Systems and Control
A Hybrid Two-Stage Machine Learning Pipeline for Fault Detection and Classification in Power Transmission Systems
Sahil Manikshete, Atharva Gujarathi, Thanh Long Vu et al. (+2 more)
Rapid and accurate fault detection in high-voltage transmission networks is essential for grid reliability and equipment protection. Transmission fault
datasets are frequently imbalanced, and certain fault types produce electrical signatures that fall within the normal operating envelope, causing single-model classifiers to fail on safety-critical cases. This paper proposes a hybrid two-stage machine learning pipeline that decouples detection from classification. Stage 1 combines an Isolation Forest anomaly detector with an optional supervised binary detector through an OR-fusion rule; the supervised branch is allocated automatically during training for any fault class the anomaly detector cannot resolve, and is omitted when no such class exists. Stage 2 applies a Random Forest multiclass classifier only to samples flagged by Stage 1. Feature engineering is expressed as a per-measurement-point operator mapping six raw channels to eighteen features, including zero-sequence symmetrical components derived from Fortescue's
theorem, yielding 18L features for L measurement points. On the TLFaultDataset, the pipeline raises Line-fault end-to-end accuracy from 31.3% to 95.8%. On an independent single-point
dataset, the same framework attains 97.25% end-to-end accuracy across all classes including normal operation, exceeding the TLFed
federated benchmark of 94.84% without GPU or
federated infrastructure, at 0.05 ms per sample on CPU. Ablation on both
datasets shows zero-sequence features resolving the three-phase versus three-phase-to-ground ambiguity, raising the F1-score of that class pair from 0.39 to 0.997. The direction of the zero-sequence signature is found to be system-dependent, motivating a learned decision boundary in place of a fixed relay threshold.
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All authors Sahil Manikshete, Atharva Gujarathi, Thanh Long Vu, Akhtar Hussain, Van-Hai Bui
Systems and Control · Cross-listed from math.PR
Stochastic Dynamics of Low Earth Orbit Near Full Capacity
Priyank Behera, Aditya S. Gopalan and Harsha Honnappa
The capacity of Low Earth Orbit (LEO) to sustain space operations is under mounting pressure from megaconstellations, legacy fragmentation debris, and new payload classes. Existing assessments of orbital capacity and debris
evolution are largely deterministic, tracking mean populations of intact satellites and fragments with ordinary differential equations; they cannot capture the inherent randomness of collisions, breakup sizes, and launch schedules. We develop a
stochastic extension of the two-species Lotka–Volterra model of Bradley and Wein, formulated as a density-dependent Markov chain, and study its deterministic and
stochastic scaling limits. Because intacts and fragments differ by many orders of magnitude, these limits emerge on distinct time-scales, and different pathways to a collisional Kessler cascade become visible only on the appropriate time horizon. On a fast intact time-scale we obtain an ODE approximation and a Gaussian SDE approximation; on an intermediate fragment time-scale we obtain an ODE approximation, a Gaussian SDE approximation, and the critical Kessler threshold, above which the ODE approximation runs away in Kessler syndrome. Crucially, on a third, slow time-scale at the critical threshold, the fragment count converges to a Feller
diffusion, in which runaway is triggered purely by fluctuations rather than by the drift—an effect the ODE approximations and their Gaussian SDE approximations cannot see. Debris runaway may occur sooner, and with higher probability, than deterministic models predict: the intact population can appear well-behaved while fragments quietly accumulate risk. Constellation deployment, debris-removal investment, and slot allocation should account for these
stochastic effects, and planning for runaway must depend on the variance of the collision dynamics, not on the mean alone.
