This paper focuses on the problem of adaptive neural network sliding mode control for switching systems affected by dead zones. Distinct from existing rules defined by transition and sojourn probabilities, a broader switching rule is proposed based on duration-time-dependent sojourn probabilities. A neural network strategy for compensation is implemented to mitigate the effects of the dead zone. Moreover, a sliding mode control law incorporating a learning term is designed, effectively reducing chattering compared to conventional sliding mode control. Employing a stochastic Lyapunov function grounded in the joint distribution of duration time and system mode, sufficient criteria for designing the adaptive neural network-based controller are established. Finally, the effectiveness of the proposed method is demonstrated through two simulated examples.

Hydraulic control employs compressed fluids as both the energy carrier and the conduit for information transmission. This approach has gained extensive application within industrial control systems due to its inherent adaptability and unwavering reliability. However, hydraulic systems are notorious for their high fault obscuration, substantial sensor latency issues, and intricate mechanisms for signal propagation. Consequently, pinpointing system malfunctions becomes exceedingly challenging when contending with the potent dynamics of nonlinear, time-variant characteristics at play. The diagnosis of complex hydraulic control system is a problem facing the current research. In order to cope with these challenges, a fault diagnosis method combining parameter learning and structure learning is proposed. A fault diagnosis model based on Bayesian networks of hydraulic control system is established, which realizes the diagnosis of common faults in hydraulic control system. The independence test based on Chi-square distribution was used to test the model and realize the structure learning function. The efficacy of the proposed method is exemplified through a case study involving a redundant control system designed for subsea blowout preventers, with the results affirmatively illustrating its high degree of accuracy.

This brief investigates the prescribed-time formation tracking problem of uncertain heterogeneous multi-agent systems (HMASs) under directed graphs. To achieve the goal, an innovative hierarchical control strategy consisting of a distributed observer and a local formation controller is established. First, a novel distributed observer with dynamic-gain feedback is constructed to estimate the state of the leader in prescribed time. Moreover, the adaptive gain is wisely designed in the observer such that the global topology information can be avoided. Further, an innovative controller with robust terms is designed, which is able to mitigate the impacts of uncertainties, disturbances, and the leader's unknown input. As a result, the convergence time of formation tracking errors can be arbitrarily preassigned by the designer, regardless of the initial states. The simulation results demonstrate the effectiveness of the proposed approach.

The smoothing process of the roaming path coordinates and camera direction at each path point proceeds with the Gaussian filtering algorithm. The resultant connected roaming path exhibits enhanced naturalness and smoothness, mitigating the abruptness between path points. The processed virtual camera, during movement, demonstrates smoother and more fluid changes in direction, thus avoiding sudden camera shifts and reducing both visual jitter and user discomfort. Employing multithreading techniques, a dedicated timer thread ensures the consistent update of the roaming virtual camera's position and direction at a fixed frame rate. This approach diminishes the incongruent effects of virtual camera motion caused by varying frame rates and addresses inconsistencies in user input response times. The proposal enhances the temporal consistency, predictability, and physical simulation stability of the virtual camera's runtime performance. A quantitative assessment of the smoothness of the camera's turning along the path is introduced by calculating the root mean square (RMS) value of camera direction changes. This methodology is applicable for detecting abnormal paths, optimizing paths, and comparing the smoothness of camera turns along distinct routes.

In this paper, the quadratic polynomial and cubic polynomial functions were applied to analyze the en-vironmental Kuznets curve (EKC) of carbon emissions in Hebei Province. The improved STIRPAT model was also applied to assess the driving factors and reduction paths for carbon emissions in Hebei Province. The results lead to three main conclusions. Firstly, carbon emissions and economic growth in Hebei Province are in a positive cor- relation stage which has not formed the EKC curve, and the "decoupling" stage between carbon emissions and economic growth has not arrived yet. Secondly, the industrial structure, per capita GDP, fixed assets investment, population size and urbanization rate account for the highest proportion of carbon emissions. Carbon emissions can be reduced greatly by changing the energy structure, in which the proportion of coal is decreased year by year. Environmental regulation also has an obvious effect on the reduction of carbon emissions. Thirdly, it is suggested that the reduction of carbon emissions in Hebei Province should focus on four tasks: controlling the development of heavy industry, avoiding overcapacity, optimizing the industrial structure and accelerating the de-velopment of clean energy.

