Unknown Nonlinear Multi-agent Systems Research Articles

Data-Based Optimal Synchronization Control for Discrete-Time Nonlinear Heterogeneous Multiagent Systems.

This article investigates the optimal synchronization problem for unknown discrete-time nonlinear heterogeneous multiagent systems (MASs). It is very intractable to derive the analytical solutions of coupled Bellman's equations, which are necessary to overcome this problem. We propose a data-based optimal synchronization control strategy based on a hierarchical and distributed optimal control framework composed of a model reference adaptive control (MRAC) layer and a distributed control layer. In the MRAC layer, the similar-offline MRAC algorithm is developed to make subsystems of MASs track their reference models, respectively. Then, the distributed optimal control problem of nonlinear heterogeneous MASs is transformed into that of homogeneous MASs composed of the reference models and the leader. In the distributed control layer, the distributed reference policy iteration algorithm is proposed to derive the solutions of coupled composite nonlinear Bellman's equations, which ensure that the homogeneous MASs reach synchronization with optimum. The suboptimal synchronization control is achieved via optimization further. Convergence analysis of both algorithms is rigorously provided. The simulation results verify the effectiveness of the proposed strategy.

Adaptive Event-Triggered Control for Unknown Second-Order Nonlinear Multiagent Systems

This article investigates adaptive control problems for unknown second-order nonlinear multiagent systems (MASs) via an event-triggered approach. An adaptive event-triggered consensus controller is given to second-order MAS with unknown nonlinear dynamics. We prove that the proposed consensus controller is free from Zeno behavior. Next, an adaptive event-triggered tracking controller is developed for leader-follower MAS with the leader having bounded nonzero control input. Both consensus and tracking controllers are fully distributed, which means that event-triggered controllers only use local cooperative information. Finally, an unknown second-order nonlinear MAS is used to verify the given event-triggered controllers.

Adaptive NN Cooperative Control of Unknown Nonlinear Multiagent Systems With Communication Delays

In this article, we address the distributed adaptive neural network (NN) control problem for approximate state consensus under communication delays. High-order agent models are considered with unknown nonlinearities and unknown, nonidentical control directions. A novel set of variables called proportional and delayed integral (PdI) consensus error variables are introduced that allow us to recast the approximate consensus problem as an approximate regulation problem. Each PdI variable associated with a certain agent uses only delayed measurements of its neighbors' states in accordance to our delayed communication protocol. Radial basis function (RBF) NNs are employed to approximate the unknown nonlinearities and distributed adaptive NN control laws with Nussbaum gains are proposed that ensure approximate consensus by steering all PdI variables to a neighborhood of zero. Simulation results are also presented that verify the validity of our theoretical analysis.

Adaptive fault-tolerant fixed-time tracking consensus control for high-order unknown nonlinear multi-agent systems with performance constraint

This paper investigates fixed-time tracking consensus problem for high-order nonlinear multi-agent systems (MASs) with actuator faults and performance constraint. Different from existing results that focus on first/second/high-order MASs with integral structure, the investigated MASs involve complex nonlinear dynamics with each agent being modeled as high-order non-strict-feedback form. That is, unknown nonlinear function appears in every state component equation of each subsystem, and contains all the states of the corresponding subsystem. Due to the adverse effects from complex nonlinear dynamics, the previous methods may be unavailable, which motivates the work. To address the problems arising from unknown nonlinear dynamics and actuator faults, fuzzy systems and robust technique are employed. Meanwhile, the performance constraints on the tracking errors can be ensured by appropriately utilizing barrier Lyapunov functions and graph theory. Furthermore, power integrator technique incorporated with Lyapunov functions is used to guarantee the property of fixed time convergence. It is shown that, by using the proposed control strategy, despite the presence of high-order complex nonlinear dynamics and actuator faults, the tracking consensus errors can converge into a neighborhood around zero within fixed time. In addition, the tracking consensus performance can be guaranteed during the whole operation, and all the signals in MASs are bounded. Finally, the effectiveness of the proposed control strategy has been proved by rigorous stability analysis and two simulation examples.

