Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems

The high-speed motorized spindle has been wildly used in the field of aerospace processing, due to its advantages such as high speed, high precision, and high efficiency. CNC machine tools used for processing aerospace products require high machining accuracy, and once the spindle fails, it will seriously affect the quality of product processing. Thus, it is important to study the faults of the spindle, especially the faults caused by subtle errors. In this work, a dynamic model of a spindle with unbalanced mass fault and spindle inclination fault is established, and the natural frequencies and mode shapes of the motorized spindle are calculated by using the whole transfer matrix method (WTMM). The deflections of the spindle initial end in the different situations are discussed when the two faults happen independently. The results show that the spindle end deflection of the same fault has different sensitivity at different speeds. At the third order of natural frequencies, the deflection of a motorized spindle is greatest regardless of the fault that occurs. Although the motorized spindle rotates at the same speed, different faults could cause different mode shapes. At the lower speed, when the unbalanced mass fault happens, the mode shape is in an arched shape, and while the spindle inclination fault happens, the mode shape is in a concave shape. Full article

This paper proposes an event-triggered state estimation method for parameter-uncertain systems with a binary encoding transmission scheme. Firstly, a binary encoding transmission scheme is introduced between the state estimator and the system to improve the efficiency of network communication. Secondly, an event-triggering mechanism (ETM) is designed to ensure the accuracy of state estimation and reduce the computational burden of the state estimator. At the event-triggered moments, considering the uncertainty of the system, the binary encoding transmission scheme, and the ETM, a moving horizon estimator (MHER) is designed using the robust least squares optimization method to obtain optimal state estimation. At the no-event-triggered moments, the state estimation of the system is computed based on an open-loop state estimator (OLER). Furthermore, stability analysis showed that the state estimation error of the proposed method is bounded. Finally, the practical value of the proposed in this paper is confirmed through numerical simulation. Full article

This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations on the basis of the Laplace transform method and convolution theorem, which are solved by applying the successive approximation method in the theory of integral equations. Compared with the results obtained by constructing Lyapunov functions or calculating the conditional Lyapunov exponents, the uncertain parameters and the scaling function factors considered in this paper have fewer restrictions, and the parameter update laws designed for the estimation of the uncertain parameters are simpler and easier to realize physically. Full article

Point absorber wave energy converter (WEC) control strategies often require accurate models for maximum energy extraction. While linear models are suitable for small motions, the focus is on the nonlinear model of an hour-glass shaped buoy undergoing large vertical displacements. Closed-form expressions for the static and dynamic Froude–Krylov forces are developed. It is shown that, in general, the dynamic and static forces are of similar magnitude, which is not the case for a spherical buoy. While the dynamic force reduces the amplitude of the net buoy force, its shape predicts a larger buoy response than if neglected, causing the nonlinear terms to have an even more significant effect. An input-state feedback linearizing controller is developed to show how the nonlinear model can be used in a control law. A 2.5 m buoy example is simulated to illustrate the approach of tracking an arbitrary displacement reference. For the case considered, the extracted power is 30% larger when the nonlinear dynamic FK force is used in the control law. The hourglass buoy is also compared to a spherical buoy to illustrate differences in their response to regular waves and energy extraction when using the same control laws. A spherical buoy diameter of 7.5 m was required to obtain the same power output as a 5 m tall hourglass buoy. A power-force-amplitude (PFA) metric is introduced to compare energy extraction performance and power take-off requirements. The hourglass buoy’s PFA was 13% larger than the spherical buoy implying that it can produce similar power but with less control effort. Full article

