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The objective of this paper was to present a new inverse problem statement and numerical method for the Volterra integral equations with piecewise continuous kernels. For such Volterra integral equations of the first kind, it is assumed that kernel discontinuity curves are the desired ones, but the rest of the information is known. The resulting integral equation is nonlinear with respect to discontinuity curves which correspond to integration bounds. A direct method of discretization with a posteriori verification of calculations is proposed. The family of quadrature rules is employed for approximation purposes. It is shown that the arithmetic complexity of the proposed numerical method is O (N 3) . The method has first-order convergence. A generalization of the method is also proposed for the case of an arbitrary number of discontinuity curves. The illustrative examples are included to demonstrate the efficiency and accuracy of proposed solver. [ABSTRACT FROM AUTHOR]

The difficulties in implementing the model predictive control (MPC) in interior permanent-magnet synchronous motors (IPMSMs) consist of the nonlinear behavior of IPMSMs and the computational effort required by MPC. This paper presents an IPMSM controller design method for electric vehicles based on explicit MPC (EMPC), which uses a different linearization method. The proposed controller combines the speed and current controllers and replaces the traditional cascade structure. First, the nonlinear terms in the system model are added into the control input as voltage compensation to obtain a simple linear model. Next, the proposed controller based on MPC is designed, which considers the effects of load torque and uses an increment model. Furthermore, the controller applies both current and voltage constraints. The EMPC method based on a binary search is used to accelerate the solution of the optimization problem. Finally, the simulation results show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

The efficient construction and employment of block operators are vital for contemporary computing, playing an essential role in various applications. In this paper, we prove a generalisation of the Frobenius formula in the setting of the theory of block operators on normed spaces. A system of linear equations with the block operator acting in Banach spaces is considered. Existence theorems are proved, and asymptotic approximations of solutions in regular and irregular cases are constructed. In the latter case, the solution is constructed in the form of a Laurent series. The theoretical approach is illustrated with an example, the construction of solutions for a block equation leading to a method of solving some linear integrodifferential system. [ABSTRACT FROM AUTHOR]

At present, the entire world is moving towards digitalization, including in the electric power industry. Digitalization is in its heyday and a lot of articles and reports are devoted to this topic. At the same time, the least digitalized of the electrical networks are distribution networks that account for a very large share in electric power systems. The article proposes a methodology for creating a flexible distribution network based on the use of digital technology. Additionally, we elaborate a methodology with the identification and collection of the necessary information to create digital networks, develop ways to adapt the required equipment, and suggest methods of recognition of some short circuits. Furthermore, we address the issue of reliability of the information obtained from digital devices, develop a technique for arranging the devices to cover the entire network as required to improve the power system protection of electrical power distribution networks. The above measures make it possible to ensure the flexibility of the active distribution network, as well as to adjust the parameters of the actuation of power system protection depending on changes in external conditions and in the event of emergencies. We propose a technique for controlling the distribution network, based on the factoring-in of the type of damage during an emergency in real time, as well as a technique for arranging the measuring devices and the creation of an information and communication network. We provide recommendations for the design and operation of electric power distribution networks with digital network control technology. [ABSTRACT FROM AUTHOR]

We prove the logarithmic convergence rate of the families of usual and modified iterative Runge-Kutta methods for nonlinear ill-posed problems between Hilbert spaces under the logarithmic source condition, and numerically verify the obtained results. The iterative regularization is terminated by the a posteriori discrepancy principle. [ABSTRACT FROM AUTHOR]

The online estimation of battery state of health (SOH) is crucial to ensure the reliability of the energy supply in electric and hybrid vehicles. An approach for enhancing the generalization of SOH estimation using a parallel layer extreme learning machine (PL-ELM) algorithm is analyzed in this paper. The deterministic and stable PL-ELM model is designed to overcome the drift problem that is associated with some conventional machine learning algorithms; hence, extending the application of a single SOH estimation model over a large set of batteries of the same type. The PL-ELM model was trained with selected features that characterize the SOH. These features are acquired as the discrete variation of indicator variables including voltage, state of charge (SOC), and energy releasable by the battery. The model training was performed with an experimental battery dataset collected at room temperature under a constant current load condition at discharge phases. Model validation was performed with a dataset of other batteries of the same type that were aged under a constant load condition. An optimum performance with low error variance was obtained from the model result. The root mean square error (RMSE) of the validated model varies from 0.064% to 0.473%, and the mean absolute error (MAE) error from 0.034% to 0.355% for the battery sets tested. On the basis of performance, the model was compared with a deterministic extreme learning machine (ELM) and an incremental capacity analysis (ICA)-based scheme from the literature. The algorithm was tested on a Texas F28379D microcontroller unit (MCU) board with an average execution speed of 93 μs in real time, and 0.9305% CPU occupation. These results suggest that the model is suitable for online applications. [ABSTRACT FROM AUTHOR]

This paper provides a literature review of some of the most important concepts, techniques, and methodologies used within autonomous car systems. Specifically, we focus on two aspects extensively explored in the related literature: tracking, i.e., identifying pedestrians, cars or obstacles from images, observations or sensor data, and prediction, i.e., anticipating the future trajectories and motion of other vehicles in order to facilitate navigating through various traffic conditions. Approaches based on deep neural networks and others, especially stochastic techniques, are reported. [ABSTRACT FROM AUTHOR]

An integro-differential equation describes the non-equilibrium thermal response of glass-forming substances with a dynamic (time-dependent) heat capacity to fast thermal perturbations. We found that this heat transfer problem could be solved analytically for a heat source with an arbitrary time dependence and different geometries. The method can be used to analyze the response to local thermal perturbations in glass-forming materials, as well as temperature fluctuations during subcritical crystal nucleation and decay. The results obtained can be useful for applications and a better understanding of the thermal properties of glass-forming materials, polymers, and nanocomposites. [ABSTRACT FROM AUTHOR]

This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR]

The importance of efficient utilization of biomass as renewable energy in terms of global warming and resource shortages are well known and documented. Biomass gasification is a promising power technology especially for decentralized energy systems. Decisive progress has been made in the gasification technologies development during the last decade. This paper deals with the control and optimization problems for an isolated microgrid combining the renewable energy sources (solar energy and biomass gasification) with a diesel power plant. The control problem of an isolated microgrid is formulated as a Markov decision process and we studied how reinforcement learning can be employed to address this problem to minimize the total system cost. The most economic microgrid configuration was found, and it uses biomass gasification units with an internal combustion engine operating both in single-fuel mode (producer gas) and in dual-fuel mode (diesel fuel and producer gas). [ABSTRACT FROM AUTHOR]