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In this paper, we developed a novel numerical method for solving general nonlinear fractional ordinary differential equations (FODEs). First, we transformed the nonlinear FODEs into the equivalent Volterra integral equations. We then developed a time-stepping algorithm for the numerical solution of the Volterra integral equations based on the third-order Taylor expansion for approximating the integrands in the Volterra integral equations on a chosen mesh with the mesh parameter $ h $. This approximation led to implicit nonlinear algebraic equations in the unknowns at each given mesh point, and an iterative algorithm based on Newton's method was developed to solve the resulting implicit equations. A convergence analysis of this numerical scheme showed that the error between the exact solution and numerical solution at each mesh point is $ \mathcal{O}(h^{3}) $, independent of the fractional order. Finally, four numerical examples were solved to verify the theoretical results and demonstrate the effectiveness of the proposed method.

Abstract The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples.

Abstract Issue COVID-19 has resulted in mortality worldwide and exposed vulnerabilities in public health systems. Although countries have since transitioned to the endemic phase, it is nonetheless important to identify inequities within populations to improve public health strategies in light of another health crisis. Purpose This study aims to offer deeper insights into the sex and age differentials in COVID-19 fatality across different states in Malaysia, from the pandemic’s start to the country’s transition to the endemic phase. Methodology Analyses utilized data on the number of COVID-19 cases and deaths in Malaysia from January 2020 until April 2022. Case fatality rate (CFR) was computed for each state based on sex and age groups, for four periods (January–December 2020, January–June 2021, July–December 2021, and January–April 2022). Principal component analysis (PCA) uncovered patterns in the data and produced a multivariate visualization of the COVID-19 fatality within Malaysia. Findings Findings revealed heterogeneity in fatality and identified several vulnerable states, notably in the northern region (Kelantan, Perlis) and on the East Coast (Sabah, Sarawak). A sex disparity was apparent in Kelantan as the CFR among older females was higher than their male counterparts. Sabah exhibited relatively higher CFR among the child population from 2020 to 2021. Implication The findings deepened our understanding of COVID-19 fatality complexity, providing recommendations for Malaysia’s government in preparing for future health crises. Malaysia’s case study offers lessons on the need to address regional disparities and implement targeted strategies to protect vulnerable subgroups.

Abstract The problem of blood transshipment and allocation in the context of the COVID-19 epidemic has many new characteristics, such as two-stage, trans-regional, and multi-modal transportation. Considering these new characteristics, we propose a novel multi-objective optimization model for the two-stage emergent blood transshipment-allocation. The objectives considered are to optimize the quality of transshipped blood, the satisfaction of blood demand, and the overall cost including shortage penalty. An improved integer encoded hybrid multi-objective whale optimization algorithm (MOWOA) with greedy rules is then designed to solve the model. Numerical experiments demonstrate that our two-stage model is superior to one-stage optimization methods on all objectives. The degree of improvement ranges from 0.69 to 66.26%.

Abstract This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous‐time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient‐based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real‐world practical problem involving a bioreactor tank model is solved using the method proposed.

In this paper, a financial risk model, which is formulated from the risk management process of financial markets, is studied. By considering the presence of Gaussian white noise, the financial risk model is reformulated as a stochastic optimal control problem. On this basis, two efficient computational approaches for state estimation, which are the extended Kalman filter (EKF) and unscented Kalman filter (UKF) approaches, are applied. Later, based on the state estimate given by the EKF and UKF approaches, a linear feedback control policy is designed from the stationary condition. For illustration, some parameter values and the initial conditions of the financial risk model are used for the simulation of the stochastic optimal control problem. From the results, it is noticed that the UKF algorithm provides a better state estimate with a smaller value of the sum of squared errors (SSE) as compared to the SSE given by the EKF algorithm. Thus, the estimated output trajectory has a high accuracy that is close to the real output. Moreover, the control effort assists in estimating the state dynamics at the minimum cost. In conclusion, the efficiency of the computational approaches for optimal control of the financial risk model has been well presented.

