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With the rapid development of renewable energy and the continuous pursuit of efficient energy utilization, distributed photovoltaic power generation has been widely used in village-level microgrids. As a key platform connecting distributed photovoltaics with users, energy storage systems play an important role in alleviating the imbalance between supply and demand in VMG. However, current energy storage systems rely heavily on lithium batteries, and their frequent charging and discharging processes lead to rapid lifespan decay. To solve this problem, this study proposes a hybrid energy storage system combining supercapacitors and lithium batteries for VMG, and designs a hybrid energy storage scheduling strategy to coordinate the “source–load–storage” resources in the microgrid, effectively cope with power supply fluctuations and slow down the life degradation of lithium batteries. In order to give full play to the active support ability of supercapacitors in suppressing grid voltage and frequency fluctuations, the scheduling optimization goal is set to maximize the sum of the virtual inertia time constants of the supercapacitor. In addition, in order to efficiently solve the high-complexity model, the reason for choosing the snow goose algorithm is that compared with the traditional mathematical programming methods, which are difficult to deal with large-scale uncertain systems, particle swarm optimization, and other meta-heuristic algorithms have insufficient convergence stability in complex nonlinear problems, SGA can balance global exploration and local development capabilities by simulating the migration behavior of snow geese. By improving the convergence effect of SGA and constructing a multi-objective SGA, the effectiveness of the new algorithm, strategy and model is finally verified through three cases, and the loss is reduced by 58.09%, VMG carbon emissions are reduced by 45.56%, and the loss of lithium battery is reduced by 40.49% after active support optimization, and the virtual energy inertia obtained by VMG from supercapacitors during the scheduling cycle reaches a total of 0.1931 s. Full article

The subject of this paper is the computational homogenisation and identification of heterogeneous materials in the form of auxetic structures made of materials with nonlinear characteristics. It is assumed that some of the material and topological parameters of the auxetic structures are uncertain and are modelled as interval numbers. Directed interval arithmetic is used to minimise the width of the resulting intervals. The finite element method is employed to solve the boundary value problem, and artificial neural network response surfaces are utilised to reduce the computational effort. In order to solve the identification task, the Pareto approach is adopted, and a multi-objective evolutionary algorithm is used as the global optimisation method. The results obtained from computational homogenisation under uncertainty demonstrate the efficacy of the proposed methodology in capturing material behaviour, thereby underscoring the significance of incorporating uncertainty into material properties. The identification results demonstrate the successful identification of material parameters at the microscopic scale from macroscopic data involving the interval description of the process of deformation of auxetic structures in a nonlinear regime. Full article

This paper investigates a class of uncertain fractional-order delayed cellular neural networks (UFODCNNs) with fuzzy operators and nonlinear activations. Both fuzzy AND and fuzzy OR are considered, which help to improve the robustness of the model when dealing with various uncertain problems. To achieve the finite-time (FT) synchronization and Mittag–Leffler synchronization of the concerned neural networks (NNs), a nonlinear adaptive controller consisting of three information feedback modules is devised, and each submodule performs its function based on current or delayed historical information. Based on the fractional-order comparison theorem, the Lyapunov function, and the adaptive control scheme, new FT synchronization and Mittag–Leffler synchronization criteria for the UFODCNNs are derived. Unlike previous feedback controllers, the control strategy proposed in this article can adaptively adjust the strength of the information feedback, and partial parameters only need to satisfy inequality constraints within a local time interval, which shows our control mechanism has a significant advantage in conservatism. The experimental results show that our mean synchronization time and variance are $11.397\%$ and $12.5\%$ lower than the second-ranked controllers, respectively. Full article

The Minimum Spanning Tree (MST) problem addresses the challenge of identifying optimal network pathways for critical infrastructure systems, including transportation grids, communication backbones, power distribution networks, and reliability optimization frameworks. However, inherent uncertainties stemming from disruptive events demand robust analytical models for effective decision-making. This research introduces an uncertainty-theoretic framework to assess MST stability in uncertain network environments through novel constructs: lower set tolerance (LST) and dual lower set tolerance (DLST). Both LST and DLST provide quantifiable measures characterizing the resilience of element sets relative to edge-weighted MST configurations. LST captures the maximum simultaneous risk variation preserving current MST optimality, while DLST identifies the minimal variation required to invalidate it. We evaluate MST robustness by integrating uncertain reliability measures and risk factors, with emphasis on computational methods for set tolerance determination. To overcome computational hurdles in set tolerance derivation, we establish bounds and exact formulations within an uncertainty programming paradigm, offering enhanced efficiency compared with conventional re-optimization techniques. Full article