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Systems and Control
Fair Dynamic Operating Envelopes using Distributed Multi-Period Optimal Power Flow and Jain Index for Active Distribution Networks
Pedro Salomão Quessongo, Daniel Gebbran and Clodomiro Unsihuay-Vila
Dynamic operating envelopes (DOEs) are increasingly used to publish time-varying export limits that keep distribution networks within operational limits. Purely technical DOE allocation, however, can systematically privilege electrically favorable prosumers, while
embedding fairness directly into a single-period optimal power flow (OPF) objective mixes network feasibility, equity and efficiency in a way that obscures the cost of
fairness. This paper proposes a two-stage, multi-period framework that addresses both of these. Initially, a technical distributed OPF computes network-feasible export envelopes. The subsequent stage then applies a dynamic aggregate export budget and redistributes capacity through cumulative proportional
fairness, limiting the additional curtailment by an admissible efficiency budget. The resulting fair DOEs are treated as first-stage decisions, while battery storage provides scenario-dependent recourse under demand and renewable uncertainty. The operational problem is solved by a calibrated regional alternating direction method of multipliers (ADMM) on a lossless LinDistFlow model and independently validated using AC power flow. On the IEEE 33-bus feeder over a 24-hour horizon, the technical
benchmark yields 2.1097 MWh of renewable curtailment, whereas the
fairness-constrained allocation increases curtailment to 5.7216 MWh but caps the maximum cumulative curtailment ratio at 11.20% and raises Jain
fairness indices close to unity, with AC voltage deviations below 0.01 p.u. and no voltage or thermal violations under the adopted 0.90-1.05 p.u. limits. Results show that considering both storage (which alleviates curtailment impact) and multi-period
fairness (which increases curtailment) is an interesting approach for modern DOE design, which in turn requires a multi-period, co-designed approach.
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Systems and Control
Temporal Property-driven Design Space Exploration with Reinforcement Learning for Cyber-Physical Systems
Tagir Fabarisov and Maxime Cordy
Design-space exploration of configurable Cyber-Physical Systems (CPS) requires executable evaluation when design choices affect timing, fault propagation, recovery behavior, and temporal-property satisfaction. Repeated
stochastic executions make exhaustive exploration impractical for large design spaces. This paper presents a temporal-property-driven CPS design workflow using Reinforcement Learning (RL). At design time, the RL
agent selects subsystem alternatives to assemble a candidate system model. The model is then evaluated through simulation, during which online temporal-property monitors observe runtime traces and produce functional-property violation indicators. These indicators are combined with evaluated non-functional terms for budget, recoverability, sustained compliance, and operational use to calculate the reward used for subsequent candidate selection. The workflow is evaluated on a methane-sensitive mine-pump CPS. The corresponding executable case-study model is provided as additional contribution. RL-guided search identifies the highest-reward design observed in the experiments after 26 episodes (corresponds to 130 executable simulations). These designs were reached with fewer simulations than surrogate-guided
Bayesian Optimization and population-based Genetic
Algorithm baselines under the same executable model and reward formulation. Ablation study results indicate that value-based feedback and reuse of previous simulation traces contribute to this reduction.
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Systems and Control
Graph-Native Attention Acceleration for Attack Detection in Cyber-Physical Systems
Zhenan Feng and Ehsan Nekouei
Cyber-physical systems (CPSs) consist of sensors, controllers, and actuators through communication and physical interactions, making them vulnerable to attacks on measurements, control logic, and equipment operation. Graph-based attack detectors, especially graph
attention models, can localize such attacks by learning edge-adaptive interactions over communication and physical interaction graphs. However, their computational cost grows rapidly with neighborhood size, and their inference latency can reach tens to hundreds of milliseconds in large-scale or densely connected graphs, delaying time-critical alarm generation. To enable real-time deployment of graph
attention mechanisms for attack detection, we propose GraphGHHA, a graph-native
attention acceleration layer designed as a replacement for graph
attention layers in attack detection units. GraphGHHA combines (i) a graph-local sparse
attention branch that is constrained by the adjacency
matrix of the CPS, and (ii) a global linear mixing branch to retain system-wide information. A learnable gate combines the two branches node-wise, preserving detection accuracy under strict latency constraints. We evaluate GraphGHHA on a networked heating, ventilation, and air conditioning (HVAC) cyber-physical system under representative attack scenarios and demonstrate up to an eight-fold reduction in detection latency while maintaining high detection accuracy. These results indicate that GraphGHHA enables practical, real-time alarm generation for large-scale CPS monitoring.
