In existing scheduling systems, processing times and energy consumption during the production scheduling process are typically determined based on workers’ experience. However, in real manufacturing environments, various environmental factors often cause these values to deviate from those used in the actual scheduling systems. Therefore, to investigate the impact of uncertainty-induced fluctuations on completion time and energy consumption, Interval Grey Numbers (IGNs) are used to represent processing times and energy consumption. Furthermore, considering the characteristics of the machines, the effects of varying processing speeds on processing time and energy consumption are studied within the framework of IGNs. To address the flexible job shop scheduling problem with IGNs and variable processing speeds (GVPS-FJSP), a two-stage reinforcement learning algorithm based on evolutionary strategy (BES-TRL) is proposed. The algorithm incorporates five initialization strategies to generate diverse sets of initial solutions and designs and five targeted neighborhood structures during the iterative stage to ensure that high-quality solutions gradually converge to the Pareto front. In the numerical experiments, the effectiveness of the designed operators and the BES-TRL algorithm is first validated. Finally, comparison experiments with other advanced algorithms demonstrate the effectiveness and usefulness of the BES-TRL algorithm in solving the GVPS-FJSP problem. Additionally, a case study is conducted to verify the practical applicability of the algorithm in real-world production scenarios. Case study on IMK20 shows that the algorithm can reduce energy consumption by 19.7% when production time is sufficient and shorten the makespan by 14.6% when production time is insufficient, which verifies its practical applicability and effectiveness.
The incorporation of renewable energy sources (RES) into grid-connected microgrids, especially in the manufacturing industry, has added significant complications to power generation forecasting, control, and management. As microgrids rely on RES, such as solar and wind power, there is a crucial need for more accurate energy predictions and better management systems. Research investigates the use of ML methods, particularly Adaptive tunicate swarm optimized random forests (ATSO-RF), to increase the efficacy and reliability of microgrid power systems in the manufacturing industry. It utilizes historical energy generation data, weather patterns, and dynamic grid conditions to create a sophisticated model for power generation forecasting and management systems. Pre-processing with Z-score normalization and Linear Discriminant Analysis (LDA) was used to reduce the number of topographies by decreasing variance across different energy states or microgrid conditions, thereby allowing for more accurate energy forecasting classification. The ATSO-RF algorithm outperforms traditional models by providing better predictive accuracy and improved energy management. The proposed method is implemented by using Python 3.10.1. In a comparative analysis, the suggested method is assessed with various evaluation measures, such as R-squared (96.85%), MAE (3.01), and RMSE (4.81). The proposed model improves energy forecasting, allowing for better energy production planning and scheduling, decreasing reliance on external power sources, and increasing cost savings within the manufacturing industry. Additionally, the greater forecasting capabilities permit real-time adaptive energy management, which contributes to maintaining the grid, reducing peak load demand, and enhancing the utilization of RES and energy management in microgrids.
We study nonlinear Caputo–Katugampola fractional differential equations with general causal deviating arguments and prescribed histories. The problem is first written as an equivalent Volterra–Katugampola equation on the causal phase space [Formula: see text]. Under standard local or global Lipschitz hypotheses we establish local well-posedness, finite-horizon continuation, continuous dependence on the history, and an explicit residual-to-solution stability estimate. Computation is organized in three complementary layers: a beta-kernel Caputog marching method for differential-residual certification, a PECE product-integration solver for the Volterra equation, and shifted-Chebyshev surrogates. For an affine pantograph benchmark, the Caputog differential residual is [Formula: see text], while the PECE discrete Volterra residual is [Formula: see text]; on [Formula: see text], a degree-13 Chebyshev surrogate agrees with the PECE trajectory to below [Formula: see text]. A new fixed-step horizon study on [Formula: see text] confirms causal prefix invariance and shows that a fixed-degree global surrogate loses accuracy as the interval grows. We also delineate which parts of the framework transfer to Caputo, Caputo–Hadamard, Hilfer, Atangana–Baleanu, and Erdélyi–Kober operators.
This study examines the exponential stability of singularly perturbed systems with unknown dynamics and bounded disturbances within a data-driven framework. Instead of relying on an explicit mathematical model of the plant, the proposed method designs the controller based solely on measured input-state data collected offline. The controller design problem is cast as the feasibility of a single linear matrix inequality (LMI), whose feasibility ensures semi-global practical exponential stability of the resulting closed-loop system. An explicit algorithm is further developed to construct a stabilizing feedback gain directly from data, without requiring system identification or model reconstruction. In addition, the allowable ranges of the decision variables and disturbance-related parameters are characterized, which provides insight into the feasible design region and clarifies how robustness is preserved under bounded uncertainties. In this way, the proposed approach offers a fully model-free control strategy for singularly perturbed systems subject to disturbances, while ensuring exponential stability performance. Finally, a case study on a subsystem of a switched electrical circuit is presented to demonstrate the effectiveness of the proposed method. Simulation results show that the closed-loop system maintains stability and exhibits satisfactory performance despite the presence of disturbances.
Power systems that incorporate renewable energy sources such as photovoltaic and wind energy, battery storage, and traditional generators to form hybrid power systems need effective management to ensure power balance and minimize operating costs. However, the intermittency of renewable resources and uncertainty in load demand make conventional rule-based or optimization-based control methods less effective in dynamic environments. This paper proposes an adaptive energy management approach based on Deep Q-Network (DQN) reinforcement learning for hybrid power systems. The energy management problem is formulated as a Markov Decision Process (MDP), where system states include renewable generation levels, battery state-of-charge, load demand, and diesel generator status. The DQN agent learns an optimal control policy by interacting continuously with the environment and optimizing a reward function focused on fuel cost minimization, reducing power deficit, and maximizing renewable energy utilization. Experimental results show that the proposed method achieves 90.4% system efficiency, reduces power shortage to 172.5 kWh, increases renewable energy penetration to 55%, and reduces CO 2 emissions to 290.3 kg compared with the conventional strategy, while achieving a lower loss of load probability of 33.3% than the compared energy management strategies.