Unmanned aerial vehicles (UAVs) operating in uncertain environments must plan safe and efficient trajectories while avoiding obstacles. This work addresses this challenge by formulating UAV path planning as a stochastic optimal control problem using covariance control. The objective is to generate a closed-loop guidance policy that steers both the mean and covariance of the UAV’s state toward a desired target distribution while ensuring probabilistic collision avoidance with ellipsoidal obstacles. The stochastic problem is convexified and reformulated as a sequence of deterministic optimization problems, enabling efficient computation even from coarse initial guesses. Simulation results demonstrate that the proposed method successfully produces robust trajectories and feedback policies that satisfy chance constraints on obstacle avoidance and reach the target with prescribed statistical characteristics. Full article

The parameter estimation problem is one of the research hotspots in the field of uncertain differential equations. However, most studies at present focus on parameter estimation based on residuals of uncertain differential equations, which relies strictly on the solvability of residuals. In view of this disadvantage, this paper derives a symmetrical statistical invariant, which is different from residuals based on the difference scheme, and proposes the least squares estimation of general uncertain differential equations based on the statistical invariant and the principle of least squares. In order to consider parameter estimation in more general cases, this paper also studies the least squares estimation of time-varying parameters in general uncertain differential equations and designs corresponding to numerical algorithms to calculate the numerical solutions of these least squares estimations. Finally, this paper also proposes two numerical examples and an empirical study to illustrate the above methods. Full article

This article addresses the problem of singularity-free fixed-time tracking control for multiple unmanned surface vehicles (USVs) with model uncertainties. To compensate for the uncertain nonlinearities in the multi-USV systems, fuzzy logic approximators are employed to estimate unknown hydrodynamic parameters. By integrating adaptive fixed-time control theory with backstepping methodology, a novel singularity-free fixed-time consensus control scheme is developed, incorporating a error switching mechanism to prevent singularities arising from the differentiation of speed control laws. Through rigorous analysis via fixed-time stability theory, the proposed control scheme guarantees that consensus tracking errors reach a small region around zero within fixed-time. Numerical simulations demonstrate the efficacy of the presented method. Full article

Aiming at the problems that traditional maintenance task scheduling schemes for damaged equipment have, poor adaptability to changes in uncertain factors and difficult-to-deal-with emergency scenarios, this paper proposes a maintenance task scheduling method for battle-damaged equipment based on digital twin (DT) and robust optimization. The purpose is to realize the dynamic synchronization between physical entities and virtual models through DT technology, and to leverage the anti-interference characteristics of robust optimization. The method involves constructing a multi-objective optimization model that maximizes the comprehensive importance of damaged equipment and minimizes maintenance time, and solving the model using the discrete particle swarm optimization (DPSO) algorithm. Simulation results show that this method can improve the efficiency of maintenance scheduling and the anti-interference ability in emergency situations. Through the comparison of three indicators, DT-DPSO performs the best in the maintenance scheduling of battle-damaged equipment: its convergence speed is 33.3% faster than that of DPSO and 20% faster than that of DT-non-dominated sorting genetic algorithm II (DT-NSGAII); its robustness is 16.3% higher than that of DPSO and 10.7% higher than that of DT-NSGAII; its dynamic reallocation speed is more than 40% faster than that of DPSO and more than 30% faster than that of DT-NSGAII. This method is suitable for maintenance scheduling requirements of high speed, stability, and anti-interference. Full article