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Systems and Control
Data-Driven Synthesis of Robust Positively Invariant Sets: From State Feedback to Output Feedback
Zhijie Ning
This paper develops a direct data-driven framework for robust positively invariant (RPI) set synthesis for unknown linear time-invariant systems under state-feedback and observer-based output-feedback scenarios. The feedback and observer gains, along with the RPI sets, are directly synthesized from noisy offline data by solving semidefinite programs (SDPs), avoiding intermediate model identification or explicit model-uncertainty set construction. In the state-feedback case, a linear-quadratic (LQ)-type feedback gain is first computed, and an ellipsoidal RPI set is then synthesized for the resulting closed-loop dynamics. In the observer-based output-feedback case, offline data are used to compute the observer gain and the corresponding RPI set for the system state through an augmented-state formulation. This design provides a unified method for invariant-set computation in both scenarios, and the direct data-driven formulation avoids the explicit construction and propagation of an intermediate model-uncertainty set. Numerical examples illustrate the effectiveness of the proposed method.
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Systems and Control
Artificial intelligence-based predictive fuel blending control for flare gas mitigation
Josip Kir Hromatko, Šandor Ileš, Rube Huljev et al. (+1 more)
This paper describes a fuel blending
algorithm based on artificial intelligence and model predictive control. A gas-fired power plant was modeled using physical laws and on-site measurements. A neural network is used to calculate the methane number of the fuel and determine the fuel blending ratio limits so that the methane number is within the limits specified by the engine manufacturer. A model predictive controller adjusts the final blending ratio to meet safety requirements and minimize operating costs. The
algorithm was tested in simulations with different scenarios and a reduction in both the operating costs and amount of flaring was observed.
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All authors Josip Kir Hromatko, Šandor Ileš, Rube Huljev, Velibor Vučković
Systems and Control
Admissible Unit Range of Plug-and-Play Distributed Energy Resource (DER) Systems Under Delay: A Scalable Design Framework
Haruhisa Ichikawa, Shinji Yokogawa, Yuusuke Kawakita et al. (+1 more)
This paper addresses the fundamental design problem of plug-and-play distributed energy resource (DER) systems, which are emerging as a scalable solution for integrating distributed generation through user-driven connection of modular units. In such systems, the number of connected units is not fixed but dynamically varies due to user operation and system conditions, requiring stability and operational constraints to be guaranteed over a range of system sizes rather than for a single configuration. To address this challenge, we propose the Plug-in DER Orchestrated Grid (PDOG) and develop a normalized analytical framework in terms of normalized delay and aggregate loop gain. This formulation enables explicit characterization of the stability boundary together with a lower bound derived from the no-reverse-power constraint, defining a feasible region for system operation. By mapping this feasibility condition into the number of DER units, the admissible range of connectable units is obtained as a function of delay. The analysis reveals a fundamental trade-off: while the theoretical stability limit increases with normalized delay, implementation-induced gain amplification reduces the practical hosting capacity. As a result, the admissible system size exhibits a non-monotonic dependence on delay, and a feasibility boundary may emerge beyond which no admissible system size exists. These results provide explicit design guidelines for determining the number of DER units under delay and implementation constraints, establishing a new paradigm in which system scalability is explicitly constrained and engineered.
