Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PD^α-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a D^α-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.     

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.     

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.     

Fixed-time composite neural learning control of state-constrained nonlinear uncertain systems

This paper presents a fixed-time composite neural learning control scheme for nonlinear strict-feedback systems subject to unknown dynamics and state constraints. To address the problem of state constraints, a new unified universal barrier Lyapunov function is proposed to convert the constrained system into an unconstrained one. Taking the unconstrained system, a modified fixed-time convergence state predictor is explored, enabling the prediction error for compensating the neural adaptive law to be obtained and improving the learning ability of online neural networks (NNs). Without employing fractional power terms or a complicated switching strategy to build the control law, a new method of constructing a smooth fixed-time dynamic surface control scheme is proposed. This overcomes the potential singularity problem and the explosion of complexity often encountered in fixed-time back-stepping designs. The representative features of our design are threefold. First, it is free of the fractional power terms, yet offers fixed-time convergence. Second, it addresses the state constraint problem without requiring a feasibility check. Third, it constructs a new state-predictor and enhances the approximation accuracy of NNs. The stability of the proposed control scheme is analyzed using the Lyapunov technique. Simulation results are presented to illustrate the effectiveness of the proposed controller.     

Iterative learning control for linear delay systems with deterministic and random impulses

This paper investigates convergence of iterative learning control for linear delay systems with deterministic and random impulses by virtute of the representation of solutions involving a concept of delayed exponential matrix. We address linear delay systems with deterministic impulses by designing a standard P-type learning law via rigorous mathematical analysis. Next, we extend to consider the tracking problem for delay systems with random impulses under randomly varying length circumstances by designing two modified learning laws. We present sufficient conditions for both deterministic and random impulse cases to guarantee the zero-error convergence of tracking error in the sense of Lebesgue-p norm and the expectation of Lebesgue-p norm of stochastic variable, respectively. Finally, numerical examples are given to verify the theoretical results.     

Adaptive iterative learning control for MIMO nonlinear systems performing iteration-varying tasks

The present work aims to develop a novel adaptive iterative learning control(AILC) method for nonlinear multiple input multiple output (MIMO) systems that execute various control missions with iteration-varying magnitude-time scales. In order to reduce the variations of the systems, this work proposes a series of time scaling transformations to normalize the iteration-varying trial lengths. An AILC scheme is then developed for the transformed control systems on a uniform trial length, which is shown to be capable of ensuring the asymptotic convergence of the tracking error. In other words, the proposed AILC algorithm is able to relax the constraint in conventional ILC where the control task must remain the same in the iteration domain. Additionally, the basic assumption in classic ILC that the control system must repeat on a fixed finite period is also removed. The convergence analysis of the AILC is derived rigorously according to the composite energy function (CEF) methodology. It is shown that the newly developed learning control strategy works well for control plants with either time-invariant or time-varying parametric uncertainties. To show the effectiveness of the AILC, three examples are illustrated in the end. Meanwhile, the proposed learning method is also implemented to a traditional X–Y table system.     

Analysis of iterative learning control for one-sided Lipschitz nonlinear singular systems

This paper deals with the problem of iterative learning control for a class of singular systems with one-sided Lipschitz nonlinearity. In order to track the given desired trajectory, a closed-loop D-type learning algorithm is proposed for such nonlinear singular systems. Then the convergence result is derived by utilizing the one-sided Lipschitz and quadratically inner-bounded conditions. In this work, the main contribution is to apply the iterative learning approach to one-sided Lipschitz singular systems, while most researches are focus on the Lipschitz systems. It is shown that the algorithm can guarantee the system output converges to the desired trajectory on the whole time interval. Finally, the effectiveness of the presented algorithm is verified by a numerical example.     