The aim of this study is to present the numerical solutions of the Liénard nonlinear model by designing the structure of the computational Gudermannian neural networks (GNNs) along with the global/local search efficiencies of genetic algorithms (GAs) and interior-point algorithm (IPA), i.e. GNNs–GAs–IPA. A merit function in terms of differential system and its boundary conditions is designed and optimization is performed by using the proposed computational procedures of GAs–IPA to solve the Liénard nonlinear differential system. Three different highly nonlinear examples based on the Liénard differential system have been tested to check the competence, exactness and proficiency of the proposed computational paradigm of GNNs–GAs–IPA. The statistical performances in terms of different operators have been provided to check the reliability, consistency and stability of the computational GNNs–GAs–IPA. The plots of the absolute error, performance measures, results comparison, convergence analysis based on different operators, histograms and boxplots are also illustrated. Moreover, statistical gauges using minimum, mean, maximum, semi-interquartile range, standard deviation and median are also provided to authenticate the optimal performance of the GNNs–GAs–IPA.

Since ecological systems are history-dependent, incorporating fractional calculus and especially variable order ones could significantly improve the emulation of these systems. Nonetheless, in the literature, no study considers ecological processes by variable-order fractional (VOF) model. This study is motivated by this issue. At first, we propose to extend a predator–prey mathematical model with VOF derivatives. The underlying assumption in the proposed model lies in considering values of fractional derivatives as time-varying functions instead of constant parameters. Some system’s dynamic features are investigated, and then the control of the proposed system is studied. To this end, a nonlinear model predictive control is offered for the VOF system. The necessary optimality and sufficient conditions for solving the nonlinear optimal control problem in the form of fractional calculus with variable-order derivative are formulated, and the controller’s design procedure is delineated. Finally, numerical simulations are performed to demonstrate the developed control technique’s effectiveness and performance for the VOF predator–prey model.

Mathematical modeling can be utilized to find out how the coronavirus spreads within a population. Hence, considering models that can precisely describe natural phenomena is of crucial necessity. Besides, although one of the most significant benefits of mathematical modeling is designing optimal policies for battling the disease, there are a few studies that employ this beneficial aspect. To this end, this study aims to design optimal management policies for the novel coronavirus disease 2019 (COVID-19). This is a pioneering research that designs optimal policies based on multi-objective evolutionary algorithms for control of the fractional-order model of the COVID-19 outbreak. First, a fractional-order model of the disease dynamic is presented. The impacts of the fractional derivative’s value on the modeling and forecasting of the disease spread are considered. After that, a multi-objective optimization problem is proposed by considering the rate of communication, the transition of symptomatic infected class to the quarantined one, and the release of quarantined uninfected individuals. Numerical results clearly corroborate that by solving the proposed multi-objective problem, governments can control the massive disease outbreak while economic factors have reasonable values that prevent economic collapse.

Nowadays, advances in different fields of technology have increased demands for reliable controllers. Uncertainty, disturbances, and limitations in control inputs are inevitable with most systems. Hence, considering them in designing a practical controller seems indispensable to any system. We propose an adaptive, robust, and finite time control technique for both multi-input multi-output (MIMO) and single-input single-output (SISO) systems. In the design of the proposed control technique, due to the undeniable existence of disturbances and control input limitations, their effects are fully taken to account. On the basis of a finite time sliding mode strategy, controllers and disturbance observers are designed. Then, the stability and finite time convergence of the proposed control scheme and disturbance observer are proven via the Lyapunov stability theory. Eventually, to investigate the performance of the proposed method in real-world applications, a hardware-in-the-loop (HIL) test is carried out for the proposed control scheme. Through numerical simulation and the results of the HIL test, the high-effective performance of the proposed controller for uncertain chaotic systems was demonstrated. Moreover, the results of the HIL test showed that by implementing continuous functions in the design of the controller, chattering, which has detrimental effects on systems, will be reduced in practical applications. Numerical simulations and the results of the HIL test bench for the modified controller clearly confirmed the effective performance of the offered control technique for practical systems. Thereby applying the proposed control technique for complex nonlinear systems subject to control input limitations, disturbances, and time-varying uncertainties will be useful.