An unmanned surface vehicles (USV) set point tracking problem is investigated in this paper. The stochastic model predictive control (SMPC) scheme is utilized to design the controller in order to reject the environment disturbances and meet the physical constraints. The design problem is formulated as a chance-constrained stochastic optimization problem, which is non-convex. Thus, the problem is computationally prohibitive. For this, the convex conditional value at risk (CVaR) approximation is introduced to convert the chance constraints into deterministic convex constraints. The converted constraints are then further transformed into the second order cone (SOC) constraints. Therefore, the proposed method is computationally tractable and hence can be implemented online. A numerical example is provided to illustrate the effectiveness of the proposed method.

In the study of many real-world problems such as engineering design and industrial process control, one often needs to select certain elements/controls from a feasible set in order to optimize the design or system based on certain criteria [...]

BackgroundThe aim of the study was to visualize the global spread of the COVID-19 pandemic over the first 90 days, through the principal component analysis approach of dimensionality reduction.MethodsThis study used data from the Global COVID-19 Index provided by PEMANDU Associates. The sample, representing 161 countries, comprised the number of confirmed cases, deaths, stringency indices, population density and GNI per capita (USD). Correlation matrices were computed to reveal the association between the variables at three time points: day-30, day-60 and day-90. Three separate principal component analyses were computed for similar time points, and several standardized plots were produced.ResultsConfirmed cases and deaths due to COVID-19 showed positive but weak correlation with stringency and GNI per capita. Through principal component analysis, the first two principal components captured close to 70% of the variance of the data. The first component can be viewed as the severity of the COVID-19 surge in countries, whereas the second component largely corresponded to population density, followed by GNI per capita of countries. Multivariate visualization of the two dominating principal components provided a standardized comparison of the situation in the161 countries, performed on day-30, day-60 and day-90 since the first confirmed cases in countries worldwide.ConclusionVisualization of the global spread of COVID-19 showed the unequal severity of the pandemic across continents and over time. Distinct patterns in clusters of countries, which separated many European countries from those in Africa, suggested a contrast in terms of stringency measures and wealth of a country. The African continent appeared to fare better in terms of the COVID-19 pandemic and the burden of mortality in the first 90 days. A noticeable worsening trend was observed in several countries in the same relative time frame of the disease's first 90 days, especially in the United States of America.

In this paper, we construct a regional logistics model from a macroperspective. First, based on the gravity model, the index of logistics attraction between cities is established as the weight of the model, and hence the regional logistics weighted model is constructed. Next, we use the social network analysis method to analyze its structure and make specific recommendations for the construction of logistics networks. Finally, we analyze the model’s response to random attacks and deliberate attacks. From our study, it is found that when the failure nodes or edges reach a certain percentage, the regional logistics network will collapse on a large scale. Therefore, it is important to optimization the threshold of the regional logistics network. This clearly provides a new perspective for the study of the regional logistics networks.

This manuscript addresses a new multivariate generalized predictive control strategy using the least squares support vector machine for parabolic distributed parameter systems. First, a set of proper orthogonal decomposition-based spatial basis functions constructed from a carefully selected set of data is used in a Galerkin projection for the building of an approximate low-dimensional lumped parameter systems. Then, the temporal autoregressive exogenous model obtained by the least squares support vector machine is applied in the design of a multivariate generalized predictive control strategy. Finally, the effectiveness of the proposed multivariate generalized predictive control strategy is verified through a numerical simulation study on a typical diffusion-reaction process in radical symmetry.

Genetic information, such as single nucleotide polymorphism (SNP) data, has been widely recognized as useful in prediction of disease risk. However, how to model the genetic data that is often categorical in disease class prediction is complex and challenging. In this paper, we propose a novel class of nonlinear threshold index logistic models to deal with the complex, nonlinear effects of categorical/discrete SNP covariates for Schizophrenia class prediction. A maximum likelihood methodology is suggested to estimate the unknown parameters in the models. Simulation studies demonstrate that the proposed methodology works viably well for moderate-size samples. The suggested approach is therefore applied to the analysis of the Schizophrenia classification by using a real set of SNP data from Western Australian Family Study of Schizophrenia (WAFSS). Our empirical findings provide evidence that the proposed nonlinear models well outperform the widely used linear and tree based logistic regression models in class prediction of schizophrenia risk with SNP data in terms of both Types I/II error rates and ROC curves.

