. Finally, two simulation examples are used to illustrate the effectiveness of the designed schemes.

Event-Triggered/Self-Triggered Leader-Following Control of Stochastic Nonlinear Multiagent Systems Using High-Gain Method.

In this article, the event-triggered and self-triggered leader-following output-feedback control problems are investigated for a class of high-order stochastic nonlinear multiagent systems (MASs) under an undirected graph. First, using the high-gain method, the observer is designed to estimate the unmeasured state variables of the given nonlinear system. Then, by introducing an internal dynamic variable, a distributed Zeno-free dynamic event-triggered controller is constructed. Compared with the static event-triggering results, the interevent time of the proposed dynamic event-triggering mechanism is shown to be prolonged and, thus, the advantages of the event-triggered control approaches can be enhanced. Further, to avoid continuously monitoring the states, a Zeno-free self-triggering mechanism is given. It is shown that the expectations of the output tracking errors converge to an arbitrarily small set if the diffusion terms are different for all agents, and that the expectations of all state tracking errors converge to an arbitrarily small set if the diffusion terms are the same for all agents. Finally, simulation studies are given to illustrate the effectiveness of the proposed methods.

Practical output consensus of nonlinear heterogeneous multi-agent systems with limited data rate

This paper investigates the consensus problem for nonlinear heterogeneous multi-agent systems with limited communication data rate. Each agent is modeled by a higher-order strict-feedback continuous-time system with unknown nonlinearities and external disturbance, and only the first state variable being measurable. Extended state observers (ESOs) are used to estimate the unmeasurable agent states and the unknown nonlinear dynamics. An ESO-based distributed output feedback protocol with dynamic encoding and decoding is then presented. It is shown that, for a connected undirected network, the proposed protocol guarantees practical output consensus, in which the steady-state consensus error can be made arbitrarily small. The ESO-based protocol also shapes the transient consensus performance, as it is capable of recovering the consensus performance of a linear counterpart with fully measurable states. Furthermore, we prove that for higher-order uncertain nonlinear multi-agent systems, consensus can be achieved with merely one bit information exchange between each pair of adjacent agents at each time step. Finally, simulations on third-order pendulum systems are given, which verify the theoretical results.

A Separation-Based Methodology to Consensus Tracking of Switched High-Order Nonlinear Multiagent Systems.

This work investigates a reduced-complexity adaptive methodology to consensus tracking for a team of uncertain high-order nonlinear systems with switched (possibly asynchronous) dynamics. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping methods successfully developed for low-order systems fail to work. Even the adding-one-power-integrator methodology, well explored for the single-agent high-order case, presents some complexity issues and is unsuited for distributed control. At the core of the proposed distributed methodology is a newly proposed definition for separable functions: this definition allows the formulation of a separation-based lemma to handle the high-order terms with reduced complexity in the control design. Complexity is reduced in a twofold sense: the control gain of each virtual control law does not have to be incorporated in the next virtual control law iteratively, thus leading to a simpler expression of the control laws; the power of the virtual and actual control laws increases only proportionally (rather than exponentially) with the order of the systems, dramatically reducing high-gain issues.

Fully Distributed Scaled Consensus Tracking of High-Order Multiagent Systems With Time Delays and Disturbances

This article focuses on scaled consensus tracking for a class of high-order nonlinear multiagent systems. Different from the existing results, for high-order nonlinear multiagent systems with time delays and external disturbances, a fully distributed consensus protocol is designed to drive all agents to achieve scaled consensus with preassigned ratios. The control gains are varying and updated by distributed adaptive laws. As a result, the presented protocol is independent of any global information, and thus, could be implemented in a fully distributed manner. Simultaneously, the fully distributed control protocol using an adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -modification technique is presented to deal with external disturbances, which can guarantee the tracking errors and coupling weights of all following agents are uniformly ultimately bounded. To tackle with the derivatives of the functionals with time delays, the Lyapunov–Krasovskii functional is employed to analyze and compensate them by introducing multiintegral terms. Finally, simulation examples are included to verify the effectiveness of the theoretical results.

Asymptotic Synchronization Control of High-order Nonlinear Multiagent Systems Using Barrier Functions

This paper studies the adaptive control problem for unknown time-varying high-order nonlinear multiagent systems (MASs) with directed topology. A novel low-complexity distributed adaptive backstepping controller is developed to achieve the asymptotic synchronization. The designed controller regards the unknown system non-linearities as “disturbance-like” terms, which are guaranteed to be bounded by using the barrier functions, such that detail models of system nonlinearities are released. Then, the “disturbance-like” terms are compensated adaptively by designing the novel compensator at each step, such that the synchronization error is eliminated to zero eventually for each agent. In addition, unlike the existing backstepping-like synchronization approaches for high-order nonlinear MASs, the “explosion of complexity” issue is avoided without extra low-pass filters. Some simulations are shown to demonstrate the effectiveness and advantages of the developed method.

