This paper investigates the formation composition and keeping problem for multi-quadrotor systems under time-varying communication delays. First, a distributed model predictive control (MPC) approach is employed to transform the formation composition and keeping of multi-quadrotor systems into an online rolling optimization issue, accompanied by the event-triggered mechanism to reduce solution frequency and communication load. Second, to address the asynchrony and time-varying communication delays introduced by event-triggered distributed MPC, a set of constraints is designed to restrict deviations between the current predictive state and previously broadcasted states. Consequently, based on the previously predicted states of neighbors, the cooperation of the multi-quadrotor systems is achieved under asynchronous communication and time-varying delays. This approach guarantees robust asymptotic stability and satisfactory formation performance for multi-quadrotor systems under various delay scenarios. Finally, the numerical and software-in-the-loop (SIL) simulations validate the effectiveness of the proposed algorithm of multi-quadrotors under communication delays.

The series includes two parts, articulating the two novel avenues of research on intelligent fault diagnosis (FD) for nonlinear feedback control systems. In Part I of the series, we design a novel FD paradigm by elaborating an invertible neural network (INN) for feedback control systems.

Formation tracking (FT) control aims at handling cooperative tasks in multi-agent systems (MASs) to achieve desired performance. In these tasks, the leader’s input is generally non-zero and  unknown to all followers, i.e., its trajectory can be arbitrary and non-repetitive. In this paper, the additive property of linear systems is exploited to develop a unified framework for FT tasks of MASs, consisting of adaptive observer-based control (AOC) and iterative learning control (ILC). This framework employs an AOC controller to guarantee a fixed-shape formation between the leader and followers during the whole process, which reserves the initial condition for ILC. Also, it employs ILC to improve the FT performance of certain repetitive tasks (followers rotating around the leader) over the trials. This gives rise to a fully distributed algorithm working for a directed communication graph containing a spanning tree without requiring any eigenvalue information from the Laplacian matrix of the graph, which enables its application to MASs with a large number of agents. Comparisons are provided via a numerical simulation to show that the proposed combined AOC-ILC algorithm has less FT error than pure AOC (without ILC), which validates the feasibility and efficacy of this algorithm.

Unsupervised neural networks (NNs) specialize in mining potential patterns from unlabeled data in a self-organizing manner. Recently, they have also been employed as observers for process monitoring using the generated residual signals. However, few studies have explained the model behavior and analyzed the monitoring performance of unsupervised NNs awing to their multilayer nonlinear structure. The interpretability of NN covers the analysis of its working principle to seek better network design and achieve improved performance. Thus, this paper develops explainable residual generators based on unsupervised NNs, which are applicable to deep autoencoder (DAE) and variational autoencoder (VAE). Through Taylor expansion, the residual deviation caused by the fault signal, a.k.a. the fault-affected term, is proven not to disappear in the presence of a non-zero Hessian matrix. Then, the consistency of achieving the optimal monitoring performance and the training loss of NNs is presented. A new indicator function is established based on the sum martingale, a representative of a weakly dependent stochastic process. Freedman’s inequality is first applied to describe the reliability of the learned thresholds during fault evaluation, which requires a smaller sample size for training. Finally, simulations on the continuous stirred tank reactor verify the effectiveness of the proposed methods.

Over the last decade, transfer learning has attracted a great deal of attention as a new learning paradigm, based on which fault diagnosis (FD) approaches have been intensively developed to improve the safety and reliability of modern automation systems. Because of inevitable factors such as the varying work environment, performance degradation of components, and heterogeneity among similar automation systems, the FD method having long-term applicabilities becomes attractive. Motivated by these facts, transfer learning has been an indispensable tool that endows the FD methods with self-learning and adaptive abilities. On the presentation of basic knowledge in this field, a comprehensive review of transfer learning-motivated FD methods, whose two subclasses are developed based on knowledge calibration and knowledge compromise, is carried out in this survey paper. Finally, some open problems, potential research directions, and conclusions are highlighted. Different from the existing reviews of transfer learning, this survey focuses on how to utilize knowledge specifically for the FD tasks, based on which three principles and a new classification strategy of transfer learning-motivated FD techniques are also presented. We hope this work will constitute a timely contribution to transfer learning-motivated techniques regarding the FD topic.

This paper proposes a performance evaluation method for few-shot learning-based system identification. The basic idea behind the proposed approach is to use “probably approximately correct (PAC)” to assess the obtained boundary of identification errors. The study demonstrates effectiveness of the proposed solution when the noise is not white and there are only limited data samples for the identification in practical applications. The contributions of this study include: 1) modeling errors are quantified via the $L_\infty$ norm; 2) the bounded noises are considered; 3) it is shown that both the modeling and prediction errors can be reduced by increasing the size of training data. Rigorous mathematical analysis and a case study demonstrate the effectiveness of the proposed performance evaluation strategy.

The increased complexity and intelligence of automation systems require the development of intelligent fault diagnosis (IFD) methodologies. By relying on the concept of a suspected space, this study develops explainable data-driven IFD approaches for nonlinear dynamic systems. More in detail, we parameterize nonlinear systems through a generalized kernel representation used for system modeling and the associated fault diagnosis. An important result obtained is a unified form of kernel representations, applicable to both unsupervised and supervised learning. More importantly, through a rigorous theoretical analysis we discover the existence of \emph{a bridge} (i.e., a bijective mapping) between some supervised and unsupervised learning-based entities. Notably, the designed IFD approaches achieve the same performance by the use of this bridge. In order to have a better understanding of the results obtained, unsupervised and supervised neural networks are chosen as the learning tools to identify generalized kernel representations and design the IFD schemes; an invertible neural network is then employed to build the bridge between them. This study is a perspective article, whose contribution lies in proposing and detailing the fundamental concepts for explainable intelligent learning methods, contributing to system modeling and data-driven IFD designs for nonlinear dynamic systems.

This paper presents a segmental autoencoder-based fault detection (FD) framework for nonlinear dynamic systems. The basic idea behind the proposed FD scheme is to identify a generalized kernel representation based on the representation knowledge learned from an autoencoder. By using the system data, several cascades, linking nonlinear operators, are employed to obtain a data-based model which describes the nonlinear dynamic behaviors. With the help of the segmental structure of an autoencoder, a residual generator is then constructed. Rigorous mathematical analysis and an application on a continuous stirred tank reactor demonstrate the effectiveness of the proposed FD method.

Unpredicted faults occurring in automation systems deteriorate the performance of soft sensors and may even lead to incorrect results. In order to address the problem, this study develops three novel data-driven approaches for development of soft sensors. The three proposed soft sensors have fault-tolerant abilities. They are respectively called measurement space-aided scheme (MSaS), subspace-aided scheme (SSaS), and improved MSaS (IMSaS). As means to obtain more accurate results of soft sensors in the online phase, 1) MSaS constructs an optimal estimator of faults in the measurement space; 2) SSaS removes the influences caused by unknown sensor faults with the aid of a constructed subspace; 3) IMSaS is an improved version of MSaS, eliminating the influences of the past prediction error that may accumulate and affect the current prediction result. They are the output-driven fault-tolerant soft sensors because their implementations rely on system measurements only. Furthermore, performance analysis is also conducted to investigate the estimation errors. Both the sufficient and necessary conditions for these designs are provided, and illustrations of the effectiveness and feasibility of the three proposed fault-tolerant soft sensors based on two case studies are given.