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All authors Haruhisa Ichikawa, Shinji Yokogawa, Yuusuke Kawakita, Yoshito Tobe
Systems and Control
Dynamic Inversion: An Incrementally Evolving Methodology for Flight Control Design
Daniel Milz and Gertjan Looye
Nonlinear Dynamic Inversion (NDI) has become a standard methodology in flight control law design. It offers an intuitive approach to decouple commanded variable responses, handle system nonlinearities, and adapt to operating conditions. NDI also comes with a well-structured architecture that reduces design effort by addressing various functional aspects in separate components, and that allows straightforward integration of extended capabilities, such as envelope protection, control saturation handling, and compensating for faults or damage. A development that has resulted in considerable renewed
attention is the use of (angular) acceleration sensors to partially replace inverse model equations. Known as incremental NDI, or INDI, this development offers reduced sensitivity to modeling errors and lower control law complexity. Incremental NDI, however, lacks useful design degrees of freedom in the previously present inverse model equations and underlying feedback signal synthesis, and comes with pitfalls in design aspects like control allocation, disturbance rejection, and inter-disciplinary couplings. This has given rise to recently developed hybrid and mathematically restructured approaches. The aim of this article is to give an up-to-date, structured overview of the various evolved forms of NDI from conceptual, historical, architectural, and mathematical perspectives. It hereby intends to provide useful considerations for future flight control law developments by reviewing its various forms and potentials from methodological, design, and application points of view.
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Systems and Control · Cross-listed from math.OC
Zeroth-Order Nonsmooth Nonconvex Optimization with Convex Liftings and Its Application to State-Feedback $H_\infty$ Policy Optimization
Xuhao Wang and Yujie Tang
Direct policy optimization is widely used in reinforcement learning and control, but generally leads to nonconvex optimization problems. For state-feedback $H_\infty$ control, the policy objective is also nonsmooth, despite possessing a benign landscape whose hidden convexity can be revealed by the recently developed extended convex lifting framework. Motivated by recent advances in hidden convex optimization, we study zeroth-order optimization of nonsmooth, nonconvex problems admitting a convex lifting. We propose a zeroth-order proximal point
algorithm: An inexact proximal-point outer loop constructs strongly convex subproblems, while an inner loop approximately solves each subproblem using only function evaluations. With probability at least $1-\delta$, our proposed
algorithm returns an $\epsilon$-optimal solution using $\widetilde{O}\left(d\epsilon^{-3}\right)$ function evaluations, while all iterates remain feasible without explicit projection. Finally, we verify that the assumptions underlying our analysis hold for discrete-time state-feedback $H_\infty$ policy optimization, yielding an oracle complexity of $\widetilde{O}\left(n_u n_x\epsilon^{-3}\right)$ for attaining a prescribed objective value gap, where $n_u\times n_x$ is the dimension of the feedback gain to be optimized over.
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Systems and Control
Leveraging UAV Autonomy for Minimum 4D Flight Authorization Volumes
Christian Vitale, Yiannis Grigoriou, Panayiotis Kolios et al. (+1 more)
The increasing
UAV traffic in urban areas has prompted the creation of U-space, an EASA framework for safe and efficient unmanned aerial vehicle (
UAV) operations. Within this context, this work presents a flight authorization framework that leverages autonomous
UAVs, using their motion models and control characteristics to improve authorization efficiency. In the proposed framework, probabilistic spatial-temporal envelopes are generated to predict future
UAV locations within a desired confidence level, and this information is then used to determine the minimum 4D operational volumes that form a valid authorization request for the mission. By reserving only the necessary airspace, the approach enhances capacity and supports simultaneous
UAV operations. Simulations comparing the proposed method with a conventional rule-based strategy demonstrate consistently more compact and efficient airspace reservations across a range of mission types.
