New distributed adaptive protocols for uncertain nonlinear leader-follower multi-agent systems via a repetitive learning control approach

In this paper, the distributed consensus problem of leader-follower multi-agent systems with unknown time-varying coupling gains and parameter uncertainties are investigated, and the fully distributed protocols with the adaptive updating laws of periodic time-varying parameters are designed by using a repetitive learning control approach. By virtue of algebraic graph theory, Barbalat’s lemma and an appropriate Lyapunov-Krasovskii functional, it is shown that each follower agent can asymptotically track the leader even though the dynamic of the leader is unknown to any of them, i.e., the global asymptotic consensus can be achieved. At last, a simulation example is given to illustrate the feasibility and efficiency of the proposed protocols.     

Adaptive tracking control for nonlinear heterogeneous multi-agent systems with unknown dynamics

This paper is concerned with the tracking control problem for nonlinear heterogeneous multi-agent systems with a static leader, where the leader’s state is only available to a small portion of follower agents. The considered multi-agent system is composed of first- and second-order follower agents with unknown nonlinearities and unknown disturbances, and the communication graph of follower agents is fixed and directed. A robust adaptive neural network controller is designed for each follower agent. By applying the Lyapunov theory with the singular value analysis method, it is shown that all follower agents will synchronize to the leader agent with bounded residual errors. A numerical example is presented to demonstrate the effectiveness of the theoretical findings.     

Behavior learning based distributed tracking control for human-in-the-loop multi-agent systems

In this study, the distributed tracking problem for human-in-the-loop multi-agent systems (HiTL MASs) has been investigated. First, we construct an HiTL MAS model with a non-autonomous leader which can receive the control signal from a human operator and generate the desired trajectory. The human control signal is assumed to be generated by a leader’s state feedback control law with an unknown gain matrix that represents the control behavior of the human operator. Then, we propose a fully distributed adaptive control method that enables all followers to simultaneously track the human-controlled leader and online learn the unknown human operator’s feedback gain matrix. Furthermore, the parameter estimation error is also discussed, and all followers will learn the true value of the human operator’s feedback gain matrix when the state of the leader satisfies the persistent excitation (PE) condition. Moreover, a novel distributed adaptive control law is developed for each follower to remove the PE condition by utilizing the concurrent learning (CL) technique. Finally, simulated examples demonstrating the effectiveness of the proposed methodologies are presented.     

Distributed fuzzy learning sliding mode cooperative control for non-affine nonlinear multi-missile guidance systems via a prescribed performance observer

This paper focuses on the distributed fuzzy learning sliding mode cooperative control issue for non-affine nonlinear multi-missile guidance systems. The dynamics of each follower is non-affine form with unknown lumped factor. To estimate the unknown lumped factor, a generalized fuzzy hyperbolic model (GFHM) based prescribed performance observer (PPO) is proposed. Different from the traditional disturbance observers, a residual set of error transient behavior is incorporated additionally so that the peak phenomenon can be avoided. Meanwhile, an auxiliary system is employed to convert the system of each follower to augmented affine form. Then, a distributed fuzzy learning sliding mode cooperative control approach is designed which consists of two parts. The adaptive sliding mode control (SMC) part is designed to force the states to move along the predefined integral sliding surface. For the equivalent sliding dynamics, the distributed optimal control part with GFHM is developed to minimize the cooperative performance function. Thus, the stability and the optimality of the closed-loop system are guaranteed synchronously. Finally, all signals of closed-loop system are rigorously proved bounded and the multi-missile cooperative guidance scenario is applied to verify the effectiveness of proposed method.     

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

In this paper, the containment control problem of heterogeneous uncertain high-order linear Multi-Agent Systems (MASs) is addressed and solved via a novel fully-Distributed Model Reference Adaptive Control (DMRAC) approach, where each follower computes its adaptive control action on the basis of local measurements, information shared with neighbors (within the communication range) and the matching errors w.r.t. its own reference model, without requiring any previous knowledge of the global directed communication topology structure. The approach inherits the robustness of the direct model reference adaptive control (MRAC) scheme and allows all agents converging towards the convex hull spanned by leaders while fulfilling at the same time local additional performance requirements at single-agent level, such as prescribed settling time, overshoot, etc. The asymptotic stability of the whole closed-loop network is analytically derived by exploiting the Lyapunov theory and the Barbalat lemma, hence proving that each follower converges to the convex hull spanned by the leaders, as well as the boundedness of the adaptive gains. Extensive numerical analysis for heterogeneous MAS composed of stable, unstable and oscillating agent dynamics are presented to validate the theoretical framework and to confirm the effectiveness of the proposed approach.     

