Practical time‐varying formation tracking for high‐order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

Practical time‐varying formation tracking analysis and design problems for high‐order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time‐varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time‐varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer‐based practical time‐varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well‐informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time‐varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time‐varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed‐loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

Input-constrained optimal output synchronization of heterogeneous multiagent systems via observer-based model-free reinforcement learning

This paper presents a new formulation of input-constrained optimal output synchronization problem and proposes an observer-based distributed optimal control protocol for discrete-time heterogeneous multiagent systems with input constraints via model-free reinforcement learning. First, distributed adaptive observers are designed for all agents to estimate the leader's trajectory without requiring its dynamics knowledge. Subsequently, the optimal control input associated with the optimal value function is derived based on the solution to the tracking Hamilton-Jacobi-Bellman equation, which is always difficult to solve analytically. To this end, motivated by reinforcement learning technique, a model-free Q-learning policy iteration algorithm is proposed, and the actor-critic neural network structure is implemented to iteratively find the optimal tracking control input without knowing system dynamics. Moreover, inputs of all agents are constrained in the permitted bounds by inserting a nonquadratic function into the performance function, where input constraints are encoded into the optimization problem. Finally, a numerical simulation example is provided to illustrate the effectiveness of the proposed theoretical results.     

Adaptive flexible performance function approach for dynamic obstacle avoidance to distributed formation tracking of range-constrained switched nonlinear multiagent systems

Prescribed performance control allows preselected transient and steady-state bounds of formation control performance. However, owing to the predetermined decaying property of performance functions, it is unavailable for the formation tracking problem with dynamic obstacle avoidance. Thus, it is essential to design a flexible performance function to accommodate the increasing formation error during dynamic obstacle avoidance. This article pays attention to the development of an adaptive flexible performance (AFP) function usable for the avoidance of dynamic obstacles with unknown velocities in the distributed formation framework. We develop an AFP-based distributed formation tracker design for range-constrained switched multi-input multi-output nonlinear multiagent systems with asynchronous switching. The AFP functions for ensuring graph connectivity and dynamic obstacle avoidance are derived by designing time-varying variables adjusted by an adaptive relaxation signal. The neural-network-based adaptive distributed formation tracker using the derived performance functions is constructed with the adaptive relaxation signal to ensure the stability of the closed-loop formation system, regardless of asynchronous switching and dynamic obstacles. The effectiveness of the proposed method is shown by simulation results.     

基于自适应分布式滤波观测器的多智能体系统编队控制

本文考虑了全局指令系统输出信息受到信道扰动情况下线性多智能体系统的编队控制问题.首先,基于协作式输出调节理论框架对线性多智能体系统的编队控制问题进行数学建模.其次,针对受到信道扰动的全局指令系统输出信息,提出了一类基于受扰输出的自适应分布式滤波观测器,在降低网络信息交换量的同时消除扰动的影响.最后,设计了输出反馈确定等价控制律,解决了线性多智能体系统的分布式编队控制问题.给出了数值仿真结果检验控制性能.     

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

This paper focuses on the distributed event‐triggered fixed‐time consensus control problem of leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances. Two distributed fixed‐time consensus protocols are proposed based on distributed event‐triggered strategies, which can substantially reduce energy consumption and the frequency of the controller updates. It is proved that under the proposed distributed event‐triggered consensus tracking control strategies, the Zeno behavior is avoided. Compared with the finite‐time consensus tracking, the fixed‐time consensus tracking can be achieved within a settling time regardless of the initial conditions. Finally, 2 examples are performed to validate the effectiveness of the distributed event‐triggered fixed‐time consensus tracking controllers.     

Distributed adaptive control for time-varying formation tracking of a class of networked nonlinear systems

This paper considers the time-varying formation problem of tracking a reference for a class of networked systems consisting of multiple nonlinear subsystems with unknown parameters and non-identical nonlinear dynamics. The communication status among the subsystems is represented by a directed graph. A portion of subsystems have no access to the information of reference. Distributed adaptive controllers are proposed by employing backstepping technique. It is proved that, with the proposed scheme, all the closed-loop signals are globally bounded and all the subsystems can track the reference while building and keeping the prescribed time-varying formation shape. Simulation results are given to illustrate the effectiveness of the proposed scheme.     