资源投入、学习与中外合资企业控制

针对国内不少企业在与外方合资过程中陷入被动这一现状,本文从资源观角度对中外合资企业内的控制权问题进行了探讨。文章认为,中外合资企业内的控制取决于双方的资源投入特别是关键资源投入状况,并且是一个动态变化的过程,改变初始控制权的动力来源于学习,通过学习与随之而来的创新,合资方可以加强对关键资源的投入与进入权,并朝着有利于自己的方向配置控制权。文章结合达能这一外资饮料巨头在华一系列合资企业的控制权演变过程,从各方的资源投入及学习加以分析,从而对目前合资企业的状况给出解释和相应建议。     

Terminal iterative learning control for discrete-time nonlinear systems based on neural networks

The terminal iterative learning control is designed for nonlinear systems based on neural networks. A terminal output tracking error model is obtained by using a system input and output algebraic function as well as the differential mean value theorem. The radial basis function neural network is utilized to construct the input for the system. The weights are updated by optimizing an objective function and an auxiliary error is introduced to compensate the approximation error from the neural network. Both time-invariant input case and time-varying input case are discussed in the note. Strict convergence analysis of proposed algorithm is proved by the Lyapunov like method. Simulations based on train station control problem and batch reactor are provided to demonstrate the effectiveness of the proposed algorithms.     

私营企业诚信问题博弈分析

由于私营企业自身存在的一些问题以及我国法律法规和制度的不健全,造成我国私营企业诚信缺失问题严重。利用博弈分析方法,概括了私营企业诚信缺失的原因,并提出提高私营企业诚信的相关对策。     

P-type iterative learning control algorithm for a class of linear singular impulsive systems

This paper is focused on the iterative learning control problem for linear singular impulsive systems. For the purpose of tracking the desired output trajectory, a P-type iterative learning control algorithm is investigated for such system. Based on the fundamental property of singular impulsive systems and the restricted equivalent transformation theory of singular systems, the convergence conditions of the tracking errors for the system are obtained in the sense of λ norm. Finally, the validation of the algorithm is confirmed by a numerical example.     

Consensus control via iterative learning for distributed parameter models multi-agent systems with time-delay

Most of the available results of iterative learning control (ILC) are that solve the consensus problem of lumped parameter models multi-agent systems. This paper considers the consensus control problem of distributed parameter models multi-agent systems with time-delay. By using the knowledge between neighboring agents, considering time-delay problem in the multi-agent systems, a distributed P-type iterative learning control protocol is proposed. The consensus error between any two agents in the sense of L² norm can converge to zero after enough iterations based on proposed ILC law. And then we extend these conclusions to Lipschitz nonlinear case. Finally, the simulation result shows the effectiveness of the control method.     

An improved event-triggered control method for fuzzy systems under membership functions online learning

This paper is concerned with the problem of adaptive event-triggered (AET) based optimal fuzzy controller design for nonlinear networked control systems (NCSs) characterized by Takagi–Sugeno (T–S) fuzzy models. An improved AET communication scheme with a memory adaptive rule is proposed to enhance the utilization of the state response vertex data. Different from the existing ET based results, the improved AET scheme can save more communication resources and acquire better system performance. The sufficient criteria of performance analysis and controller design are presented for the closed-loop control system subject to mismatched membership functions (MFs) and AET scheme. And then, a new MFs online learning algorithm on the basis of the gradient descent approach is employed to optimize the MFs of fuzzy controller and obtain optimal fuzzy controller for further improving system performance. Finally, two simulation examples are presented to verify the advantage and effectiveness of the provided controller design technique.     

Consensus control for multi-agent systems with distributed parameter models via iterative learning algorithm

This paper deals with the problem of iterative learning control algorithm for a class of multi-agent systems with distributed parameter models. And the considered distributed parameter models are governed by the parabolic or hyperbolic partial differential equations. Based on the framework of network topologies, a consensus-based iterative learning control protocol is proposed by using the nearest neighbor knowledge. When the iterative learning control law is applied to the systems, the consensus errors between any two agents on L² space are bounded, and furthermore, the consensus errors on L² space can converge to zero as the iteration index tends to infinity in the absence of initial errors. Simulation examples illustrate the effectiveness of the proposed method.     