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All authors Christian Vitale, Yiannis Grigoriou, Panayiotis Kolios, Georgios Ellinas
Systems and Control · Cross-listed from cs.RO
Switched Turn-based Adaptive Source Seeking Strategy using Estimation and Information-driven Direction of Improvement
Shubhra Banerjee and Satadal Ghosh
Source seeking arises in applications such as gas leak localization, radiation monitoring, and environmental surveillance, where the origin of an unknown signal field must be estimated from spatial measurements. In practice, the source location is not directly observable and must be inferred from noisy scalar measurements collected during motion.In robotic source seeking, estimation and motion are closely linked: measurements improve the source estimate, while the chosen trajectory affects the quality of future measurements.Existing loop-based
geometric strategies generate feasible motion but do not explicitly use estimation uncertainty to regulate direction updates.This paper presents a loop-based source-seeking framework that combines Extended Kalman Filter (EKF) estimation with Fisher Information
Matrix (FIM)-based direction selection. The source estimate is updated during motion, and the heading is changed at loop boundaries using both estimation uncertainty and predicted information gain. A measurement-based stopping condition is used to detect convergence without requiring prior knowledge of the source location.Simulation results under stationary and moving source scenarios demonstrate improved tracking performance and reduced estimation error compared to purely information-driven or estimate-driven strategies.
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Systems and Control · Cross-listed from cs.RO
CSymPlan: Certified Symbolic Planning and Control for High-DOF Manipulators
Aditya Narendra, Ashok Kumar Saini, Mahathi Anand et al. (+3 more)
Robot manipulators are commonly engineered around a decoupled motion-generation stack: a planner computes a collision-free path and a lower-level controller tracks the resulting reference. This separation is computationally convenient, but it can produce references that are difficult to execute under actuator limits, tracking error, model mismatch, and small obstacle clearances. We present CSymPlan, a certified symbolic planning and control framework for high-DOF manipulators with two complementary implementations: an offline implementation that precomputes certified reach-avoid feedback policies for known workspaces; and an online implementation that synthesizes or updates symbolic policies at runtime from changing task and perception information using parallelization. The offline implementation reduces the manipulator dynamics to a sampled perturbed double-integrator model in operational space through feedback linearization, treats torque-realization errors, modeling inaccuracies, and measurement uncertainty as bounded disturbances, and refines the synthesized symbolic policy to the Franka FR3 through a quantization–lookup–torque realization pipeline. The online implementation uses the same abstraction and refinement interface, but replaces the precomputed policy table with a runtime pFaces request–synthesis–execution loop. In randomized simulated
benchmarks and perception-driven Franka FR3 experiments, both implementations complete reach-avoid tasks with zero safety violations; whenever no certified action exists, the
robot holds, replans, or stops safely instead of executing an uncertified command.
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All authors Aditya Narendra, Ashok Kumar Saini, Mahathi Anand, Mahmoud Khaled, Fares J. Abu-Dakka, Abdalla Swikir
Systems and Control · Cross-listed from cs.RO
Reproducible Vision-Guided 6-DoF Robotic Manipulator with a Mixed Stepper-Driver Architecture and Browser-Native Control
Lasan Perera, Deneth Priyadarshana, Dulana Pitiwaduge et al. (+2 more)
We present the NeuralNexus Arm, an open, low-cost 6-DOF robotic manipulator built by an undergraduate engineering team, together with the design decisions and debugging experience needed to reproduce it. The arm is driven by a single STM32H743 microcontroller on a custom printed
circuit board (PCB) and combines two stepper-driver strategies on one controller: push-pull 3.3 V step/direction outputs for onboard TMC2209 drivers on the three wrist joints, and open-drain outputs for external CL57T and DM542 drivers on the three high-torque proximal joints. We describe the mechanical design, mixed-driver electronics, interrupt-driven firmware, a MATLAB/Simscape-based inverse-kinematics pipeline, a browser-native control interface using the Web Serial API, and a lightweight
vision pipeline for object localisation and autonomous pick-and-place tasks. We also document non-obvious hardware and firmware failure modes encountered during the transition from a development board to the custom PCB as reproducibility guidance. All design files and firmware are released openly. The platform actuates all six axes under coordinated control at a 2 kHz update rate and executes both manual and pre-recorded motions from the browser interface.
