Discrete Time Research Articles

A novel intelligent control of discrete-time nonlinear systems in the presence of output saturation

In this paper, a model free control method for a class of discrete time nonlinear systems is introduced. A type-3 fuzzy system estimates the unknown parameters required by the control system. The control system only uses the input and output data of the plant and therefore does not need to know its mathematical equations. On the other hand, the phenomenon of output saturation is a challenging problem for all control systems, addressed in detail in the proposed method. The convergence of the proposed method is guaranteed, and the control system is very robust in the face of changes in the dynamics of the plant. The simulation results on discrete-time nonlinear systems show that the proposed method is very accurate despite the high speed of convergence. In addition, the proposed method is robust for modeling uncertainties and has a better root mean square error and step response time compared to the other methods. Also, a comparison has been made between type-1 to type-3 fuzzy systems and control system based on trial and error, which shows firstly the importance of the presence of fuzzy system and secondly the superiority of type-3 fuzzy system compared to the other two types.

Hopf bifurcation and stability analysis for a delayed equation with φ-Laplacian

A formal framework for the analysis of Hopf bifurcations for a kind of delayed equation with $\varphi$-Laplacian and with a discrete time delay is presented, thus generalizing known results for the sunflower equation given by Somolinos in 1978. Also, under appropriate assumptions we prove the gradient-like behavior of the equation which, in turn, implies the non-existence of nonconstant periodic solutions. Our conditions improve previous results known in the literature for the standard case $\varphi(x)=x$.

Spatiotemporal complexity analysis of a discrete space-time cancer growth model with self-diffusion and cross-diffusion

We investigate spatiotemporal pattern formation in cancer growth using discrete time and space variables. We first introduce the coupled map lattices (CMLs) model and provide a dynamical analysis of its fixed points along with stability results. We then offer parameter criteria for flip, Neimark–Sacker, and Turing bifurcations. In the presence of spatial diffusion, we find that stable homogeneous solutions can experience Turing instability under certain conditions. Numerical simulations reveal a variety of spatiotemporal patterns, including patches, spirals, and numerous other regular and irregular patterns. Compared to previous literature, our discrete model captures more complex and richer nonlinear dynamical behaviors, providing new insights into the formation of complex patterns in spatially extended discrete tumor models. These findings demonstrate the model’s ability to capture complex dynamics and offer valuable insights for understanding and treating cancer growth, highlighting its potential applications in biomedical research.

Optimization based data enrichment using stochastic dynamical system models

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system. Application of the proposed approach to a Monte Carlo simulation exhibits significant performance improvement in comparison to a common existing method.

A new space–time localized meshless method based on coupling radial and polynomial basis functions for solving singularly perturbed nonlinear Burgers’ equation

In this paper, the singularly perturbed nonlinear Burgers’ problem (SPBP) with small kinematic viscosity 0<ϵ≪1 is solved using a new Space–Time Localized collocation method based on coupling Polynomial and Radial Basis Functions (STLPRBF). To our best knowledge, it is the first time that the solution of SPBP is accurately approximated using the space–time meshless method without applying any adaptive refinement technique. The method is based on solving the problem without distinguishing between space and time variables, which eliminates the need for time discretization schemes. To address the inherent non-linearity of the problem, the method employs an iterative algorithm based on quasilinearization technique. The efficiency and accuracy of the proposed method are demonstrated by solving different examples of one- and two-dimensional SPBP with very small ϵ up to 10−10. Additionally, the numerical convergence of the method with respect to ϵ and also to the number of collocation points has been investigated. The comparison of the STLPRBF results with other published ones is presented.

Gestational urinary concentrations of glyphosate and aminomethylphosphonic acid in relation to preterm birth: the MIREC study.

Few high-quality studies have evaluated associations between urinary glyphosate or its environmental degradate (aminomethylphosphonic acid (AMPA)] and preterm birth (PTB). To quantify associations between urinary glyphosate and AMPA and preterm birth in the pan-Canadian Maternal-Infant Research on Environmental Chemicals (MIREC) study and determine if associations differ by fetal sex. We measured first trimester urinary glyphosate and AMPA concentrations in MIREC participants who were recruited between 2008-2011 from 10 Canadian cities. Of the 1880 participants whose first trimester urine samples were analyzed for glyphosate or AMPA, 1765 delivered a singleton, live birth. Our primary outcome was preterm birth (PTB) defined as births occurring between 20 and <37 weeks. Secondary outcomes were spontaneous preterm births (sPTB) and gestational age. We modelled the hazard of PTB and sPTB using discrete time survival analysis with multivariable logistic regression to calculate odds ratios (OR). We used multivariable linear regression models to quantify associations between analytes and gestational age. To assess effect modification by fetal sex, we stratified all models and calculated interaction terms. In the logistic regressions models we additionally calculated the relative excess risk due to interaction. Six percent (n = 106) of the study population delivered preterm, and 4.7% (n = 83) had a spontaneous preterm birth. Median specific-gravity standardized concentrations of glyphosate and AMPA were 0.25 and 0.21 µg/L. Associations between both glyphosate or AMPA and PTB, sPTB, and gestational age centered around the null value. The adjusted ORs of PTB for each doubling of glyphosate and AMPA concentrations were 0.98 (95% CI: 0.94, 1.03) and 0.99 (95% CI: 0.92, 1.06) respectively. We observed no evidence of differences by fetal sex. In this Canadian pregnancy cohort, neither glyphosate nor AMPA urinary concentrations was associated with PTB or reduced gestational length.

