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 specifically, we parameterize nonlinear systems through a generalized kernel representation 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 a bridge (i.e., a bijective mapping) between some supervised and unsupervised learning-based entities. Notably, the designed IFD approaches achieve the same performance with the use of this bridge. In order to have a better understanding of the results obtained, both unsupervised and supervised neural networks are chosen as the learning tools to identify the generalized kernel representations and design the IFD schemes; an invertible neural network is then employed to build the bridge between them. This article is a perspective article, whose contribution lies in proposing and formalizing the fundamental concepts for explainable intelligent learning methods, contributing to system modeling and data-driven IFD designs for nonlinear dynamic systems.
This paper investigates the exponential synchronization of coupled memristor-based chaotic neural networks with both time-varying delays and general activation functions. And here, we adopt nonsmooth ...analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new criteria ensuring exponential synchronization of two memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the new proposed results here are very easy to verify and also complement, extend the earlier publications. Numerical simulations on the chaotic systems are presented to illustrate the effectiveness of the theoretical results.
The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications ...of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.
This paper deals with the problem of global exponential synchronization of a class of memristor-based recurrent neural networks with time-varying delays based on the fuzzy theory and Lyapunov method. ...First, a memristor-based recurrent neural network is designed. Then, considering the state-dependent properties of the memristor, a new fuzzy model employing parallel distributed compensation (PDC) gives a new way to analyze the complicated memristor-based neural networks with only two subsystems. Comparisons between results in this paper and in the previous ones have been made. They show that the results in this paper improve and generalized the results derived in the previous literature. An example is also given to illustrate the effectiveness of the results.
An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies of the problem have become possible, stimulating ...theoretical interest. In generic isolated systems, non-equilibrium dynamics is expected to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete. Some recent studies even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems. Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki. A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages-any eigenstate in the microcanonical energy window will do, because they all give the same result.
Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This article ...focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis and demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3-D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1 g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m <inline-formula> <tex-math notation="LaTeX">\times 7 </tex-math></inline-formula> m and 3-m tall. We also demonstrate the robustness of the controller by attaching a drag plate to the UAV in flight tests and by pulling on the UAV with a rope during hover.
This paper investigates the synchronization problem of coupled switched neural networks (SNNs) with mode-dependent impulsive effects and time delays. The main feature of mode-dependent impulsive ...effects is that impulsive effects can exist not only at the instants coinciding with mode switching but also at the instants when there is no system switching. The impulses considered here include those that suppress synchronization or enhance synchronization. Based on switching analysis techniques and the comparison principle, the exponential synchronization criteria are derived for coupled delayed SNNs with mode-dependent impulsive effects. Finally, simulations are provided to illustrate the effectiveness of the results.
The dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism (NSM) are studied. The mathematical equations governing the nonlinear dynamics of ...the system are derived. The averaging method is used to obtain the frequency response function of the system subject to harmonic excitations. It is found that adding NSM can greatly enlarge the frequency band for effective vibration isolation. Numerical simulations reveal that sub-harmonic resonance may occur even when the excitation frequency is well above the natural frequency of the linearized system. As the effects of sub-harmonic response cannot be reflected by the averaging formulations, numerical integrations are used to obtain the dynamic responses including sub-harmonic and other frequency components. Furthermore, power flow characteristics of this nonlinear isolation system are examined for a better assessment of the isolation performance. The results show that the occurrences of sub-harmonic resonance may considerably increase both the time-averaged input power and the maximum kinetic energy. Compared with linear systems, the power flows of the nonlinear system might be non-unique and sensitive to the initial conditions. Some suggestions on restricting the maximum deflection and suppressing sub-harmonic resonances are provided for effective designs of nonlinear isolation systems.
► A nonlinear isolation system with a negative stiffness mechanism (NSM) is studied. ► Adding NSM extends greatly the frequency range for effective vibration isolation. ► Effects of amplitude/frequency/initial condition/a on power flow are analysed. ► Isolation performance assessed using power flow is better than transmissibility. ► How to suppress sub-harmonic resonances in NSM isolation system is discussed.
PDF