This paper is concerned with the boundedness and attractiveness of nonlinear switched delay systems whose subsystems have different equilibria. Some sufficient conditions which can guarantee the system’s boundedness are obtained. In addition, we work out the region where the solution will remain and furthermore the relationship between the initial function and the bounded region. Based on the new concept of attractor with switching laws, we show that the nonlinear switched delay system is attractive and then obtain the attractive region.

We introduce and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces. Not only the existence of approximate solutions of the equilibrium problem is proven, but also the strong convergence of approximate solutions to an exact solution of the equilibrium problem is shown. Furthermore, we give some iterative schemes for solving some generalized mixed variational-like inequalities to illuminate our results.

Envelope constrained filter design is concerned with the time domain synthesis of a filter whose response to a specified input signal stays within prescribed upper and lower bounds and in addition has minimal noise enhancement. In many practical applications, a ``soft`` approach, such as least mean square, is not the most suitable and it becomes necessary to use ``hard`` constraints such as the ones considered in the paper. We present an overview of key ideas related to robust continuous time envelope constrained filter design.

For a multi-switching system, it consists of multiple parallel switching systems. The optimal control problem controlled by a multi-switching system is to determine the optimal time sequence for each of the parallel switching systems. The time-scaling transformation is a well-known switching time optimization approach which has been widely used in various problem settings. However, the time-scaling transformation requires that these parallel switching systems have the same number of subsystems and are designed to switch simultaneously. Thus, it is not applicable for solving optimal control problems of general multi-switching systems. This paper presents a new technique for optimizing the switching times of multi-switching systems. [ABSTRACT FROM AUTHOR]

The optimal design of finite impulse response (FIR) filters is considered with coefficients expressed as sums of signed powers-of-two (SPT) terms. Problems are transformed into equivalent integer programming problem and solved using discrete filled function.

Several new optimization approaches that include the finite word-length properties of the overall filter into the optimization process are developed. These new approaches produce filters with excellent finite word-length performance with almost no degradation in frequency response performance.

An efficient algorithm for solving semi-infinite programming problems is proposed. The application of the algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, reduces the time required to obtain a globally optimal solution as compared with that of the previous proposed algorithm.

The optimized design of interpolative sigma delta modulators is considered and the objective is to minimize the passband energy of the denominator of the loop filter transfer function depending on the continuous constraint of the function defined in frequency domain. The results showed that the design gives a larger improvement in the signal-to-noise ratio and have a larger stability range as compared to the existing designs.

A magnitude design of rational infinite impulse response filters is formulated as a nonsmooth nonconvex optimization problem with continuous functional constraints. The experiments conducted show small transition bandwidth filters are obtained.

The Davies transformation is a method that transforms the steering vector of a uniform circular array (UCA) to one with Vandermonde form. This method allows techniques such as spatial smoothing for direction-of-arrival (DOA) estimation in a correlated signal environment, developed originally for uniform linear arrays, to be applied to UCAs.

An optimum nonuniform finite impulse response (FIR) transmultiplexer design problem subject to specifications in the frequency domain is considered to minimize the sum of the ripple energy for all the individual filters, subject to the specifications on amplitude and aliasing distortions and to the passband and stopband specifications for the individual filters.

In this paper, we consider a nonlinear time-delay dynamic (NTDD) system with uncertain time-delay in batch culture of glycerol bioconversion to 1; 3-propanediol (1;3-PD) induced by Klebsiella pneumoniae. Our goal is to design an optimization scheme for the NTDD system with the aim of balancing two competing objectives: (i) system cost (the relative error between experimental data and the output of the mathematical model); (ii) system sensitivity (the variation of the system cost with respect to uncertain time-delay). Thus, a multi-objective optimization problem (MOOP) governed by the NTDD system and subject to continuous state inequality constraints is proposed, where the two competing objective functions are to be minimized. The optimization variables in this problem are the initial concentrations of biomass and glycerol along with the free terminal time. The MOOP is first converted into a sequence of single-objective optimization problems (SOOCPs) by using convex weighted sum and modified normal boundary intersection methods. By incorporating the time scaling transformation, the constraint transcription and locally smoothing approximation, a parallel hybrid SOOCP solver is developed based on gradient-based method and genetic algorithm. Finally, numerical results are provided to verify the effectiveness of the proposed solution method. [ABSTRACT FROM AUTHOR]