Global Dynamics of Piecewise Smooth Systems with Switches Depending on Both Discrete Times and Status

Global Dynamics of Piecewise Smooth Systems with Switches Depending on Both Discrete Times and Status

Improved functional interval observer for mecanum‐wheels omnidirectional automated guided vehicle

AbstractThis article presents a study of interval estimation approach based on functional interval observers for mecanum‐wheels omnidirectional automated guided vehicle (MOAGV). In the context of MOAGV, the nonlinear system in discrete time incorporates model uncertainty and unknown bounded disturbances. A functional observer is developed by integrating terminal sliding mode and techniques, aiming to reduce the impact of lumped disturbances/uncertainties. Additionally, a novel observer structure is introduced to increase the degrees of freedom in the design process. Subsequently, the linear function bounds are obtained using the reachability analysis of the estimation error. Finally, the performance of the improved functional interval observer is demonstrated by numerical simulations.

Efficient Pump Scheduling for Large‐Scale Multiproduct Pipelines Using Deep Reinforcement Learning

ABSTRACTOptimizing pump scheduling in multiproduct pipelines can significantly reduce energy consumption and carbon emissions. For pump scheduling in multiproduct pipelines, to describe hydraulic losses more accurately, the model needs to adopt shorter discrete time intervals, which will lead to longer decision‐making time. It combined with the large solution space of large‐scale pipelines, will lead to low solution efficiency with dynamic programming methods and poor solution quality with heuristic optimization algorithms. Given that, this article develops a multiproduct refined oil transmission simulation system and employs the enhanced Proximal Policy Optimization (PPO) algorithm with action space shaping trick to optimize pump scheduling for large‐scale multiproduct pipelines. The method of converting discrete action space to multi‐discrete action space through action shaping can address PPO's low convergence efficiency issue resulting from the large discrete action space challenge common in large‐scale multiproduct pipelines. The experimental results indicate that the proposed method, that is, PPO algorithm with multidiscrete action space exhibits significant advantages in terms of efficiency and robustness in large‐scale pipelines compared to mainstream methods for pump scheduling such as dynamic programming (DP), genetic algorithms (GA), and ant colony optimization (ACO). Furthermore, we demonstrate the effectiveness of action space shaping in large‐scale pipelines from the perspectives of exploration and exploitation.

Implicit-integral dynamic optimization based on spatial partitioning and temporal segmentation for the power jumps of renewable energy sources

With the widespread development of renewable energy sources, the increasing short-term power volatility poses a significant challenge to the normal operation of power systems. This paper presents a two-timescale adaptive dynamic optimization (TADO) strategy based on implicit trapezoidal integral to address dynamic state fluctuations due to renewable power jumps. Firstly, a static optimization model is established utilizing the model predictive control (MPC) to obtain the optimal states on a longer temporal scale, considering the uncertain renewable power jumps. Next, provide a partitioning method based on modularity to divide the power system into several independent subsystems with constant tie-line power. Using an implicit trapezoidal integral algorithm, each subsystem's dynamic reactive power optimization model is constructed with an appropriate discrete time granularity, accounting for the electromechanical transient processes due to renewable power jumps. Then, to improve the solving efficiency of the dynamic optimization model, a new solution method is proposed based on temporal segmentation. The whole process's optimal state trajectory is achieved by splicing all sub-optimization results. Finally, case studies conducted on the IEEE 9-bus power system and IEEE 39-bus power system validate the feasibility of the proposed strategy.

Averaging principle for reflected stochastic evolution equations

An averaging principle for reflected stochastic evolution equations is established in this paper. To this end, we firstly construct the averaged equations corresponding to the original equations and then demonstrate, by utilizing the time discretization method, that the original equations converge to the corresponding averaged equations in probability, as the parameter goes to zero. Our model includes stochastic Navier–Stokes equations as a special example.

