Nonlinear Discrete Systems Research Articles

Thermal radiation impact on bioconvection flow of nano-enhanced phase change materials and oxytactic microorganisms inside a vertical wavy porous cavity

This work examines the bioconvection of nano-enhanced phase change materials (NEPCMs) and oxytactic microorganisms in a vertical wavy cavity saturated by a porous medium. The novelty of this work is demonstrating the significance of wavy surface and thermal radiation on the bioconvection flow of NEPCMs and oxytactic microorganisms within a porous wavy cavity. Further, a novel attempt in achieving high-performance conductivity by combining the NEPCM and oxytactic microorganisms during the bioconvection flow in a complex wavy cavity is examined. The dimensionless governing partial differential equations are discretized using the finite element method and the discrete nonlinear systems are handled using the adaptive Newtons method. The results showed the contributions of thermal radiation to enhancing the strength of streamlines. The undulation number of a wavy wall affects the bioconvection flow and contours of streamlines and heat capacity inside a wavy cavity. The Rayleigh number strengthens the streamlines and bioconvection flow. Increasing the Darcy parameter improves the isotherms, oxygen isoconcentration, and microorganisms isoconcentration. Consequently, the PCM shifts towards the right side of a cavity along with a growth in the Darcy parameter. The mean Nusselt number Nuavg and Sherwood number Shavg are altered by the involved physical parameters. Increasing Rayleigh's number from 103 to 106 augments Nuavg by around 153.8% and declines Shavg by 33.3%.

Fusion event-triggered model predictive control based on shrinking prediction horizon

Purpose This paper aims to design an algorithm which is used to deal with non-linear discrete systems with constraints under the lower computation burden. As a result, we solve the non-holonomic vehicle tracking problem with the lower computational load and the convergence performance. Design/methodology/approach A fusion event-triggered model predictive control version is developed in this paper. The authors designed a shrinking prediction strategy. Findings The fusion event-triggered model predictive control scheme combines the strong points of event triggered and self-triggered methods. As the practical state approaches the terminal set, the computational complexity of optimal control problem (OCP) decreases. Originality/value The proposed strategy has proven to stabilize the system and also guarantee a reproducible solution for the OCP. Also, it is proved to be effected by the performance of the simulation results.

Investigation of complex dynamics and chaos control of the duopoly supply chain under the mixed carbon policy

Against the background of the mixed carbon policy (carbon tax‑carbon trading) implemented in China, the authors analyze the complexity of a series of competition decisions between supply chains through constructing Cournot(Duopoly)game model between supply chains. The dynamics of the proposed game model and the time evolution of the supply chains are described by a nonlinear discrete dynamical system. The equilibrium point of the discrete dynamical system is obtained and its local stability is discussed. The stability of the equilibrium point is further discussed by numerical simulation, which is affected by the speed of adjusting parameters and some other cost parameters. Finally, we apply the delayed feedback control method to suppress and overcome the chaos of the discrete dynamical system. It can effectively promote the discrete dynamical system to return to the stable behavior. It is hoped that the current research can provide a theoretical basis for the competitive decision-making of supply chain node enterprises.

State estimation for networked uncertain nonlinear systems with time-delays

This paper investigates state estimation for uncertain nonlinear discrete systems with time-delays over unreliable communication channels. The Bernoulli model is used to describe the packet dropout conditions of the control information and the measurement. The extended state approach is introduced to deal with the nonlinear uncertainty, and an extended state system is obtained. The state predictor and the state estimator are designed based on unreliable control inputs and measurements, and their error systems are derived. The iterative equation of the state predictive error covariance is achieved, and its optimal estimator gain is derived. An iterative algorithm is proposed to further optimize the state predictive error covariance. A necessary and sufficient condition to ensure the stability of the state predictive error covariance is achieved. Finally, a numerical example is presented to illustrate the effectiveness of the developed results.

Nonlinear discrete system model of tobacco supply chain information

Abstract In order to understand the real environment and specific needs of China’s current tobacco industry, master the signal information in the tobacco supply chain, and timely discover the source of the tobacco supply chain, this paper puts forward the detection method of anti-counterfeiting at the source of the tobacco supply chain. Based on this, this article constructs a nonlinear discrete system model, which mainly studies the logistics information existing in the tobacco supply chain, utilizes the noise existing in the tobacco supply chain information obtained by EKF filtering, and combines it with Support vector machine data analysis method. The results showed that out of 450 sample tests, 0 real sample errors and 1 misuse of 49 false samples, with a total detection rate of up to 100% was achieved. The results show that the nonlinear discrete system model is better, has higher detection effect of tobacco supply source, and improves the detection accuracy.