As robotic systems advance in autonomy and sophistication while being used in uncertain environments, the challenge of building reliable and robust electric motors that are embedded into robotic systems has never been a more important engineering problem. Thermal distress caused by extended operation or excessive loading can negatively affect a motor’s performance and efficiency and lead to catastrophic hardware failure. This paper proposes a novel intelligent control framework that includes real-time thermal feedback for hybrid electric motors that are embedded into robotic systems. The framework relies on adaptive control techniques and lightweight machine learning techniques to estimate internal motor temperatures and dynamically change operational parameters. Unlike traditional reactive methods, this framework provides a spacious active/predictive method of heat management, while preserving efficiency and allowing for responsive control. Simulations, experimental validations, and preliminary trials that deployed real robotic systems demonstrated that our framework allows for reductions in peak temperatures by up to 18% and extends motor lifetime by 22%, while retaining control stability and a range of variations in PWM adjustments of ±12% across disparate workloads. These results demonstrate the efficacy of intelligent and thermally aware motor control architectures and processes to improve the reliability of autonomous robotic systems and open the door for next-generation embedded controllers that will allow robotic platforms to self-manage thermal effects in resilient, adaptable robots. Full article

This paper addresses the cooperative task assignment problem for heterogeneous unmanned aerial vehicles with time windows considering uncertain fuel consumption. In the scenario where probabilistic fuel consumption exists and its distribution needs to be estimated from historical data samples, we first formulate the problem as a chance-constrained combinatorial optimization problem and utilize the sample average approximation method to solve it. Further, to address the issue of ambiguous distribution, we introduce distributionally robust chance constraints, which consider a set of probability distributions that are contained within a 1-Wasserstein ball centered around the empirical distribution of field data. We approximate the distributionally robust chance-constrained cooperative task assignment problem by applying a CVaR-based tractable approximation such that the problem can be transformed into a deterministic mixed-integer linear programming problem, which can be efficiently solved by state-of-the-art optimization solvers. Finally, we conduct a series of numerical experiments, which not only verify the computational efficiency of the distributionally robust chance-constrainted models but also reduce the degree of constraint violation in out-of-sample tests compared with a sample average approximation method. Full article

To address the severe challenges of task allocation for UAV swarms in uncertain complex environments, this paper introduces the concept of equivalent load, constructs the load capability matrix of a single UAV and the task required load matrix of the task area, and designs a new task resilience capability indicator accordingly to conduct research on a resilience-based optimization framework. Aiming at this multi-objective optimization problem, the “Problem Decomposability Theorem” is proposed, which theoretically proves the feasibility of decomposing the UAV swarm problem into “lower-level Integer Linear Programming (ILP) cost optimization” and “upper-level Particle Swarm Optimization (PSO) resilience optimization”. Based on this, a Particle Swarm Optimization–Integer Linear Programming (PSO-ILP) two-layer nested optimization algorithm is designed. Simulation experiments covering three task areas, five payload types and multiple UAV types are carried out, and the results show that the proposed method has outstanding performance in multi-objective optimization, especially in terms of algorithm convergence and the comprehensive efficiency of swarm load cost and task resilience. In particular, when the interruption probability is in the range of 0.2 to 0.6, it can not only maintain high task resilience but also achieve cost minimization, with a significant improvement in resilience performance. These results not only enrich the theoretical research on UAV swarm resilience but also provide a universal solution for UAV swarm task optimization in multiple fields. Full article

Our goal was to identify and understand perspectives of different stakeholders in the field of climate policy and test a process of co-creative policy development to support the implementation of climate protection measures. As the severity of climate change grows globally, perceptions of climate science and climate-based policy have become increasingly polarized. The one-solution consensus or compromise that has encapsulated environmental policymaking has proven insufficient or unable to address accurately or efficiently the climate issue. Because climate change is often described as a wicked problem (multiple causes, widespread impacts, uncertain outcomes, and an array of potential solutions), a clumsy solution that incorporates ideas and actions representative of varied and divergent worldviews is best suited to address it. This study used the Theory of Plural Rationality, which uses a two-dimensional spectrum to identify four interdependent worldviews as well as a fifth autonomous perspective to define the differing perspectives in the field of climate policy in Austria. Stakeholder inputs regarding general worldviews, climate change, and climate policy were evaluated to identify agreeable actions representative of the multiple perspectives. Thus, we developed and tested a co-creative process for developing clumsy solutions. This study concludes that while an ideological consensus is unlikely, agreement is more likely to occur on the practical level of concrete actions (albeit perhaps for different reasons). Findings suggested that creating an ecological tax reform was an acceptable policy action to diverse stakeholders. Furthermore, the study illuminated that the government is perceived to have the most potential influence on climate protection policy and acts as a key “broker”, or linkage, between other approaches that are perceived to be more actualized but less impactful. Full article