The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier transform coefficients outside the δ wave band, the θ wave band, the α wave band, the β wave band and the γ wave band. Second, the singular spectrum analysis is performed on the filtered electroencephalogram to obtain the singular spectrum analysis components. The singular spectrum analysis components are sorted according to the magnitudes of their corresponding eigenvalues. The singular spectrum analysis components are sequentially added together starting from the last singular spectrum analysis component. If the variance of the summed singular spectrum analysis component under the unit energy normalization is larger than a threshold value, then the summation is terminated. The summed singular spectrum analysis component forms the first scale of the electroencephalogram. The rest singular spectrum analysis components are also summed up together separately to form the residue of the electroencephalogram. Next, the low-rank decomposition is performed on the residue of the electroencephalogram to obtain both the low-rank component and the sparse component. The low-rank component is added to the previous scale of the electroencephalogram to obtain the next scale of the electroencephalogram. Finally, the above procedures are repeated on the sparse component until the variance of the current scale of the electroencephalogram under the unit energy normalization is larger than another threshold value. The computer numerical simulation results show that the spike suppression performance based on our proposed method outperforms that based on the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper considers a dynamic optimization problem for a class of switched systems characterized by two key attributes: (i) the switching mechanism is invoked automatically when the state variables satisfy certain switching conditions; and (ii) the subsystem dynamics involve time-delays in the state variables. The decision variables in the problem, which must be selected optimally to minimize system cost, consist of a set of time-invariant system parameters in the initial state functions. To solve the dynamic optimization problem, we first show that the partial derivatives of the system state with respect to the system parameters can be expressed in terms of the solution of a set of variational switched systems. Then, on the basis of this result, we develop a gradient-based optimization algorithm to determine the optimal parameter values. Finally, we validate the proposed algorithm by solving an example problem arising in the production of 1,3-propanediol. [ABSTRACT FROM AUTHOR]

This article studies KL*-stability (the stability expressed by KL*-class function) for a class of hybrid dynamical systems (HDS). The notions ofKL*K*-property and KL*-stability are proposed for HDS with respect to the hybrid-event-time. The KL*-stability, which is based on K or L property of the continuous flow, the discrete jump and the event in an HDS, extends theKLL-stability and the event-stability reported in the literature for HDS. The relationships between KL*K*-property and KL*-stability are established via introducing the hybrid dwell-time condition (HDT). The HDT generalizes the average dwell-time condition in the literature. For an HDS with KL*K*-property consisting of stabilizing L-property and destabilizing K-property, it is shown that there exists a common HDT under which the HDS will achieve KL*-stability. Thus HDT may help to derive some easily tested conditions for HDS to achieve uniform asymptotic stability. Moreover, a criterion ofKL*-stability is derived by using the multiple Lyapunov-like functions. Examples are given to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The blending operation is a key process in alumina production. The real-time optimization (RTO) of finding an optimal raw material propor- tioning is crucially important for achieving the desired quality of the product. However, the presence of uncertainty is unavoidable in a real process, lead- ing to much dificulty for making decision in real-time. This paper presents a novel robust real-time optimization (RRTO) method for alumina blending operation, where no prior knowledge of uncertainties is needed to be utilized. The robust solution obtained is applied to the real plant and the two-stage operation is repeated. When compared with the previous intelligent optimiza- tion (IRTO) method, the proposed two-stage optimization method can better address the uncertainty nature of the real plant and the computational cost is much lower. From practical industrial experiments, the results obtained show that the proposed optimization method can guarantee that the desired quality of the product quality is achieved in the presence of uncertainty on the plant behavior and the qualities of the raw materials. This outcome suggests that the proposed two-stage optimization method is a practically significant approach for the control of alumina blending operation. [ABSTRACT FROM AUTHOR]

In this paper, we present a dynamic pricing model for two firms selling products displaying network effects for which consumers are with bounded rationality. We formulate this model in the form of differential games and derive the open-loop equilibrium prices for the firms. Then, we show the existence and uniqueness of such open-loop equilibrium prices. The model is further extended to the case with heterogeneous network effects. Their steady-state prices obtained are compared. A numerical example is solved and the results obtained are used to analyze how the steady-state prices and market shares of both firms are influenced by the cost, price sensitivity and the network effects of the products. [ABSTRACT FROM AUTHOR]