In this study, a synchronization problem for spatio-temporal partial differential systems is addressed and researched within a subjectivist framework. In light of Lyapunov direct method and some proposed nonlinear controllers, a new scheme is established to accomplish a full synchronization between two reaction–diffusion systems of integer- and fractional-order. In particular, a novel vector-valued control law is analytically derived to attain the desired synchronization between two chemical models, namely, the Lengyel–Epstein and Gray–Scott models. To validate the obtained theoretical results, further numerical simulations are carried out in 2D and 3D configurations.

In this study, a novel heuristic computing technique is presented to solve bioinformatics problem for the corneal shape model of eye surgery using Morlet wavelet artificial neural network optimized by the global search schemes, i.e. genetic algorithm (GA), local search technique, i.e. sequential quadratic programming (SQP) and the hybrid of GA-SQP. To measure the performance of the design network configuration, different cases based on nonlinear second-order differential equations governing the corneal model have been solved effectively. The numerical procedure of Adams method is implemented for the comparison purpose of the presented outcomes of the stochastic solver, which shows the worth of the present scheme based on accuracy and convergence with negligible values of absolute error in the range 10[Formula: see text] to 10[Formula: see text]. Furthermore, statistical measures are presented based on “mean absolute error”, “root mean square error” and “coefficient of Theil’s inequality” which additionally endorsed consistently accurate performance of integrated intelligent computing framework for solving the corneal shape model.

In December 2019, a novel coronavirus disease (COVID-19) appeared in Wuhan, China. After that, it spread rapidly all over the world. Novel coronavirus belongs to the family of Coronaviridae and this new strain is called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epithelial cells of our throat and lungs are the main target area of the SARS-CoV-2 virus which leads to COVID-19 disease. In this article, we propose a mathematical model for examining the effects of antiviral treatment over viral mutation to control disease transmission. We have considered here three populations namely uninfected epithelial cells, infected epithelial cells, and SARS-CoV-2 virus. To explore the model in light of the optimal control-theoretic strategy, we use Pontryagin’s maximum principle. We also illustrate the existence of the optimal control and the effectiveness of the optimal control is studied here. Cost-effectiveness and efficiency analysis confirms that time-dependent antiviral controlled drug therapy can reduce the viral load and infection process at a low cost. Numerical simulations have been done to illustrate our analytical findings. In addition, a new variable-order fractional model is proposed to investigate the effect of antiviral treatment over viral mutation to control disease transmission. Considering the superiority of fractional order calculus in the modeling of systems and processes, the proposed variable-order fractional model can provide more accurate insight for the modeling of the disease. Then through the genetic algorithm, optimal treatment is presented, and its numerical simulations are illustrated.

Control of supply chains with chaotic dynamics is an important, yet daunting challenge because of the limitations and constraints there are in the amplitude of control efforts. In real-world systems, applying control techniques that need a large amplitude signal is impractical. In the literature, there is no study that considers the control of supply chain systems subject to control input limitations. To this end, in the current study, a new control scheme is proposed to tackle this issue. In the designed control input, limitations in control inputs, as well as robustness against uncertainties, are taken into account. The proposed scheme is equipped with a fixed time disturbance observer to eliminate the destructive effects of uncertainties and disturbances. Additionally, the super-twisting sliding mode technique guarantees the fixed-time convergence of the closed-loop system. After that, a symmetric supply chain system is presented, and its chaotic attractors are demonstrated. Finally, the proposed controller is applied to the symmetric supply chain system. Numerical simulations exhibit the proposed scheme’s excellent performance even though the system is subjected to control input limitations and time-varying uncertainties.

In the present study, a new neural network-based terminal sliding mode technique is proposed to stabilize and synchronize fractional-order chaotic ecological systems in finite-time. The Chebyshev neural network is implemented to estimate unknown functions of the system. Moreover, through the proposed Chebyshev neural network observer, the effects of external disturbances are fully taken into account. The weights of the Chebyshev neural network observer are adjusted based on adaptive laws. The finite-time convergence of the closed-loop system, which is a new concept for ecological systems, is proven. Then, the dependency of the system on the value of the fractional time derivatives is investigated. Lastly, the proposed control scheme is applied to the fractional-order ecological system. Through numerical simulations, the performance of the developed technique for synchronization and stabilization are assessed and compared with a conventional method. The numerical simulations strongly corroborate the effective performance of the proposed control technique in terms of accuracy, robustness, and convergence time for the unknown nonlinear system in the presence of external disturbances.