A dynamic model of the working mechanism of a compound pendulum jaw crusher with clearance is established by the Lagrange multiplier method (LMD) based on the L-N contact force model and modified Coulomb friction force model. The correctness of the dynamic model is verified by MATLAB and Adams comparison simulation, and the best selection range of driving speed and clearance size is determined according to the laminating crushing theory (LCT). The effects of driving speed and clearance size on the shock and chaos phenomenon in the clearance mechanism are analyzed, as well as the vibration force applied to the foundation. The results show that, under the premise of meeting the requirements of crusher production capacity, increasing the driving speed and reducing the clearance size can weaken the shock and chaos phenomenon during the operation of the mechanism, improve the dynamic performance and enhance the operation stability, and the service life of foundation is prolonged with the stability of vibration force. Furthermore, the optimal combination of driving speed and clearance size is determined, which provides a theoretical basis for the optimization of the vibration force of the jaw crusher. Full article

This paper investigates the formation problem of an array of large-scale mobile sensor networks. A new framework for the dynamic of mobile sensors as a continuum described by the parabolic system with boundary disturbance is proposed. The communication topology of agents is a chain graph and fixed. Leader feedback laws which are designed in a manner to the boundary control of large-scale mobile sensor networks allow the mobile sensors to achieve the formation steadily. By referring to the Lyapunov functional method and employing a boundary control approach, a new protocol is established to deal with a formation problem for the large-scale mobile sensor networks. Finally, numerical examples are given to illustrate the usefulness of the results. Full article

Large-scale industrial processes usually adopt centralized control and optimization methods. However, with the growth of the scale of industrial processes leading to increasing computational complexity, the online optimization capability of the double-layer model predictive control algorithm is challenged, exacerbating the difficulty of the widespread implementation of this algorithm in the industry. This paper proposes a distributed double-layer model predictive control algorithm based on dual decomposition for multivariate constrained systems to reduce the computational complexity of process control. Firstly, to solve the problem that the original dual decomposition method does not apply to constrained systems, two improved dual decomposition model prediction control methods are proposed: the dual decomposition method based on the quadratic programming in the subsystem and the dual decomposition method based on constraint zones, respectively. It is proved that the latter will certainly converge to the constraint boundaries with appropriate convergence factors for the controlled variables. The online optimization ability of the proposed two methods is compared in discussion and simulation, concluding that the dual decomposition method based on the constraint zones exhibits superior online optimization ability. Further, a distributed double-layer model predictive control algorithm with dual decomposition based on constraint zones is proposed. Different from the objective function of the original dual decomposition model predictive control, the proposed algorithm’s dynamic control-layer objective function simultaneously tracks the steady-state optimization values of the controlled and manipulated variables, giving the optimal solution formulation of the optimization problem consisting of this objective function and the constraints. The algorithm proposed in this paper achieves the control goals while significantly reducing the computational complexity and has research significance for promoting the industrial implementation of double-layer model predictive control. Full article

In this paper, a three-dimensional (3D) autonomous chaotic system is introduced and analyzed. In the system, each equation contains a quadratic crossproduct. The system possesses a chaotic attractor with a large chaotic region. Importantly, the system can generate both one- and two-scroll chaotic attractors by choosing appropriate parameters. Some of its basic dynamical properties, such as the Lyapunov exponents, Lyapunov dimension, Poincaré maps, bifurcation diagram, and the chaotic dynamical behavior are studied by adjusting different parameters. Further, an equivalent electronic circuit for the proposed chaotic system is designed according to Kirchhoff’s Law, and a corresponding response electronic circuit is also designed for identifying the unknown parameters or monitoring the changes in the system parameters. Moreover, numerical simulations are presented to perform and complement the theoretical results. Full article

Online prediction of maneuvering target trajectory is one of the most popular research directions at present. Specifically, the primary factors balancing, between prediction accuracy and response time, will give the research substance. This paper presents an online trajectory prediction algorithm based on small sample chaotic time series (OTP-SSCT). First, we optimize in terms of data breadth. The dynamic split window is built according to the motion characteristics of the maneuvering target, thus realizing trajectory segmentation and constructing a small sample chaotic time series prediction set. Second, since fully considering the motion patterns of maneuvering targets, we introduce the spatiotemporal features into the particle swarm optimization (PSO) model identification algorithm, which improves the identification sensitivity of key trajectory data points. Furthermore, we propose a feedback optimization strategy of residual compensation to correct the trajectory prediction values to improve the prediction accuracy. For the initial value sensitivity problem of the PSO model identification algorithm, we propose a new initial population strategy, which improves the effectiveness of initial parameters on model identification. Through simulation experiment analysis, it is verified that the proposed OTP-SSCT algorithm achieves better prediction accuracy and faster response time. Full article

The synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social to physical and biological systems. This phenomenon is often described mathematically by the Kuramoto model, which assumes oscillators of fixed natural frequencies connected by an equal and uniform coupling strength, with an analytical solution possible only for an infinite number of oscillators. However, most real-life synchronization systems consist of a finite number of oscillators and are often perturbed by external fields. This paper accommodates the perturbation using a time-dependent coupling strength $K\left(t\right)$ in the form of a sinusoidal function and a step function using 32 oscillators that serve as a representative of finite oscillators. The temporal evolution of order parameter $r\left(t\right)$ and phases ${\theta }_j\left(t\right)$, key indicators of synchronization, are compared between the uniform and time-dependent cases. The identical trends observed in the two cases give an important indication that the synchrony persists even under the influence of external factors, something very plausible in the context of real-life synchronization events. The occasional boosting of coupling strength is also enough to keep the assembly of oscillators in a synchronized state persistently. Full article

We studied the N-species competitive coexistence model with direct effect on habitat destruction to analyze the behaviors of abundant and extinct species in the system caused by habitat loss. The nontrivial equilibrium points of the system are determined for a general habitat destruction function. For the trivial equilibrium, species that survived the habitat destruction are identified using eigenvalues of the Jacobian matrix. Solutions of the system are also presented using the recursive method. Three special cases of habitat destruction functions are addressed: continuous destruction, which is a typical habitat destruction; sudden habitat destruction, which is similar to natural phenomena such as earthquakes or floods; and sudden habitat destruction with aftershocks. The proportional abundances of 50 species are numerically portrayed in each case. We found that the survival of a species is guaranteed if its corresponding eigenvalue is positive. However, the fact that a species has negative corresponding eigenvalue does not guarantee its extinction, as this also depends on the initial number of that species. Full article

The relationship between the Chinese market and the US market is widely concerned by researchers and investors. This paper uses transfer entropy and local random permutation ($LRP$) surrogates to detect the information flow dynamics between two markets. We provide a detailed analysis of the relationship between the two markets using long-term daily and weekly data. Calculations show that there is an asymmetric information flow between the two markets, in which the US market significantly affects the Chinese market. Dynamic analysis based on weekly data shows that the information flow evolves, and includes three significant periods between 2004 and 2021. We also used daily data to analyze the dynamics of information flow in detail over the three periods and found that changes in the intensity of information flow were accompanied by major events affecting the market, such as the 2008 financial crisis and the COVID-19 pandemic period. In particular, we analyzed the impact of the S&P500 index on different industry indices in the Chinese market and found that the dynamics of information flow exhibit multiple patterns. This study reveals the complex information flow between two markets from the perspective of nonlinear dynamics, thereby helping to analyze the impact of major events and providing quantitative analysis tools for investment practice. Full article

This paper studies the consensus fault-tolerant control problem of a class of second-order leader–follower multi-agent systems with unknown disturbance and actuator faults, and proposes an integral non-singular terminal sliding mode control algorithm based on a finite-time observer. First, a finite-time disturbance observer was designed based on a combination of high-order sliding mode and dual layers adaptive rules to realize fast estimation and compensation of disturbance and faults. Then, a sliding surface with additional integral links was designed based on the conventional sliding surface, and an integral non-singular terminal sliding mode controller is proposed to realize the robust consensus in finite time and accurately diminish the chattering phenomena. Finally, a numerical example and simulation verify the effectiveness. Full article