Finite‐time fault detection for discrete nonlinear systems with time‐varying delays under the dynamic event‐triggered mechanism

AbstractThis article is concerned with the finite‐time fault detection (FTFD) problem for discrete networked systems subject to nonlinearities and time‐varying delays under the dynamic event‐triggered mechanism. The dynamic event‐based communication scheme is adopted to improve the efficiency of the bandwidth utilization, reduce the transmission of redundant signals and decrease the transmission pressure of the network. Then, by constructing a new Lyapunov functional and utilizing the appropriate inequality techniques, some sufficient conditions are derived under which the addressed augmented system achieves the finite‐time stability and attains a satisfactory performance index. Additionally, the expression forms of the fault detection filter (FDF) parameters are presented based on the solutions to certain matrix inequalities. In the end, a numerical simulation is employed to demonstrate the effectiveness and feasibility of the proposed FTFD strategy.

Data-based modeling and identification for general nonlinear dynamical systems by the multidimensional Taylor network

PurposeThe present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).Design/methodology/approachThe authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.FindingsCompared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.Research limitations/implicationsOnce models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.Practical implicationsMTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.Social implicationsThe operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.Originality/valueNonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

Adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter with recursive noise estimation

In this study, we propose a Masreliez–Martin fractional interpolatory cubature Kalman filter and an adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter to design the estimators for fractional-order discrete-time nonlinear systems under non-Gaussian measurement noise and unknown process noise covariance. Ther Masreliez–Martin fractional interpolatory cubature Kalman filter is developed by extending the interpolatory cubature Kalman filter to the fractional nonlinear discrete system to increase the robustness of estimation under noisy environment by applying the Masreliez–Martin method, including both time update and measurement update. Meanwhile, the adaptive Masreliez–Martin fractional interpolatory cubature Kalman filter is put forward to enhance the state estimation adaptive to the fractional system with uncertain process noise through recursive estimation. Simulation results on the re-entry target tracking system have demonstrated the adaptiveness, robustness and effectiveness of the propose filters.

Approach to the Stability Analysis of Partial Equilibrium States of Nonlinear Discrete Systems

Approach to the Stability Analysis of Partial Equilibrium States of Nonlinear Discrete Systems

Stochastic model predictive control based on multi‐step control strategy for discrete nonlinear systems

Stochastic model predictive control (SMPC) is a popular approach to control uncertain systems by incorporating the probabilistic distribution of the uncertainty into the controller design. However, the performance of the SMPC deteriorates rapidly when the system becomes nonlinear. In this article, an efficient SMPC is derived after decomposing the discrete nonlinear systems into a linear stochastic model and a bounded model mismatch. The proposed controller includes a linearized-model-based SMPC and an RMPC for the model mismatch. The multi-step control strategy is incorporated to reduce the conservativeness by introducing more degrees of freedom. The feasibility of the recursiveness of the proposed controller is thoroughly discussed. The control performance is illustrated by examples involving both a numerical nonlinear stochastic system and a wind-blade pitch system.

The stability of a dynamic duopoly Cournot–Bertrand game model

The paper is devoted to exploring the complex dynamics of a Cournot–Bertrand model, where one agent chooses quantity and the other chooses price. A nonlinear discrete system is built to illustrate the game model with bounded rationality. Theoretically, the local and global stability of equilibrium are investigated. The simulation reveals that Flip and Neimark–Sacker​ bifurcation phenomena occur when the adjustment speed of one firm increases through different boundary curves. Therefore three different chaotic attractors are presented. The standard Logistic mapping is applied to analyze the dynamics of the system on invariant axes. The critical curves classify the number of preimage of the quantity or price. Besides, simulations give more intuitive results: the cycle attractor, chaotic attractor and the basin of attraction with “holes” are given.