Adaptive Consensus Control of High-Order Uncertain Nonlinear Multi-agent Systems with Fuzzy Dead-Zone

This paper considers the distributed consensus control of nth-order uncertain nonlinear multi-agent systems (MASs) with fuzzy dead-zone (DZ). Unlike the existing works which describes the DZ constraint by the conventional deterministic models, this work describes the DZ by the fuzzy and uncertain value. Therefore, some imposed restricting assumptions on the DZ parameters such as known bounds of the DZ slopes, or linear and deterministic model for DZ description which exist in the previous works are removed in this work. In the proposed scheme, the neural network (NN) is invoked to model the uncertain nonlinearities of the follower agents and uncertain interaction of their neighbors. To decrease the number of adaptive parameters and computational load, maximum norm of the weight coefficients of the NN is considered as an adjustable parameter and tuned online. Also, to decrease the controller complexity and eliminate the repeated derivatives of nonlinear functions in the controller, the dynamic surface control (DSC) method is used to develop the proposed distributed consensus scheme. Stability analysis based on the Lyapunov direct method guarantees that all of the signals in the closed-loop MAS are semi-globally uniformly ultimately bounded and the consensus error converges to a bound dependent on the design parameters. Therefore, appropriate choice of the design parameters makes the bound small. Simulation results on a well-known example demonstrate the effectiveness of the developed consensus algorithm.

Distributed Adaptive Consensus Tracking Control for Multi-Agent System With Communication Constraints

Aiming at a class of high-order strict feedback nonlinear multi-agent systems with communication constraints, a novel distributed adaptive back-stepping control method is proposed to cooperatively track the moving targets. First, five agents are used as controlled objects, and all five agents form a “leader-follower” mode with a distributed control structure. Meanwhile, the leader's moving velocity is considered the forward velocity of the whole formation system, and remaining agents follow the leader's movement. Then, each agent tracks the desired formation with a time-varying reference trajectory, thereby achieving the consensus tracking purpose of multi-agent system. Moreover, the multi-agent formation system avoids obstacles with the optimal trajectory and maintains the desired formation movement. Finally, the simulation results show that the designed controller can achieve the lateral and horizontal tracking errors of the multi-agent system to converge quickly, and then keep the system asymptotically stable during tracking process.

Neuro-adaptive cooperative control for high-order nonlinear multi-agent systems with uncertainties

Neuro-adaptive cooperative control for high-order nonlinear multi-agent systems with uncertainties

Predefined-Time Adaptive Neural-Network-Based Consensus Tracking Control for Nonlinear Multiagent Systems With Zero Tracking Error

This paper is dedicated to addressing the predefined-time consensus tracking control problem for unknown high-order nonlinear multiagent systems. The prominent difference compared with some existing papers is that the follower is modeled in the form of non-strict-feedback structure. Meanwhile, instead of being constants, the real control gains are unknown functions. A distinct advantage in our work is that the outputs of followers are able to track the output of leader within the time specified in advance. In order to get our desired predefined-time controller, radial basis function (RBF) neural networks (NNS) are applied to compensate those unknown nonlinearities. Then in the design framework of adaptive backstepping, the predefined-time virtual control laws are presented and their derivatives are approximated by using finite-time differentiators. Under our proposed predefined-time controller, it is rigorously demonstrated that the whole closed-loop system remains stable and all outputs of the followers track the reference signal in predefined time. In the end, a simulation example is given to ulteriorly verify the efficacy of the suggested predefined-time control scheme.

Distributed adaptive consensus tracking control for non‐linear multi‐agent systems with time‐varying delays

In this study, a novel distributed adaptive controller is provided for consensus control of high-order non-linear multi-agent systems with unknown time-varying delays. The system is subject to uncertain disturbances, and the agents' dynamics are not known. Unlike the existing literature, the proposed method does not require time-delay terms in system dynamics to be bounded. A neural network is used to model the unknown non-linear dynamics. Then, despite the destabilising effect of the unknown delays, some adaptive rules based on the dynamic surface control are designed to achieve the consensus objective. The semi-global uniform boundedness of the resultant closed-loop signals and the convergence of the tracking errors to a neighbourhood of the origin are shown mathematically. Simulations verify the effectiveness of the results.

Distributed Adaptive Output Feedback Leader-Following Consensus Control for Nonlinear Multiagent Systems

This paper investigates the problem of the distributed adaptive output feedback leader-following consensus control for a class of high-order nonlinear multiagent systems with unknown parameters and nonlinear terms. First, the reduced order dynamic gain k-filters are built to estimate the unmeasured state variables. The bounds of the unknown parameters are estimated in order to avoid the over-estimation problem. Then, the dynamic surface control technique is used to design the distributed controller, and the computation load of the system is greatly reduced. Finally, a numerical example is shown to verify the effectiveness of the designed controller.