Distributed output‐feedback finite‐time tracking control of nonaffine nonlinear leader‐follower multiagent systems

The distributed output‐feedback tracking control for a class of networked multiagents in nonaffine pure‐feedback form is investigated in this article. By introducing a low‐pass filter and some auxiliary variables, we first transform the nonaffine system into the affine form. Then, the finite‐time observer is designed to estimate the states of the newly derived affine system. By applying the fraction dynamic surface control approach and the neural network‐based approximation technique, the distributed output‐feedback control laws are proposed and it is proved that the tracking errors converge to an arbitrarily small bound around zero in finite time. Finally, some simulation examples are provided to confirm the effectiveness of the developed method.     

Event‐triggered tracking control of heterogeneous multiagent systems based on two kinds of observers with asymmetric delay

In this paper, we consider the output tracking problem of a multiagent system with asymmetric delays and a switching topology. The multiagent system contains a leader and some followers, the dynamics of which are heterogeneous, and the output of the leader is available to only a subset of followers. We propose two types of observers to estimate states of the leader and reduce communication cost. For the informed followers that can directly obtain information of the leader, a common observer is given to reduce the complexity of observer design. Meanwhile, for the rest of the followers, a distributed observer with asymmetric communication delays for each follower is designed. The observer error system is transformed into a switched system. Through designing the average dwell‐time switching law and constructing multiple Lyapunov functionals, some sufficient conditions for stability of the observer error system are obtained. Furthermore, a distributed controller for followers based on the relative information is developed to track the output of the leader. Finally, an example is given to validate the effectiveness of the proposed results.     

Event‐triggered output consensus for heterogeneous multiagent systems with fixed and switching directed topologies

This paper studies the event‐triggered output consensus problem of heterogeneous linear multiagent systems characterized via fixed and switching directed graphs. With proper state‐dependent triggering functions, two new event‐triggered output consensus control schemes are proposed for each agent to achieve consensus. Notably, under the proposed control protocols, continuous communication among agents is not required in both controllers updating and triggering threshold detection, which means being completely continuous communication free. The communication instances are reduced significantly, and the periodic or high‐frequency communication is restrained. It is also ensured that events cannot be triggered infinitely in finite time (ie, the Zeno behavior is elegantly avoided). Meanwhile, the simulation examples are given to illustrate the theoretical analysis.     

Adaptive disturbance observer‐based control for stochastic systems with multiple heterogeneous disturbances

Antidisturbance control problem is discussed for stochastic systems with multiple heterogeneous disturbances, which include the white noise and the disturbance with unknown frequencies and amplitudes. An adaptive disturbance observer is designed to estimate the disturbance with unknown frequencies and amplitudes, based on which, an adaptive disturbance observer‐based control scheme is proposed by combining adaptive technique and linear matrix inequality method. It is proved that the closed‐loop system is asymptotically bounded in mean square when multiple heterogeneous disturbances exist simultaneously and that the equilibrium is globally asymptotically stable in probability as additive disturbance disappears. Finally, two simulation examples, including a wind turbine system, are given to show the effectiveness of the proposed scheme.     

Distributed optimal resource allocation of second‐order multiagent systems

In this paper, the resource allocation problems of multiagent systems are investigated. Different from the well‐studied resource allocation problems, the dynamics of agents are taken into account in our problem, which results that the problem could not be solved by most of existing resource allocation algorithms. Here, the agents are in the form of second‐order dynamics, which causes the difficulties in designing and analyzing distributed resource allocation algorithms. Based on gradient descent and state feedback, two distributed resource allocation algorithms are proposed to achieve the optimal allocation, and their convergence are analyzed by constructing suitable Lyapunov functions. One of the two algorithms can ensure that the decisions of all agents asymptotically converge to the exact optimal solution, and the other algorithm achieves the exponential convergence. Finally, numerical examples about the economic dispatch problems of power grids are given to verify the effectiveness of the obtained results.     

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

Decentralized adaptive consensus control for discrete‐time heterogeneous semiparametric multiagent systems

Different from the consensus control of traditional multiagent systems, this paper studies the decentralized adaptive consensus control for discrete‐time heterogeneous hidden leader‐following semiparametric multiagent system, in which the dynamic equation of each agent has both parametric uncertainties and nonparametric uncertainties. In the considered system, there is a hidden leader agent who can receive the reference signal, but it can only affect the states of those agents who are in its neighborhood. For other following agents, they do not know the leader's existence or the reference signal, and they can only receive information from their neighbors. Our goal is to design decentralized adaptive controllers to make sure that all agents can track the reference signal, and the closed‐loop system achieves consensus in the presence of mutual coupling relations. Due to the existence of both parametric and nonparametric uncertainties in the system, we need to estimate them separately. For the parametric part, we propose a novel dead zone with threshold converging to zero to modify the traditional gradient update law, while for the nonparametric part, we introduce an auxiliary variable including both two uncertainties to facilitate the nonparametric uncertainties compensation. Based on the certainty equivalence principle in adaptive control theory, the decentralized adaptive controller is designed for each agent to make sure that all of them can track the reference signal. Finally, under the proposed control protocol, strict mathematical proofs are given by using Lyapunov theory; then, simulation results are provided to demonstrate the effectiveness of proposed decentralized adaptive controllers.     