Finite Element Analysis of the Dynamics of Power-Law Fluid around an Obstacle in a Channel

Control of fluid forces is an emerging area of research with numerous engineering applications. The uneven wake behind an obstacle causes undesirable structural oscillations, which can lead to fatigue or structural failure. Controlling the wake phenomena could directly benefit a wide range of engineering applications, including skyscrapers, naval risers, bridges, columns, and a few sections of airplanes. This study is concerned with the time dependent simulations in a channel in presence of an obstacle aiming to compute fluid forces. The underlying mathematical model is based on nonstationary Navier–Stokes equations coupled with the constitutive relations of power law fluids. Because the representative equations are complex, an effective computing strategy based on the finite element approach is used. To achieve higher accuracy, a hybrid computational grid at a very fine level is used. Theℙ2−ℙ1elements based on the shape functions of the second and first-order polynomials were used to approximate the solution. The discrete nonlinear system arising from this discretization is linearized by Newton’s method and then solved through a direct linear solver PARADISO. The code validation study is also performed for Newtonian fluids as a special case, and then the study is extended to compute drag and lift forces for other cases of viscosity as described by the power law index. When looking at the phase plot, it can be seen that for the Newtonian case n = 1, there is only one closed orbit after the steady state is reached, whereas forn=0.5, there are multiple periodic orbits. Moreover, the effects of shear rate on the drag-lift phase plot are also discussed.

Stability Analysis of the Nabla Distributed-Order Nonlinear Systems

The stability of the nabla discrete distributed-order nonlinear dynamic systems is investigated in this paper. Firstly, a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems is proposed based on Lyapunov direct method. In addition, some properties of the nabla distributed-order operators are derived. Based on these properties, a simpler criterion is provided to determine the stability of such systems. Finally, two examples are given to illustrate the validity of these results.

Identification of nonlinear discrete systems using a new Hammerstein model with Volterra neural network

Identification of nonlinear discrete systems using a new Hammerstein model with Volterra neural network

Mixed bioconvection flow of Ag-MgO/water in the presence of oxytactic bacteria and inclined periodic magnetic field

In this paper, a numerical investigation on mixed bioconvection flow of silver(Ag)-magnesium oxide(MgO)-water hybrid nanofluid in a trapezoidal porous cavity under the effect of inclined periodic magnetic field is carried out. Brinkman–Forchheimer-extended Darcy model for the porous medium is adopted. Galerkin weighted residual finite element method is implemented to simulate the governing steady dimensionless equations. The resulting discrete nonlinear algebraic systems are treated using the adaptive Newton's method. The fluid flow, heat and mass transfer behavior are examined in variation of parameters as Hartmann number (Ha=0−100), angle of periodic magnetic field (θ=0∘−90∘), period of periodic magnetic field (Λ=0.1−1), bioconvection Rayleigh number (Rb=10−100), Richardson number (Ri=0.1−5), Lewis number (Le=1−10) and Peclet number (Pe=0.1−1). The rise in Hartmann number has a weakening effect on both transfer of heat and mass. When θ=0∘, convective heat and mass transfer is the smallest at Λ=1 where the most reduction in the average Nusselt and Sherwood numbers is 9.14% and 6.98% as Λ is raised from 0.1 to 1, respectively, and occurs at Ha=100. The significant decrement in the average Nusselt number is 42.57% at Ha=75 and in the Sherwood number is 10.4% at Ha=50 when θ is changed from 0∘ to 90∘.

A Dynamic System Approach to Spiking Second Order Memristor Networks

Second order memristors are two terminal devices that present a conductance depending on two orders of variables, namely the geometric parameters and the internal temperature. They have shown to be able to mimic some specific features of neuron synapses, specifically Spike-Timing-Dependent-Plasticity (STDP), and consequently to be good candidates for neuromorphic computing. In particular, memristor crossbar structures appear to be suitable for implementing locally competitive algorithms and for tackling classification problems by exploiting temporal learning techniques. On the other hand, neuromorphic studies and experiments have revealed the existence of different kinds of plasticity and have shown the effect of calcium concentration on synaptic changes. Computational studies have investigated the behavior of spiking networks in the context of supervised, unsupervised, and reinforcement learning. In this paper, we first derive a simplified, almost analytical, model of a second-order memristor, only involving two variables, the mem-conductance, and the temperature, directly attributable to the synaptic efficacy and to the calcium concentration. Then we study in detail the response of a single memristive synapse to the most relevant plasticity models, including cycles of spike pairs, triplets, and quadruplets at different frequencies. Finally, we accurately characterize memristor spiking networks as discrete nonlinear dynamic systems, with mem-conductances as state variables and pre and postsynaptic spikes as inputs and outputs, respectively. The result shows that the model developed in this manuscript can explain and accurately reproduce a significant portion of observed synaptic behaviors, including those not captured by classical spike pair-based STDP models. Furthermore, under such an approach, the global dynamic behavior of memristor networks and the related learning mechanisms can be deeply analyzed by employing advanced nonlinear dynamic techniques.