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All authors Lasan Perera, Deneth Priyadarshana, Dulana Pitiwaduge, Isitha Dinujaya, Mokshan Colambage
Systems and Control
Generative Design of Liquid-Cooling Channels for Thermal Management of 2.5D and 3D Integrated Advanced Packaging
Michael Acquah and Zheng Liu
High-power multi-chip packages require increasingly effective cooling as intensive heat is generated within a limited package area. This work presents a physics-guided generative design framework for
liquid-cooling channel
topology optimization in a 2.7 kW multi-chip package containing two high-power graphics processing units (GPUs) and one central processing unit (CPU). A conditional
diffusion model generates symmetric channel layouts using maximum GPU temperature, GPU temperature spread, and pressure drop as performance targets. Generated designs undergo connectivity and dead-end-branch screening and are evaluated using a calibrated reduced-order thermal-fluids model. Based on 5,000 generated layouts, the multi-objective analysis identified the optimal design for thermal properties, with estimated maximum GPU temperature of 70.30 degree Celsius, GPU temperature spread of 24.90 degree Celsius, and pressure drop of 89.72 kPa. Compared to a conventional reference
topology, the optimal design reduced the maximum GPU temperature, temperature spread, and pressure drop by 33.6%, 52.5%, and 72.8%, respectively. High-fidelity three-dimensional conjugate heat-transfer simulation in OpenFOAM estimated a maximum GPU temperature of 66.70 degree Celsius and a pressure drop of 92.1 kPa, showing only differences of 8.6% in temperature rise and 2.6% in pressure drop. The results demonstrate that physics-guided generative design based on the reduced-order model can efficiently discover unconventional cooling channel architectures while reducing reliance on repeating computationally expensive simulation.
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Systems and Control
Real-Time Edge-based Detection of Correlated AI Data-Center Load Episodes
Chandan Chaudhary, Abanish Tiwari, Yansong Pei et al. (+2 more)
Artificial-intelligence data centers running bulk-synchronous training can impose sub-second power swings. When several facilities synchronize their training cycles, these load variations become spatially correlated and amplify the aggregate disturbance on the grid. A grid operator without access to data-center telemetry must infer this correlation from electrical measurements alone. However, the required observation time and the feasibility of detection on substation-deployable hardware remain uncharacterized. This paper develops a correlation-based detection method to classify the multi-facility operating regime from cross-facility power measurements. Analytical derivations and experimental validation show that the resulting detection confidence increases with the observation-window length at a rate governed by the load correlation time. The method is demonstrated in a real-time hardware-in-the-loop testbed, where load setpoints generated from a validated semi-Markov data-center load model are applied to an electromagnetic-transient grid simulation on a Real-Time Digital Simulator. A compact classifier built on pairwise power correlations runs on an edge device in this loop and determines whether the data-center load variations are independent or spatially correlated. The cross-facility correlation separates the independent and correlated cases across independent realizations. The held-out detection accuracy improves with the observation window, consistent with the predicted relation. A raw-waveform network fails to generalize, supporting pairwise correlation as the discriminative signal. The detector executes in real time on commodity edge hardware. A closed-loop demonstration against the running simulator tracks a regime change within one observation window.