Distributed control of uncertain multiagent systems for tracking a leader with unknown fractional‐order dynamics

This paper proposes distributed adaptive cooperative control algorithms for second‐order agents to track a leader with unknown dynamics. The models of the followers and the leader are composed of uncertain nonlinear components. The order of the leader's dynamics is unknown and can be fractional. Only the single output information is shared among neighbored agents. To simplify the control design, linearly parameterized neural networks are used to approximate the unknown functions. We first present an adaptive control for leaderless consensus and then extend the method to the tracking problem. Thorough theoretical proofs as well as numerical simulation are included to verify the results. Compared with relevant literature, the new approach applies to a larger variety of systems because (i) knowledge about the structure of leader's model is unnecessary; (ii) the unknown functions in different agents' dynamics can be diverse and arbitrary, in other words, the algorithms apply to heterogeneous agents; (iii) the results can be simply used without parameter calculations.     

Time-varying formation control with attitude synchronization of multiple rigid body systems

In this article, we study the leader-following formation control problem for a group of rigid body systems whose followers' motions are described by dual quaternion equations. A few features are as follows. First, we introduce an exosystem to generate the leader's trajectory as well as the formation configuration, which can produce a large class of time-varying signals so that we can achieve a variety of time-varying formations. Second, to overcome the communication constraint described by a digraph, we extend the distributed observer to estimate not only the desired attitude and angular velocity but also the leader's position and linear velocity. Third, a novel distributed control law is synthesized to furnish a rigorous performance analysis of the closed-loop system. The effectiveness of our design is illustrated by a numerical example.     

Finite time time-varying formation tracking for second-order multiagent systems with prescribed transient performance

This paper studies the finite time output formation tracking for a class of second-order multiagent systems subject to prescribed transient performance. The considered leader–follower time-varying formation tracking is realized under a directed communication topology. First, a performance function is introduced into a time-varying barrier Lyapunov function (TV-BLF) for the purpose of shaping the transient behavior. Then, based on the TV-BLF and adding a power integrator technology, a distributed formation control law is constructed such that all followers can form a predefined formation pattern while tracking the leader in finite time with satisfied transient performance. Moreover, a robust term is designed in the proposed controller to improve the disturbance rejection capability of the formation system. Finally, a simulation example is carried out to verify the effectiveness and superiority of the presented formation control protocol.     

Directed spanning tree–based adaptive protocols for second‐order consensus of multiagent systems

This paper discusses the consensus problem of second‐order multiagent systems with nonlinear dynamics. A directed spanning tree–based adaptive control protocol is developed, which overcomes the drawback that the spectrum of the Laplacian matrix must be known a priori. A scheme for reordering the nodes is proposed. Applying the developed method and the Lyapunov stability theory, some distributed adaptive laws are designed in the directed network. It is found that the consensus can be achieved by randomly choosing a directed spanning tree and using the developed distributed adaptive law. Finally, an example is presented to illustrate the theoretical analysis.     

Distributed adaptive control and stability verification for linear multiagent systems with heterogeneous actuator dynamics and system uncertainties

The contribution of this paper is a control synthesis and stability verification framework for linear time-invariant multiagent systems with heterogeneous actuator dynamics and system uncertainties. In particular, we first propose a distributed adaptive control architecture in a leader-follower setting for this class of high-order multiagent systems. The proposed architecture uses a hedging method, which alters the ideal reference model dynamics of each agent in order to ensure correct adaptation in the presence of heterogeneous actuator dynamics of these agents. We then use Lyapunov stability theory and linear matrix inequalities to analyse the proposed architecture. This analysis reveals a stability condition, where evaluation of this condition with respect to a given graph topology allows stability verification of the controlled multiagent system. From a practical point of view, this condition also shows a fundamental tradeoff between heterogeneous agent actuation capabilities and unknown parameters in agent dynamics. Several illustrative numerical examples are also provided to demonstrate the efficacy of the proposed architecture.