Cooperative Adaptive Tracking Control for Unknown Nonlinear Multi-agent Systems with Signal Transmission Faults

In this paper, the cooperative adaptive fault-tolerant tracking control problem of high-order nonlinear multi-agent systems with signal transmission faults is studied. A neural network-based adaptive fault-tolerant control scheme is proposed, which guarantees that all followers asymptotically synchronize to a leader with tracking errors converging to a small neighborhood of the origin in spite of signal transmission faults. Based on algebraic graph theory and Lyapunov theory, the analysis of stability and parameter convergence of the proposed algorithm are conducted. Finally, an example is provided to validate the theoretical results.

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

ABSTRACTThis paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

SummaryThis paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.

Global Fuzzy Adaptive Consensus Control of Unknown Nonlinear Multiagent Systems

This paper investigates the global consensus problems for the first-order and second-order unknown nonlinear multiagent systems (MASs) with uncertain input disturbance. Fuzzy logic systems are applied to solve the global consensus problem for unknown nonlinear MASs. A fully distributed adaptive fuzzy control is designed to enable followers asymptotically to track the leader without using any dynamics of the leader. The global consensus conditions are also derived for the first-order and second-order unknown MASs, which overcomes the drawback of the semiglobal consensus in existing literature. It is worth mentioning that the proposed approach can greatly alleviate the computation burden because it only needs to update a few parameters. An efficient framework is also given to achieve the global formation control of the second-order unknown nonlinear MAS with an undirected connected graph. Finally, four simulated examples are given to illustrate the effectiveness of the proposed control protocols.

Model Free Adaptive Iterative Learning Consensus Tracking Control for a Class of Nonlinear Multiagent Systems

This paper proposes a distributed model free adaptive iterative learning control (MFAILC) method for a class of unknown nonlinear multiagent systems to perform consensus tracking. Here, both fixed and iteration-varying topologies are considered and only a subset of followers can access the desired trajectory in each topology. To design the control protocol, the agent’s dynamic is first transformed into a dynamic linearization model along the iteration axis, and then a distributed MFAILC scheme is constructed to guarantee that all agents can track the desired trajectory. Through rigorous analysis, it is shown that under this novel distributed MFAILC scheme, the tracking errors of all agents are convergent along the iteration axis. The main merit of this design is that consensus tracking task can be achieved only utilizing the input/output data of the multiagent system. Three examples are given to validate the effectiveness of the proposed design.

Finite-time-estimation-based surrounding control for a class of unknown nonlinear multi-agent systems

This paper deals with the surrounding control problem for a class of multi-agent systems. The followers and leaders have nonlinear heterogeneous dynamics, and the dynamics of the leaders are time-varying. In this work, it is supposed that dynamics of each follower consists of unknown parameters. For this reason, an adaptive law is used to adjust unknown parameters and an estimator to estimate the center of the leaders is used. Also, a new estimator is presented to estimate the summation of distances of the leaders from their geometric center. This estimation is used in the surrounding control protocol, especially when a sudden change happens in the movement of any leader. It is proved that the proposed estimator is stable in finite time sense. Some numerical examples to verify the theoretical results are given.

Event-triggered optimal consensus tracking control for multi-agent systems with unknown internal states and disturbances

In this paper, we propose an event-triggered consensus tracking control for unknown nonlinear multi-agent systems (NMASs) with disturbances by using adaptive dynamic programming (ADP) technique. Considering the disturbances as control inputs, the optimal consensus tracking control problem can be transformed into multi-player zero-sum differential games, where the controllers are designed to minimize the cost functions under the worst-case disturbances. To recover the unknown internal states and control coefficient functions, neural network (NN)-based observers are established. Then, NN-based critics are applied to approximate the value functions and help calculate the optimal control policies and disturbance policies. In order to save the computation resource and reduce the transmission load, the designed observers and controllers are updated only when the designed events are triggered. Stability of the proposed method is demonstrated by Lyapunov analysis for both the continuous and jump dynamics. Meanwhile, we can obtain that the weight estimated errors of the observer NNs, the critic NNs and the local neighbor consensus tracking errors are uniformly ultimately bounded (UUB). Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

