The estimation of State-of-Charge (SoC) is crucial for the safe and efficient operation of battery management systems (BMS), but no single method is able to reliably estimate the SoC under all operating conditions. In this paper, a hybrid estimator based on the Extended Kalman Filter (EKF) and Sliding Mode Observer (SMO) is presented by employing a gated bumpless-transfer switching technique for the SoC estimation of a Lithium-ion battery. The EKF generates accurate estimates when the operating condition is normal, and the SMO is triggered when the measurement innovation is larger than an adaptive threshold, enabling the EKF to provide accurate estimates when large initial SoC error, high measurement noise, and transient sensor faults exist. In this paper, a second-order RC equivalent circuit model (ECM) of a 2.6 Ah lithium-ion cell was used to implement the proposed hybrid estimator as well as the EKF-only, SMO-only, and Coulomb counting methods. The results indicate that the hybrid EKF–SMO estimator does not significantly outperform a well-tuned EKF in an ideal Gaussian noise environment; however, it is significantly more robust against faults in the sensors and large uncertainty, which is suitable for practical BMS applications.
This paper examines the conceptual and methodological parallels and divergences between two paradigms of pursuit-evasion: the discrete “cops and robbers” game on graphs and continuous-time pursuit differential games as developed by Isaacs [4]. We first review the foundations of differential games in Isaacs’ treatise, with emphasis on the Homicidal Chauffeur model and on geometric and integral constraints on the controls. We then trace the origins of the cops and robbers game as formulated by Quilliot [30] and Nowakowski-Winkler [28], highlighting graph dismantlability and its equivalence to cop-win graphs. Extensions to infinite graphs and to visibility graphs of polygons are surveyed, focusing on results by Lubiw et al. [40] and Bonato-Nowakowski [41]. We also discuss pursuit differential games described by infinite systems of first-order equations in Hilbert spaces (Ibragimov et al. [39, 50]) and games with integral constraints (Mai Umar et al. [48]), as well as Luckraz’s work [43] relating cops and robbers to extensive and stochastic games. We then introduce a common reachability framework for both paradigms: we characterize the cop’s winning region on a finite graph as the least fixed point of a controllable-predecessor operator, show that folding a dominated vertex delays capture by at most one round, and relate these sets to capture basins and discriminating kernels of differential games. Finally, we compare the two paradigms with respect to information, timing, speed constraints and computational complexity, and identify open problems.
This academic research first provides a foundational overview of hypergeometric differential equations and hypergeometric functions in specific regions of the complex plane. Building on this foundation, it develops a comprehensive set of results that reveal various relationships between the relevant classes of equations and functions, supported by carefully formulated propositions, deductions, and illustrative examples. In particular, this study emphasizes the logical consistency among the analysis, theoretical results, and applications, demonstrating how these relationships extend existing perspectives in hypergeometric theory. Moreover, the study concludes with key deductions and recommendations based on the findings, suggesting potential directions for future research. In light of the references cited, the contributions of this work aim to promote a broader understanding of hypergeometric structures and their applications in complex analysis and related fields.
The paper considers the model of a heterogeneous queuing system H K ( t ) / M / ∞ and limit evolutions in the averaging and diffusion approximation scheme. The input process of the system under study is modelled as a mixture of independent heterogeneous Poisson processes, which reflects the behaviour of modern cloud serverless platforms, where tasks arrive simultaneously from different event sources (HTTP gateways, object stores, message queues, event buses). Based on the apparatus of semi-Markovian random evolutions, the weak convergence of the queue length process L ( t ) in two asymptotic schemes: averaging (law of large numbers) and diffusion approximation (central limit theorem), with the Ornstein–Uhlenbeck limit process, is proved. As a result, simple analytical estimates of the queue length L ( t ) and the probability of exceeding the maximum length P ( sup t ∈ [ 0 , T ] L ( t ) < L MAX ) are constructed. Also, a necessary and sufficient condition for the queue's finiteness is expressed in terms of the parameters of the input and task-processing processes. The results obtained enable us to develop analytical methods for parameter estimation and predictive scaling for complex serverless systems in cloud environments, without the need to train models or neural networks on large amounts of data.
The advent of competitive power markets in recent decades has facilitated a substantial rise in transactions between producers and consumers to meet the rapidly growing load demand. Power transactions in modern electricity markets are carried out through bilateral or multilateral agreements, either directly between market participants or through common trading platforms. These transactions require the transmission network to transfer electricity from generating stations to consumers, and excessive power transfers may lead to congestion when line capacity limits are exceeded. Such congestion affects the secure and economical execution of scheduled transactions and may increase operating costs. Therefore, the Independent System Operator (ISO) plays an important role in maintaining reliable system operation by managing congestion and ensuring that all network security constraints are satisfied. This study aims to reduce transmission congestion by controlling overloaded line flows, maintaining operational limits, improving system stability, and minimizing transmission losses. Generator Sensitivity Factor (GSF) is used to identify the generating units that significantly influence congested transmission lines and require suitable rescheduling. Two enhanced Monarch Butterfly Optimization approaches, namely Improved MBO with a Linear Weighting factor (IMBO-LW) and Chaos-Embedded MBO (CHMBO), are employed to determine optimal generator rescheduling strategies. The proposed methods simultaneously minimize rescheduling cost and changes in generator power output. Their performance is evaluated using standard benchmark functions and further validated on a modified IEEE 30-bus test system, demonstrating their effectiveness in achieving secure, reliable, and economically efficient congestion management.