Signed networks, which incorporate both cooperative and antagonistic interactions, naturally give rise to symmetric behaviors in multi-agent systems. One such behavior is bipartite containment tracking, where follower agents converge to a symmetric configuration determined by multiple groups of leaders with opposing influence. Moreover, a timely response is critical to ensuring high performance in containment tracking tasks, particularly for high-order multi-agent systems operating in dynamic and uncertain environments. To this end, this paper investigates the predefined-time bipartite containment tracking problem for high-order multi-agent systems affected by external disturbances. A robust tracking control scheme is developed based on the backstepping method to ensure that the tracking errors converge to a predefined residual set within a user-specified time. The convergence time is explicitly adjustable through a design parameter, and the proposed scheme effectively avoids the singularities often encountered in conventional predefined-time control approaches. The stability and robustness of the proposed scheme are rigorously established through Lyapunov-based analysis, and extensive simulation results are provided to validate our theoretical findings. Full article

Optimizing sensor placement for the accurate localization of an uncertain source is crucial for a variety of distributed sensor network applications. To handle the uncertainty of the source locations, objective functions are typically written as an aggregation over a variety of plausible source locations. While prior research has explored how the resulting optimized sensor configurations correspond to the optimization over different objectives and various aggregations, the combined impact of both a complex noise environment and the choice of aggregation function for handling source uncertainty remains largely unexplored. This paper investigates this critical interplay. We demonstrate that incorporating distance-dependent environmental noise models reveals a strong dependence of the optimal sensor configuration on the aggregation method. This dependence affects diverse sensor types in differing ways, and this distinction is illustrated by examining both bearings-only and range-only sensors. We develop computational strategies for finding optimal configurations for each of these sensor types, and illustrate their distinctive features through canonical example problems for each type. The results underscore the importance of carefully considering both the environmental complexity and the aggregation approach when employing robust and reliable localization systems in practical applications. Full article

New energy vehicles (NEVs) have gained increasing favor among NEV consumers due to their dual advantages of “low cost” and “environmental friendliness.” In recent years, the share of NEVs in the global automotive market has been steadily rising. For instance, in the Chinese market, the sales of new energy vehicles in 2024 increased by 35.5% year-on-year, accounting for 70.5% of global NEV sales. However, as the diversity of NEV brands and models expands, selecting the most suitable model from a vast amount of information has become the primary challenge for NEV consumers. Although online service platforms offer extensive user reviews and rating data, the uncertainty, inconsistent quality, and sheer volume of this information pose significant challenges to decision-making for NEV consumers. Against this backdrop, leveraging the strengths of the quasi OWA (QOWA) operator in information aggregation and interval basic uncertain linguistic information (IBULI) information aggregation and two-dimensional information representation of “information + quality”, this study proposes a large-scale group data aggregation method for decision support based on the IBULIQOWA operator. This approach aims to assist consumers of new energy vehicles in making informed decisions from the perspective of information quality. Firstly, the quasi ordered weighted averaging (QOWA) operator on the unit interval is extended to the closed interval $\left[0,\tau \right]$, and the extended basic uncertain information quasi ordered weighted averaging (EBUIQOWA) operator is defined. Secondly, in order to aggregate groups of IBULI, based on the EBUIQOWA operator, the basic uncertain linguistic information QOWA (BULIQOWA) operator and the IBULIQOWA operator are proposed, and the monotonicity and degeneracy of the proposed operators are discussed. Finally, for the problem of product decision making in online service platforms, considering the credibility of information, a product decision-making method based on the IBULIQOWA operator is proposed, and its effectiveness and applicability are verified through a case study of NEV product decision making in a car online service platform, providing a reference for decision support in product ranking of online service platforms. Full article