Model-Free Distributed Consensus Control Based on Actor–Critic Framework for Discrete-Time Nonlinear Multiagent Systems

Conventionally, as the system’s dynamics is known, the optimal consensus control problem relies on solving the coupled Hamilton–Jacobi–Bellman (HJB) equations. In this paper, with the unknown system dynamics being considered, a local ${Q}$ -function-based adaptive dynamic programming method is put forward to deal with the optimal consensus control problem for unknown discrete-time nonlinear multiagent systems by approximating the solutions of the coupled HJB equations. First, a local ${Q}$ -function is defined, which considers the local consensus error and the actions of the agent and its neighbors. Using the ${Q}$ -function, it is convenient to get the derivatives with regard to the weights of the consensus control policies, even without the model of system dynamics. Then, with the defined local ${Q}$ -function, a distributed policy iteration technique is developed, which is theoretically proved to be convergent to the solutions of the coupled HJB equations. An actor–critic neural network framework for implementing the developed model-free optimal consensus control method is constructed to approximate the local ${Q}$ -functions and the control policies. Finally, the feasibility and effectiveness of the developed method are verified by a series of simulations.

Distributed Adaptive Consensus Control and Disturbance Suppression of Unknown Nonlinear Multi-Agent Systems

This paper considers consensus control of unknown nonlinear multi-agent systems with unknown disturbance under undirected networks. The expected output signal of the leader is not available to all subsystems, only some subsystems can obtain it, and other subsystems will obtain the output regulation error through the network connections. The critical contribution of this paper is to develop a new distributed adaptive control protocol and disturbance observer based on relative output information to achieve the consensus control objective of the subsystems. Since only the relative output information is used, the adaptive control protocol we proposed is distributed. Also, a new lemma is proposed for the first time to analyze the stability of the subsystems. Comparing to current results, the challenge exists in this paper is that the external disturbance is unknown and does not have explicit expression. Based on this, designing a disturbance observer based on relative output information to achieve consensus output regulation is the motivation of this paper. Different from the existing disturbance suppression methods, only the relative output information is used for disturbance suppression, and only the part of disturbance that affects the common trajectory will be suppressed. The stability analysis of the systems is carried out by using algebraic graph theory, Lyapunov function, and Barbalat lemma. The outcome of the paper is that all variables of the systems are bounded and the output regulation errors of the subsystems converge to zero asymptotically. Finally, a numerical simulation is given to demonstrate the effectiveness of the proposed method.

Adaptive consensus for high-order unknown nonlinear multi-agent systems with unknown control directions and switching topologies

In this paper, we provide a comprehensive assessment of the consensus of high-order nonlinear multi-agent systems with input saturation and time-varying disturbance under switching topologies. The control directions and model parameters of agents are supposed to be unknown. Our approach is based on transforming the problem of consensus for a network that consists of high-order nonlinear agents to that of perturbed first-order multi-agent systems. The unknown part of dynamics is cancelled using radial basis neural networks. Nussbaum gains and auxiliary systems are respectively employed to overcome the unknown input direction and the saturation. Adaptive sliding mode control is used to compensate for the time-varying disturbance and the imperfect approximation of the developed neural network as well. Through Lyapunov analysis, it is shown that the overall closed-loop system maintains asymptotic stability. Finally, our approach is applied to a group of multiple single-link flexible joint manipulators to highlight better its merit.

Adaptive fixed-time bipartite tracking consensus control for unknown nonlinear multi-agent systems: An information classification mechanism

This paper is concerned with the problem of bipartite tracking consensus for high-order unknown nonlinear multi-agent systems with actuator faults. Unlike the traditional condition that the directed signed graph is structurally balanced, a directed signed graph containing a spanning tree is considered. Besides, the consensus errors are required to satisfy both the prescribed performance and fast convergence (fixed-time). By proposing an information classification mechanism, each agent selectively uses neighbor information such that agents in the system are divided into two styles, which transform the bipartite tracking consensus problem into a general tracking consensus problem. By using neural networks and adaptive technologies to approximate unknown functions, the adaptive fault-tolerant fixed-time consensus controllers are developed. All signals in the system are bounded within a fixed time. Moreover, the bipartite consensus errors satisfy the prescribed performance by selecting appropriately predefined performance functions. Stability analysis and simulation results further verify the effectiveness of the proposed method.