Adaptive controller design for spacecraft formation flying using sliding mode controller and neural networks

A spacecraft formation flying controller is designed using a sliding mode control scheme with the adaptive gain and neural networks. Six-degree-of-freedom spacecraft nonlinear dynamic model is considered, and a leader–follower approach is adopted for efficient spacecraft formation flying. Uncertainties and external disturbances have effects on controlling the relative position and attitude of the spacecrafts in the formation. The main benefit of the sliding mode control is the robust stability of the closed-loop system. To improve the performance of the sliding mode control, an adaptive controller based on neural networks is used to compensate for the effects of the modeling error, external disturbance, and nonlinearities. The stability analysis of the closed-loop system is performed using the Lyapunov stability theorem. A spacecraft model with 12 thrusts as actuators is considered for controlling the relative position and attitude of the follower spacecraft. Numerical simulation results are presented to show the effectiveness of the proposed controller.     

Distributed state estimator-based consensus tracking of multi-agent systems with exogenous disturbance

The consensus tacking problem for multi-agent systems with a leader of none control input and unknown control input is studied in this paper. By virtue of the relative state information of neighboring agents, state estimator and disturbance estimator are designed for each follower to estimate the system states and exogenous disturbance, respectively. Meanwhile, a novel control protocol based on two estimators is designed to make tracking error eventually converge to zero. Furthermore, the obtained results are further extended to the leader with unknown control input. A novel state estimator with adaptive time-varying gain is proposed such that consensus tracking condition is independent of the Laplacian matrix with regard to the communication topology. Finally, two examples are presented to verify the feasibility of the proposed control protocol.     

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

To perform repetitive tasks, this paper proposes an adaptive boundary iterative learning control (ILC) scheme for a two-link rigid–flexible manipulator with parametric uncertainties. Using Hamilton?s principle, the coupled ordinary differential equation and partial differential equation (ODE–PDE) dynamic model of the system is established. In order to drive the joints to follow desired trajectory and eliminate deformation of flexible beam simultaneously, boundary control strategy is added based on the conventional joints torque control. The adaptive iterative learning algorithm for boundary control scheme includes a proportional-derivative (PD) feedback structure and an iterative term. This novel controller is designed to deal with the unmodeled dynamics and other unknown external disturbances. Numerical simulations are provided to verify the performance of proposed controller in MATLAB.     

Multi-lagged-input iterative dynamic linearization based data-driven adaptive iterative learning control

This article presents a multi-lagged-input based data-driven adaptive iterative learning control (M-DDAILC) method for nonlinear multiple-input-multiple-output (MIMO) systems by virtue of multi-lagged-input iterative dynamic linearization (IDL). The original nonlinear and non-affine MIMO system is equivalently transformed into a linear input-output incremental counterpart without loss of dynamics. The proposed learning law utilizes the desired trajectory to cancel the influence from iteration-by-iteration variations, as well as additional multi-lagged inputs to improve control performance. The developed iterative estimation law is more effective and also makes estimation of the unknown parameters easier because the dynamics for each parameter to represent are decreased by dividing the system into multiple components in the multi-lagged-input IDL formulation. Moreover, the proposed M-DDAILC does not need an explicit and accurate model. It is proved to be iteratively convergent with rigorous analysis. Both a numerical example and a practical application to a permanent magnet linear motor are provided to verify the validity and applicability of the proposed method.     

Distributed fault-tolerant tracking control for heterogeneous nonlinear multi-agent systems under sampled intermittent communications

This paper studies the distributed fault-tolerant control (FTC) problem for heterogeneous nonlinear multi-agent systems (MASs) under sampled intermittent communications. First, in order to estimate the state of leader under sampled intermittent communications, the distributed intermittent observer for each follower is constructed. By using the tool from switching system theory, the estimation error converges to zero exponentially if the communication rate is larger than a threshold value even under the impact of sampled intermittent communications. Then, by applying model reference adaptive tracking technique, a robust FTC protocol is developed to track the distributed intermittent observer. Two algorithms are presented to choose the feedback gain of the distributed intermittent observer and the tracking feedback gain of the fault-tolerant tracking controller. It is proved that the global consensus tracking error is bounded under the developed distributed control protocol. Finally, an example with the coupled pendulums is provided to verify the efficiency of the designed method.     