Periodic Flow of Non-Newtonian Fluid Over a Uniformly Heated Block With Thermal Plates: A Hybrid Mesh-Based Study

In this work, we analyze the characteristics of periodic flows in non-isothermal viscous fluid over a heated block in the presence of thermal plates at Reynolds number (Re=100). The unsteady, incompressible Navier–Stokes (NS) equations with suitable initial and boundary data in 2D are executed by the finite element technique using a highly refined hybrid mesh. The temporal discretization is performed by an implicit stable backward differencing in time and a stable choice of finite elements from the finite element library for spatial discretization. The discrete nonlinear system arising from this discretization is linearized by Newton’s method and then solved through a direct linear solver PARDISO. For this forced convective study, the range of dimensionless parameters, namely, the Prandtl number (Pr) and power law index (n), are varied from 1 to 10 and 0.6 to 1.4 with a low Grashof number varying as (1≤Gr≤10) to produce a forced convection regime, respectively. For the authentication, we have compared our results with the literature at a similar configuration. After simulation, the results accomplished in the velocity profile, pressure, isotherm contours, drag and lift coefficients (trajectory motion), average Nusselt number (Nuavg), etc. are considered. For convergence of solution at low shear rate (n<1), crosswind stabilization (CWS) function has been incorporated. It is observed that Nuavg becomes oscillatory for the shear-thinning case (n<1), while for the shear-thickening cases (n>1), it converges to a single value. Furthermore, the drag (CD) and lift (CL) coefficients are more pronounced for shear-thinning cases (n<1) as compared with shear-thickening cases (n>1).

A time two-grid algorithm for the two dimensional nonlinear fractional PIDE with a weakly singular kernel

The main aim of this paper is to solve the two-dimensional nonlinear fractional partial integro-differential equation (PIDE) with a weakly singular kernel by using the time two-grid finite difference (FD) algorithm. The second-order backward difference formula (BDF) and L1 scheme are used in time. The time two-grid algorithm is constructed to improve the solving efficiency of nonlinear systems. The Newton iteration is used to solve nonlinear discrete system on the coarse grid, and then we apply Lagrangian linear interpolation to attain the function value used in constructing the difference scheme on the fine grid. The second-order finite difference method (FDM) is used in space. The unconditional stability and convergence are attained for the two-grid fully discrete system. Numerical experiments show that the used CPU time for the presented two-grid numerical algorithm is lower than the general finite difference method for solving the nonlinear system.

Hi/H∞-optimised fault detection for a surface vessel integrated navigation system

AbstractStrapdown inertial navigation systems are widely used in surface ships and warships. Although high-precision optical fibre inertial navigation systems are available, they have high cost and limited practicality. Therefore, they cannot replace the traditional platform inertial navigation systems in all ships. Hence, microelectromechanical system (MEMS)-based inertial sensors are widely used for robust navigation. Accurate and timely identification of sensor faults while ensuring stable navigation is a challenging task. This paper proposes a robust fault detection (FD) approach for a low-cost system that loosely integrates a strapdown inertial navigation system and the global navigation satellite system, where the integrated navigation state estimation provides high-accuracy output. A cubature Hi/H∞-optimised FD filter was designed for a nonlinear discrete time-varying system considering sensitivity to faults and robustness to disturbances. Furthermore, a threshold for FD was derived considering a compromise between the false alarm rate and fault diagnosis accuracy. Finally, the proposed method was validated through simulations using multiple noise distribution sensor data generated by a ship-manoeuvring simulator.

Finite Horizon Nonlinear Suboptimal Control for an Autonomous Soaring UAV

In this paper, a suboptimal nonlinear discrete control for nonlinear discrete affine systems is implemented in an autonomous soaring unmanned aerial vehicle (UAV) to improve energy consumption and performance. General expressions for this controller are obtained from the continuous nonlinear guidance model of a fixed-wing UAV and applied in a multiloop control structure. Simulation results in the task of trajectory tracking inside a thermal updraft and a comparative study with a proportional derivative (PD) controller validated the effectiveness of this method.