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All authors Chandan Chaudhary, Abanish Tiwari, Yansong Pei, Mohammed Ben-Idris, Joydeep Mitra
Systems and Control · Cross-listed from math.OC
General-Sum Linear Regulator Games for Positive Systems
Alba Gurpegui, Monika Tomar and Takashi Tanaka
This paper studies a continuous-time general-sum non-cooperative game with linear costs, positive linear system dynamics, and elementwise linear input constraints. In the finite-horizon case, we present a verification
theorem characterizing feedback Nash
equilibria, in terms of absolutely continuous solutions of a coupled system of vector-valued ordinary differential equations, realized by time-varying feedback laws. Unlike linear-quadratic differential games, whose Riccati-based
equilibria scale quadratically with the state dimension, this formulation scales linearly. However, the resulting piecewise-constant feedback saturates between its constraint bounds rather than varying smoothly, and additional mathematical challenges arise when characterizing the solutions of the differential equations, which are generally discontinuous due to the switching nature of the feedback gains. In this work, we study the case where switching occurs only at isolated time instants. In the infinite-horizon case, under stabilizability assumptions, the
equilibrium is characterized by coupled vector-valued algebraic equations. For this game, we propose iterative methods to compute both finite and infinite-horizon
equilibria. The approach is illustrated through a large-scale pollution game.
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Systems and Control · Cross-listed from math.OC
Unit-to-Plant Stability Shaping of Multi-Electrolyzer ReP2H Plants via Interface Design and Dispatch
Miao Zhang, Yiwei Qiu, Xiaoyu Wang et al. (+5 more)
Alkaline water electrolysis (AWE) units supplied by insulated gate bipolar transistor rectifiers (IGBT-Rs) may experience oscil-lations caused by coupling between rectifier control and electro-lyzer (ELZ) dynamics. Because this risk varies with unit loading and power allocation, production-oriented dispatch may place a multi-ELZ renewable power-to-hydrogen (ReP2H) plant near or exceed its stability boundary. This paper proposes a stability-oriented framework for control design and plant production dis-patch. A three-port admittance model links the ac port, dc link, and electrolysis stack. Unit-level dc-port analysis quantifies the effects of loading, temperature, Buck bandwidth, and dc-link capacitance, while plant-level aggregation evaluates how unit commitment and power allocation affect stability. Results show that higher loading reduces stability, whereas larger dc-link ca-pacitance and higher Buck bandwidth improve it. Under the same plant loading, different power allocations result in different plant-level stability margins, with balanced allocation generally providing a larger margin than concentrated allocation. The plant-level model thus distinguishes the stability margins of ad-missible schedules. Hardware-in-the-loop (HIL) tests validate these trends and the proposed redistribution rule. The resulting operating regions and dispatch rules can be used to screen unit commitment and power allocation decisions in plant production scheduling.
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All authors Miao Zhang, Yiwei Qiu, Xiaoyu Wang, Linlin Wu, Yi Zhou, Shi Chen, Buxiang Zhou, Kaigui Xie
Systems and Control · Cross-listed from math.DS
Identifying Probability Localization Dynamics via Structured Stochastic Liftings
Fredy Vides
This work develops a discrete-time framework for identifying probability localization dynamics through finite
stochastic representations adapted in space, time,
memory, and state information. A compact dynamically relevant set is localized by a finite measurable partition, producing an observable probability state and a relational graph of admissible transitions. Structured
stochastic liftings derived from Stochastically Structured Reservoir Computing (SSRC) give lossless
polynomial representations of the observable state, while
stochastic delay liftings add finite observable
memory. These are distinguished from dynamically informed state-space enrichment: refinement of observational fibers containing states with the same present observation but different observable futures, yielding an exact obstruction-to-closure criterion. A route-network toy problem gives a minimal obstruction example, while four numerical laboratories (rotational phase dynamics, the chaotic logistic map, the Van der Pol oscillator, and a synthetic cyclic inventory system) show how spatial scale, temporal scale,
polynomial degree, and delay depth interact. The logistic map isolates representation-induced
memory in an otherwise Markovian chaotic system, using its exact invariant law as an ergodic
benchmark and its zero-mass pseudospectrum to separate relaxation from transient amplification. An exact rotational cycle calibrates pseudospectra as a robustness diagnostic rather than a closure certificate. The inventory example gives a closure-driven enrichment procedure: residence-age hazards trigger age-refined states that improve predictive scores. These results motivate a minimal adequate representation: the least complex representation meeting predictive, structural, and identifiability requirements.
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