Breast-torso movement coordination during running in different breast support

To reduce breast motion with a bra, we need to understand what drives the motion of the breasts, and what variables change as support increases. Quantifying breast-torso coordination and movement complexity across the gait cycle may offer deeper insights than previously reported discrete time lag. We aimed to compare breast-torso coordination and mutual influence across breast support conditions during running. Twelve female participants ran on a treadmill at 10 km h−1 with an encapsulation and compression sports bra, and in no bra. Nipple and torso position was recorded. Vector coding, granger causality and transfer entropy were calculated within gait cycles. In both bra conditions, a greater percentage of gait cycles was spent with the breast and torso in-phase (> 90%) compared to no bra running (~ 66%, p < 0.001), with most time spent in-phase in the encapsulation versus compression bra (p = 0.006). There was a main effect of breast support condition on Granger causality (p < 0.001), both from breast to torso and torso to breast. Transfer of information was highest from torso to breast, compared to breast to torso in all conditions. Overall, these results provide novel insight into the mutual and complex interaction between the breast and the torso while running in different bra conditions. The approaches presented allow for a greater understanding of bra support conditions than existing discrete measures, which may relate to comfort and performance. Therefore, measures of coupling, predictability and transfer of complexity should be employed in future work examining these features.

Evaluating Numerical Stability in High-Accuracy Simulations: A Comparative Study of Time Discretization Methods for the Linear Convection Equation

Evaluating Numerical Stability in High-Accuracy Simulations: A Comparative Study of Time Discretization Methods for the Linear Convection Equation

Peridynamics modelling of projectile penetration into concrete targets

A non-ordinary state-based peridynamics (NOSB-PD) model is proposed to simulate the projectile penetration into concrete targets. In this model, the Kong-Fang concrete material model recently proposed is firstly implemented into the NOSB-PD framework to describe the complex dynamic behavior and failures in concrete material subjected to penetration loading, and then an improved point-to-volume discrete frictional contact model is proposed to simulate the physical interaction between projectile and target. After the mesh-free discretization and explicit time integration, the proposed NOSB-PD model is used to numerically predict two sets of projectile penetration experiments into low-strength and high-strength concrete targets. And numerical predictions are found to be in good agreements with corresponding test data including penetration depth, projectile deceleration, deformation of projectile and failures in concrete targets.

Numerical approximation for the MHD equations with variable density based on the Gauge-Uzawa method

In this paper, we consider the numerical approximation of incompressible magnetohydrodynamic (MHD) system with variable density. Firstly, we provide first- and second-order time discretization schemes based on the convective form of the Gauge-Uzawa method. Secondly, we prove that the proposed schemes are unconditionally stable. We also provide error estimates through rigorous theoretical analysis. Then, we construct a fully-discrete first-order scheme with finite elements in space and provide its stability result. Finally, we present some numerical experiments to validate the effectiveness of the proposed schemes. Furthermore, we also present the conserved scheme and its numerical results.

Predictors of Cigar, Cigarillo, and Little Cigar Initiation Among Hip Hop-Identifying Youth

Background: We explored predictors of cigar product initiation among Hip Hop-identifying U.S. youth using data from the U.S. Food and Drug Administration’s Fresh Empire evaluation. Participants were Hip Hop-identifying youth living in evaluation markets who had not initiated cigar product use at their first survey. Objectives: We modeled cigar product initiation odds using discrete time survival analysis logistic regression models as a function of factors related to one’s large social, physical, social/normative, and intrapersonal environment, and other tobacco use. Results: In the unique sample, 26.2% initiated cigar product use. Factors associated with higher cigar product initiation odds included: current/former (vs. non-susceptible never) cigarette smoking (odds ratio [OR]=5.35; p=.008); cigarette experimentation (vs. non-susceptible never smoking) (OR=3.26; p<.001); current (vs. never) e-cigarette use (OR=2.06; p<.001) and hookah use (OR=1.83; p=.011); having at least one friend who uses marijuana (OR=1.43; p=.008); high music use (OR=1.32; p=.035); household tobacco use (OR=1.26; p =.042); increased age (OR=1.18; p< .001); and higher sensation seeking (OR=1.16; p=.018). Youth reporting higher perceived smoking risks had lower cigar product initiation odds (OR=0.86; p=.029) as did Hispanic (OR=0.53; p<.001) and non-Hispanic Other youth (OR= 0.68; p=.023) (vs. non-Hispanic Black youth). Conclusions: The finding that high music use predicted cigar product initiation should be considered in light of cigar brand sponsorship of musical artists and events and indicates a potential opportunity for counter messaging. Peer crowd segmentation in this study identified unique and differing factors that influence tobacco use risk among Hip Hop-identifying youth that are not found in the general population.