Formation control for a class of nonlinear multiagent systems using model‐free adaptive iterative learning

SummaryIn this paper, the problem of formation control is considered for a class of unknown nonaffine nonlinear multiagent systems under a repeatable operation environment. To achieve the formation objective, the unknown nonlinear agent's dynamic is first transformed into a compact form dynamic linearization model along the iteration axis. Then, a distributed model‐free adaptive iterative learning control scheme is designed to ensure that all agents can keep their desired deviations from the reference trajectory over the whole time interval. The main results are given for the multiagent systems with fixed communication topologies and the extension to the switching topologies case is also discussed. The feature of this design is that formation control can be solved only depending on the input/output data of each agent. An example is given to demonstrate the effectiveness of the proposed method.

Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems

ABSTRACTThis paper is concerned with the design of a distributed cooperative synchronisation controller for a class of higher-order nonlinear multi-agent systems. The objective is to achieve synchronisation and satisfy a predefined time-based performance. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using neural networks. The proposed robust neuro-adaptive controller drives different states of nodes systematically to synchronise with the state of the leader node within the constraints of the prescribed performance. The nodes are connected through a weighted directed graph with a time-invariant topology. Only few nodes have access to the leader. Lyapunov-based stability proofs demonstrate that the multi-agent system is uniformly ultimately bounded stable. Highly nonlinear heterogeneous networked systems with uncertain parameters and external disturbances were used to validate the robustness and performance of the new novel approach. Simulation results considered two different examples: single-input single-output and multi-input multi-output, which demonstrate the effectiveness of the proposed controller.

Decentralized Robust Synchronization of Unknown High Order Nonlinear Multi-Agent Systems With Prescribed Transient and Steady State Performance

In this paper, we consider the synchronization control problem for uncertain high-order nonlinear multi-agent systems in a leader-follower scheme, under a directed communication protocol. A robust decentralized control law of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate synchronization of the following agents with the leader. The control protocol is decentralized in the sense that the control signal of each agent is calculated based solely on local relative state information from its neighborhood set. Additionally, no information regarding the agents' dynamic model is employed in the design procedure. Moreover, provided that the communication graph is connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: 1) the underlying graph topology, 2) the control gains selection, and 3) the agents' model uncertainties, and are solely prescribed by certain designer-specified performance functions. Extensive simulation results clarify and verify the approach.

Neural-network-based distributed adaptive synchronization for nonlinear multi-agent systems in pure-feedback form

In this paper, the problem of distributed adaptive synchronization for unknown nonlinear multi-agent systems in pure-feedback form is studied under a directed graph. Neural networks are used to approximate the unknown nonlinear dynamics, and by incorporating the dynamic surface control (DSC) technique into backstepping design procedure, distributed adaptive consensus controllers are developed. A novel method is given for reducing the burden of networked communication. It is shown that the proposed distributed consensus controllers guarantee that all signals in the closed-loop system are cooperatively semi-globally uniformly ultimately bounded, and the consensus errors converge to a small neighborhood of the origin. Finally, a simulation example is given to show the effectiveness of the designed control scheme.

Distributed containment control for bounded unknown second-order nonlinear multi-agent systems with dynamic leaders

This paper investigates distributed containment control problems for second-order nonlinear multi-agent systems with dynamic leaders. In the presence of bounded unknown nonlinearity, a distributed control algorithm based on High-frequency Feedback Robust Control is proposed. Under this algorithm, a sufficient condition is proposed to ensure that all the followers will converge to the dynamic convex hull formed by dynamic leaders and the containment error can be ultimately bounded for the directed graph where at least one leader has a directed path to each follower and the communication among the followers are undirected. Numerical simulations are also presented to illustrate the effectiveness of the theoretical results.