Adaptive iterative extended state observer-based data-driven iterative learning model predictive control for semiconductor silicon single crystal batch process

Aiming at the problems of unstable batch control of key crystal quality parameters and susceptibility to batch-to-batch non-repetitive disturbances during repeated operation of single crystal furnaces, this paper proposes a data-driven iterative learning model predictive control method based on an adaptive iterative extended state observer (IESO) for designing melt temperature and crystal diameter learning controllers with disturbance suppression. By applying dynamic linearization techniques and model predictive control strategies along the iterative axis, an ILMPC scheme with disturbance compensation terms using only input and output data of the system is designed. Among them, adaptive IESO is used to estimate the disturbance compensation terms. Then, the theoretical analysis shows that the tracking error of the ILMPC scheme can converge to a bounded range as the number of iterations increases. The experimental results verify the effectiveness of the proposed control method, which not only ensures that the control system has learning ability, but also achieves stable and accurate control of crystal quality parameters.     

Distributed adaptive output-feedback tracking control of non-affine multi-agent systems with prescribed performance

This paper addresses the distributed adaptive output-feedback tracking control problem of uncertain multi-agent systems in non-affine pure-feedback form under a directed communication topology. Since the control input is implicit for each non-affine agent, we introduce an auxiliary first-order dynamics to circumvent the difficulty in control protocol design and avoid the algebraic loop problem in control inputs and the unknown control gain problem. A decentralized input-driven observer is applied to reconstruct state information of each agent, which makes the design and synthesis extremely simplified. Based on the dynamic surface control technique and neural network approximators, a distributed output-feedback control protocol with prescribed tracking performance is derived. Compared with the existing results, the restrictive assumptions on the partial derivative of non-affine functions are removed. Moreover, it is proved that the output tracking errors always stay in a prescribed performance bound. The simulation results are provided to demonstrate the effectiveness of the proposed method.     

Neural network-based adaptive optimal containment control for non-affine nonlinear multi-agent systems within an identifier-actor-critic framework

This paper addresses the adaptive optimal containment control issue for non-affine nonlinear multi-agent systems in the presence of periodic disturbances. To deal with the disturbed internal dynamics, a fourier series expansion-neural networks-based adaptive identifier is designed for each follower, such that the restrictions posed on the system dynamics are released. Then,an adaptive dynamic programming technique is adopted to acquire the optimized virtual and actual controllers under a simplified actor-critic architecture, where the critic aims to appraise control performance and the actor aims to perform control task. Note that the above updating laws are constructed by the negative gradient of a designed function, which is constructed on the basis of the partial derivative of Hamilton-Jacobi-Bellman equation. Finally, simulation results are provided to show the applicability and effectiveness of the containment control scheme.     

Coordination learning control for groups of mobile agents

Repeated practice is one of the most effective methods in improving the performance of coordination control tasks for groups of individuals, such as marching band, soldier (tank or warcraft) formation, and unmanned aerial vehicle flying queue. The key objective of this paper is to give a theoretical explanation for this observed behavior by considering a class of coordination learning problems for groups of mobile agents. To be specific, the agents are considered to preserve the desired relative formations between each other through a learning process, for which iterative rules are applied to construct distributed algorithms based on the relative information between each agent and its neighbors. Convergence results are derived by combining the graph theory based method and the Lyapunov analysis, which can address coordination learning problems for multi-agent systems both with and without a reference as the prior knowledge. In addition, numerical simulation results are provided to demonstrate the coordination learning performance for groups of mobile agents.     

Two-layer distributed hybrid affine formation control of networked Euler–Lagrange systems

This paper tackles a distributed hybrid affine formation control (HAFC) problem for Euler–Lagrange multi-agent systems with modelling uncertainties using full-state feedback in both time-varying and constant formation cases. First, a novel two-layer framework is adopted to define the HAFC problem. Using the property of the affine transformation, we present the sufficient and necessary conditions of achieving the affine localizability. Because only parts of the leaders and followers can access to the desired formation information and states of the dynamic leaders, respectively, we design a distributed finite-time sliding-mode estimator to acquire the desired position, velocity, and acceleration of each agent. In the sequel, combined with the integral barrier Lyapunov functions, we propose a distributed formation control law for each leader in the first layer and a distributed affine formation control protocol for each follower in the second layer respectively with bounded velocities for all agents, meanwhile the adaptive neural networks are applied to compensate the model uncertainties. The uniform ultimate boundedness of all the tracking errors can be guaranteed by Lyapunov stability theory. Finally, corresponding simulations are carried out to verify the theoretical results and demonstrate that with the proposed control approach the agents can accurately and continuously track the given references.     

Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics

This paper investigates adaptive finite-time practical consensus protocols for a class of second-order multiagent systems with a positive odd power, nonsymmetric input dead zone and uncertain dynamics under a directed communication topology. In this study, three major steps are employed to address the existence of the positive odd power, nonsymmetric input dead zone and uncertain dynamics. Overall, based on the technique of adding one power integrator, useful preliminary results are obtained by configuring a suitable fraction power. Furthermore, to circumvent input dead-zone nonlinearity, an adaptive fuzzy logic (FL) method is used to estimate the width of the dead zone. Finally, the difficulty in designing finite-time practical consensus protocols for the multiagent systems with uncertain dynamics is handled by using radial basis function neural networks (RBFNNs) to approximate the related unknown nonlinear functions. Then, given some reasonable assumptions, it is shown that finite-time practical consensus of the second-order multiagent systems is obtained by using the proposed distributed control protocols and adaptive laws. In addition, the proper approach for selecting parameters is provided such that the neighborhood position error and parameter estimate errors for each agent converge to predesigned small regions of the origin in a finite time. The effectiveness of the developed algorithm is finally validated through a numerical simulation.     

Iterative dynamic linearization and identification of a nonlinear learning controller: A data-driven approach

In this article, a nonlinear iterative learning controller (NILC) is developed using an iterative dynamic linearization (IDL) and a parameter iterative learning identification technique. First, the ideal NILC is transformed into a linear parameterized form by using a controller-oriented compact form IDL (controller-CFIDL) technique. Then an iterative learning identification approach is presented for tuning the parameters of the proposed controller using real-time I/O data. For the sake of analysis, a linear data model of the nonlinear plant is obtained by using the system-oriented IDL technology and a corresponding system parameter identification algorithm is developed in iteration domain. The convergence analysis is provided for the dynamically linearized nonlinear and nonaffine discrete-time system. The results are further extended by using a controller-oriented partial form iterative dynamic linearization (controller-PFIDL) method to gain a higher-order NILC utilizing additional control information from previous iterations. Simulations of two examples show the effectiveness of the proposed methods.     

Model free adaptive iterative learning control for a class of nonlinear systems with randomly varying iteration lengths

This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.     

Distributed point-to-point iterative learning control for multi-agent systems with quantization

For multi-agent system (MAS), most of existing iterative learning control (ILC) algorithms consider about the tracking of reference defined over the whole trial interval, while the point-to-point (P2P) task, where the emphasis is placed on the tracking of intermediate time points, has not been explored. Thus, a distributed ILC method is proposed, in which each agent updates the feedforward control input by learning from the experience of itself and its neighbors in previous repeated tasks to achieve the goal of improving performance. In addition, for the sake of reducing the burden of data transmission in MAS, effective data quantization is essential. In this case, the quantitative measurement of the error of the tracking time points is further used in the ILC updating law. In order to accommodate this requirement, a distributed point-to-point iterative learning control (P2PILC) with tracking error quantization for MAS is first proposed in this paper. A necessary and sufficient condition is presented for the asymptotical stability of the proposed algorithm, and simulation results show the effectiveness of it finally.     

Composite cooperative synchronization and decentralized learning of multi-robot manipulators with heterogeneous nonlinear uncertain dynamics

This paper studies the problem of composite synchronization and learning of multiple coordinated robot manipulators subject to heterogeneous nonlinear uncertain dynamics under the leader-follower framework. A new two-layer distributed adaptive learning control scheme is proposed, which consists of the first-layer distributed cooperative estimator and the second-layer decentralized deterministic learning controller. The first layer aims to enable each robotic agent to estimate the leader’s information. The second layer is responsible for not only controlling each individual robotic agent to track over desired reference trajectory, but also accurately identifying/learning each robot’s nonlinear uncertain dynamics. Design and implementation of this two-layer distributed controller can be carried out in a fully-distributed manner, which do not require any global information including global connectivity of the communication network. The Lyapunov method is applied to rigorously analyze stability and parameter convergence of the resulting closed-loop system. Numerical simulations on a team of two-degree-of-freedom robot manipulators have been conducted to demonstrate the effectiveness of the proposed results.