High-order finite volume method for solving compressible multicomponent flows with Mie–Grüneisen equation of state

In this paper, we propose a new high-order finite volume method for solving the multicomponent fluids problem with Mie–Grüneisen EOS. Firstly, based on the cell averages of conservative variables, we develop a procedure to reconstruct the cell averages of the primitive variables in a high-order manner. Secondly, the high-order reconstructions employed in computing numerical fluxes are implemented in a characteristic-wise manner to reduce numerical oscillations as much as possible and obtain high-resolution results. Thirdly, advection equation within the governing system is rewritten in a conservative form with a source term to enhance the scheme’s performance. We utilize integration by parts and high-order numerical integration techniques to handle the source terms. Finally, all variables are evolved by using Runge–Kutta time discretization. All steps are carefully designed to maintain the equilibrium of pressure and velocity for the interface-only problem, which is crucial in designing a high-resolution scheme and adapting to more complex multicomponent problems. We have performed extensive numerical tests for both one- and two-dimensional problems to verify our scheme’s high resolution and accuracy.

Fractional conformal map, qubit dynamics and the Leggett–Garg inequality

Abstract A pure state of a qubit can be geometrically represented as a point on the extended complex plane through stereographic projection. By employing successive conformal maps on the extended complex plane, we can generate an effective discrete-time evolution of the pure states of the qubit. This work focuses on a subset of analytic maps known as fractional linear conformal maps. We show that these maps serve as a unifying framework for a diverse range of quantum-inspired conceivable dynamics, including (i) unitary dynamics,(ii) non-unitary but linear dynamics and (iii) \ non-unitary and non-linear dynamics where linearity (non-linearity) refers to the action of the discrete time evolution operator on the Hilbert space. We provide a characterization of these maps in terms of Leggett-Garg Inequality complemented with No-signaling in Time (NSIT) and Arrow of Time (AoT) conditions.

Community-centred disaster recovery: A call to change the narrative.

This paper challenges current approaches to undertaking community-centred disaster recovery. Community-centred approaches are widely recognised as 'the gold standard' for effective recovery from disasters. Yet, they are rarely applied well enough in practice. Challenges include the 'authority' culture of command-and-control agencies, the emphasis on discrete recovery time frames, and the reluctance to relinquish centralised control. The paper focuses on people's experiences of community-centred recovery in New South Wales, Australia, which has experienced severe fires and floods since 2019. We undertook key informant interviews and an online survey to inquire into how community-centred recovery is enacted. Our work uncovered widespread dissatisfaction with current practices. The paper discusses key themes emerging from the research and ends with a call to change how community-centred recovery is framed and conducted by responding organisations, to include the underlying causes of vulnerability in recovery, to measure success differently, and to alter the narrative of who 'owns' disasters.

Who is afraid of modelling time as a continuous variable?

Abstract Most models of ecological and eco‐evolutionary processes involve creating trajectories of something, be it population densities, average trait values, or environmental states, over time. This requires decision‐making regarding how to represent the flow of time in models. Most ecologists are exposed to continuous‐time models (typically in the form of ordinary differential equations) as part of their training, especially since the famous Lotka‐Volterra predator–prey dynamics are formulated this way. However, few appear sufficiently well trained to produce their own work with continuous‐time models and may lack exposure to the true versatility of available methods. Specifically, knowledge that discrete individuals can be modelled in continuous time using the Gillespie algorithm is not as widespread as it should be. I will illustrate the flexibility of continous‐time modelling methods such that researchers can make informed choices, and not resort to discretizing time as a ‘default’ without a clear biological motivation to do so. I provide three example‐based tutorials: (1) a comparison of deterministic and stochastic dynamics of the Lotka‐Volterra predator–prey model, (2) an evaluation of matelessness in a hypothetical insect population (and of selection to mate more often by either searching more efficiently or by shortening the ‘time out’ after each mating) and (3) within‐season density dependence followed by a birth pulse leading to Beverton‐Holt or Ricker dynamics depending on whether the deaths of conspecifics help reduce the mortality of others or not (compensatory mortality). I highlight properties of the exponential distribution that, while counter‐intuitive, are good to know when deriving expected lifetime reproductive success or other similar quantities. I also give guidance on how to proceed if the so‐called memorylessness assumption does not hold in a given situation, and show how continuous and discrete times can be freely mixed if the biological situation dictates this to be the preferred option. Continuous‐time models can also be empirically fitted to data, and I review briefly the insight this gives into the so‐called ‘do hares eat lynx?’ paradox that has been plaguing the interpretation of the Hudson Bay hare and lynx dataset.