Q-learning solution for optimal consensus control of discrete-time multiagent systems using reinforcement learning

This paper investigates a Q-learning scheme for the optimal consensus control of discrete-time multiagent systems. The Q-learning algorithm is conducted by reinforcement learning (RL) using system data instead of system dynamics information. In the multiagent systems, the agents are interacted with each other and at least one agent can communicate with the leader directly, which is described by an algebraic graph structure. The objective is to make all the agents achieve synchronization with leader and make the performance indices reach Nash equilibrium. On one hand, the solutions of the optimal consensus control for multiagent systems are acquired by solving the coupled Hamilton–Jacobi–Bellman (HJB) equation. However, it is difficult to get analytical solutions directly of the discrete-time HJB equation. On the other hand, accurate mathematical models of most systems in real world are hard to be obtained. To overcome these difficulties, Q-learning algorithm is developed using system data rather than the accurate system model. We formulate performance index and corresponding Bellman equation of each agent i. Then, the Q-function Bellman equation is acquired on the basis of Q-function. Policy iteration is adopted to calculate the optimal control iteratively, and least square (LS) method is employed to motivate the implementation process. Stability analysis of proposed Q-learning algorithm for multiagent systems by policy iteration is given. Two simulation examples are experimented to verify the effectiveness of the proposed scheme.     

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.     

Composite learning adaptive sliding mode control of fractional-order nonlinear systems with actuator faults

This paper considers the tracking control of fractional-order nonlinear systems (FONSs) in triangular form with actuator faults by means of sliding mode control (SMC) and composite learning SMC (CLSMC). In SMC design, a fractional sliding surface is introduced, and an adaptation law is designed to update the estimation of the mismatched parametric uncertainty in the actuator faults. The proposed SMC can guarantee the convergence of the tracking error where a persistent excitation (PE) condition should be satisfied. To overcome this limitation, by using the online recorded data and the instantaneous data, a prediction error of the parametric uncertainty is defined. Both the tracking error and the prediction error are utilized to generate a composite learning law. A composite learning law is designed by using the prediction error and the tracking error. The proposed CLSMC can guarantee not only the stability of system but also the accurate estimation of the parametric uncertainties in the actuator faults. In CLSMC, only an interval-excitation (IE) condition that is weaker than the PE one should be satisfied. Finally, simulation example is presented to show the control performance of the proposed methods.     

线性时变系统变初始条件变期望轨迹的迭代学习控制

对于非严格重复线性时变连续系统,初始迭代条件和参考轨迹在一定带宽范围内都是迭代变化的.提出一种非严格的迭代学习方法来控制跟踪整流.通过该方法所获得的控制器,能保证闭环系统的所有信号是全局有界的,能够使超出初始时间间隔的输出跟踪误差收敛到一个小的残差集内,该残差集大小取决于输入矩阵的估测误差.尤其是当输入矩阵已知的情况下,能够让超出的初始时间间隔输出跟踪误差趋近于零.     

Vibrational control theory

The theory of vibrational control is developed. The necessary and sufficient conditions for vibrational stabilizability of linear dynamic systems are found. Basic relations of the vibrational control method and the optimal shape of vibrations are determined. Unlike conventional methods, based on feedback or feedforward principles, the method of the paper does not require measurement of the deviations or disturbances.     

A model-free distributed cooperative frequency control strategy for MT-HVDC systems using reinforcement learning method

The performance of the existing frequency control strategies for MT-HVDC systems relies on the accuracy of the mathematical models. However, it is hard to obtain the exact mathematical models of MT-HVDC systems. To deal with this challenge, this paper presents a distributed cooperative frequency control strategy for MT-HVDC systems by using a reinforcement learning method, i.e., value iteration algorithm. Specifically, the proposed control strategy is data driven and hence model free. Besides, the proposed control strategy is distributed in the sense that each AC area only requires the local and neighboring information, rather than the information of all the AC areas. Moreover, the proposed control strategy makes the connected AC areas compensate load disturbances together by sharing their power reserves via HVDC grids, which greatly decreases the operation costs of MT-HVDC systems. The performance of the proposed control strategy is validated by cases study.