Identifying parameters of financial and economic models with chaotic dynamics is an important, yet daunting challenge because of the complexities there exist in these chaotic systems. Although several studies have been devoted to understanding the mechanism of financial systems, the application of most state-of-the-art methods to these systems is completely ignored. To the best of our knowledge, no study identifies and predicts fractional derivatives of economic models. The current study has been motivated by this issue. Employing the Differential Evolution algorithm, Gaussian process regression, and neural networks, we propose a novel algorithm to identify and predict parameters of a symmetric chaotic fractional financial model. In the first step, a combination of Differential Evolution and the Gaussian process is utilized to identify time-varying fractional-order derivatives. Then, through numerical simulation, it is demonstrated that although this method provides bright results for estimation and interpolation purposes, it fails to extrapolate and predict time-varying parameters. Hence, in the next step, by taking advantage of a recurrent neural network, the proposed method is promoted and modified for extrapolation. Numerical simulations firmly confirm the excellent performance of the improved algorithm for both interpolation and extrapolation purposes. (C) 2021 Elsevier Ltd. All rights reserved.

This paper is concerned with recovering the shape of the scatterer for the two-dimensional time-harmonic inverse scattering problem in elasticity. The level set method is used for representing the geometry shape of the scatterer. The Bayesian inference approach provides a natural framework in which we are able to formulate the inverse problem as a statistical inference problem. The priors for the level set functions are achieved via the Whittle-Matérn Gaussian random fields, and the Markov chain Monte Carlo (MCMC) method is applied to extract the information of the posterior distribution whose well-posedness would be discussed as well. Numerical experiments demonstrate the effectiveness of the proposed approach.

This paper proposes an improved Generalized Quasi-Spectral Model Predictive Static Programming (GS-MPSP) algorithm for the ascent trajectory optimization for hypersonic vehicles in a complex flight environment. The proposed method guarantees the satisfaction of constraints related to the state and control vector while retaining its high computational efficiency. The spectral representation technique is used to describe the control variables, which reduces the number of decision variables and makes the control input smooth enough. Through Taylor expansion, the constraints are transformed into an inequality containing only decision variables, such that it can be added into GS-MPSP framework. By Gauss quadrature collocation method, only a few collocation points are needed to solve the sensitivity matrix, which greatly accelerates the calculation. Subsequently, the analytical expression is obtained by combining the static optimization with the penalty function method. Finally, the simulation results demonstrate that the proposed improved GS-MPSP algorithm can achieve both high computational efficiency and high terminal precision under the constraints.

A boundary integral equation in general form will be considered, which can be used to solve Dirichlet problems for the Helmholtz equation. The goal of this paper is to develop a fast Fourier-Galerkin method solving these boundary integral equations. To this aim, a scheme for splitting integral operators is presented, which splits the corresponding integral operator into a convolution operator and a compact operator. A truncation strategy is presented, which can compress the dense coefficient matrix to a sparse one having only O ( n ) nonzero entries, where n is the order of the Fourier basis functions used in the method. The proposed fast method preserves the stability and optimal convergence order. Moreover, exponential convergence can be obtained under suitable assumptions. Numerical examples are presented to confirm the theoretical results for the approximation accuracy and computational complexity of the proposed method.

In this paper, we study an inverse transmission scattering problem of a time-harmonic acoustic wave from the viewpoint of Bayesian statistics. In Bayesian inversion, the solution of the inverse problem is the posterior distribution of the unknown parameters conditioned on the observational data. The shape of the scatterer will be reconstructed from full-aperture and limited-aperture far-field measurement data. We first prove a well-posedness result for the posterior distribution in the sense of the Hellinger metric. Then, we employ the Markov chain Monte Carlo method based on the preconditioned Crank-Nicolson algorithm to extract the posterior distribution information. Numerical results are given to demonstrate the effectiveness of the proposed method.