Papers

Space-air-ground integrated networks (SAGINs) integrate heterogeneous platforms with different coverage, mobility, and payload constraints, which creates strong demands for flexible antenna architectures. Foldable antenna arrays (FAAs) provide a promising solution by reconfiguring array geometry, antenna positions, and orientations through controllable joints or hinges. However, existing studies on FAAs have mainly considered simple folding configurations and limited deployment benefits, while FAAs' architectures and broader potential for SAGIN remain largely unexplored. In this article, we present the fundamentals and architectures of FAA, including folding mechanisms, foldability levels, and functional capabilities. We then examine FAA applications for ground base stations, low-altitude platforms, high-altitude platforms, and satellites, together with their potential challenges and solutions. Finally, we highlight open issues and future research directions, and provide a case study to demonstrate the FAA-enabled communication performance improvement in SAGIN.

Networked low-altitude unmanned aerial vehicles (UAVs) need reliable and adaptive decision-making capabilities to operate under uncertain observations, dynamic environments, and intermittent connectivity, while many existing agentic systems remain limited by hallucination risks, data dependence, and weak generalization. This article investigates neuro-symbolic agentic AI (NSAAI) as a framework for combining neural grounding, symbolic reasoning, and closed-loop agentic interaction to support more reliable and adaptive UAV autonomy. We first examine its capability foundations in data efficiency, compositional generalization, continual learning, and zero-shot transfer, and then develop a reference architecture integrating task and goal management, neuro-symbolic planning, verification and metacognition, skill execution and network interaction, and shared knowledge and memory. An urban fire-inspection case implemented in LAESim illustrates how a UAV can coordinate sensing and cloud access under intermittent connectivity, reuse a verified image-delivery skill, and satisfy explicit evidence conditions before completing the mission. The results illustrate the potential of NSAAI to support reusable skills, evidence-grounded decision-making, and adaptive mission execution in networked UAV systems. We further discuss key research directions in uncertainty-aware reasoning, knowledge and skill expansion, adaptive self-monitoring, and standardized evaluation.

Barrier Lyapunov functions (BLFs) have been a popular choice when dealing with constrained control problems. In the current article, we present a unified asymmetric barrier Lyapunov function that generalizes the existing logarithmic symmetric Lyapunov function. We show that the proposed function is smooth and does not require the discontinuous switching function that is ubiquitous in the asymmetric barrier Lyapunov functions existing in the literature. Based on the proposed barrier Lyapunov function, a control law, guaranteeing exponentially fast output tracking, is designed for a class of single-input single-output nonlinear systems with output constraints. We show that the proposed control law unifies the control design and structure for a system with either symmetric or asymmetric output constraints. Furthermore, we constructively show that the proposed function can be bounded from above and below by symmetric class $\mathcal{K}$ functions which help in establishing local exponential convergence together with the proposed control law. Lastly, we provide numerical examples to illustrate the performance of the proposed control and compare the results with the existing logarithmic BLFs.

Battery energy storage systems (BESSs) are widely integrated into smart grids. For an isolated BESS network, however, capacity degradation and power loss of battery units increase operating costs. To alleviate this problem, two distributed economic dispatch (ED) schemes with discrete-time dynamics are developed in this paper, thus obtaining the optimal output power vector and ensuring supply-demand balance while considering dynamic line loss and capacity constraints. It is worth mentioning that proportional-integral protocols with reset mechanisms (PI+R protocols) are introduced into these schemes which can greatly improve the consensus rate and control accuracy. Specifically, a marginal cost (MC) consensus controller and an average power mismatch estimator are the core components of each scheme, where these two are coupled to each other. In this regard, the difference between the two schemes is that for the MC consensus controllers, one involves incorporating the estimated average power mismatch feedback term into the closed-loop system error to design the PI+R protocol, while the other does not. In addition, regarding to each PI+R protocol, the integral term is reset to 0 when the proportional term experiences zero crossing, in order to accelerate the convergence rate and reduce overshoot. The effectiveness, conditions under which the reset mechanism works, and stability of these schemes are all well analyzed. Finally, some simulation cases are designed and compared with an existing solution. From the simulation results, it can be seen that the designed second scheme greatly improves the performance of the previous scheme in consensus rate, convergence rate, BESS/agent plug and play, load switching, and wide area system application.

For second-order systems under continuous sliding mode control (SMC), the literature has long relied, largely through phase-portrait illustrations, on the implicit convention that the phase-plane trajectory approaches the equilibrium along a direction tangential to the designed sliding surface. This paper investigates this tangential convergence assumption through a rigorous phase-plane analysis of the double-integrator system subject to standard linear SMC. We reveal that the asymptotic state ratio is not unique but instead exhibits a bifurcation that depends on the control gains, the sliding surface parameter, and the initial conditions. The key finding is that the system may converge along an implicit secondary manifold rather than aligning with the designed sliding surface, implying that smooth entry is not globally guaranteed. We derive closed-form expressions for the convergence ratios and establish a classification framework that precisely characterizes when the smooth-entry assumption holds and when it fails. The analysis is further extended to classical PD control, and we show that the bifurcation threshold coincides with the critical damping boundary that separates the two convergence regimes. These findings bridge terminal geometry and convergence smoothness, providing a predictive framework for high-performance motion control design. Simulation results validate the proposed classification of convergence regimes.

Quantum computers are technologically novel and unusual, but at system scale they should be engineered using many of the same principles that govern classical heterogeneous accelerators. This paper argues that utility-scale quantum architecture is primarily a cost-performance problem across a coupled quantum-classical system, leading to a blueprint for scalable quantum processing unit (QPU) design. Our architecture blueprint is organized around clean logical abstractions, hiding details and complexity of physical qubit modalities below the instruction set architecture (ISA) boundary, and specializes recurring functions aggressively to minimize the cost for utility scale quantum computations. Its low-level implementation through specialized local hardware for control, readout, and quantum error correction (QEC) closely resembles the architecture of high-performance network stacks. One of our main insights is that the design principles and the resulting architecture closely follow established practice from classical computing and networking.

Traditional dynamical system models, including Koopman operator representations, are fundamentally equality-based, whereas many analysis and control tools rely on inequalities. This mismatch motivates representations that are intrinsically aligned with certification tasks involved in the analysis and control synthesis problems. In this paper, we propose a data-to-certificates (D2C) paradigm that bypasses explicit model construction and directly learns certificates from data. We introduce supereigenfunctions of the Koopman operator as an inequality-based generalization of eigenfunctions that define exponential growth envelopes encoding stability, safety, and uncertainty propagation, thereby serving as certificates for a range of control objectives. We establish their theoretical foundations and show that the associated rates recover intrinsic dynamical quantities such as Lyapunov exponents. Two complementary constructions are developed: a geometric approach based on the multiplicative ergodic theorem (MET), and a resolvent/Gramian formulation that enables computation directly from trajectory data. The resulting framework yields certificates that can be used for stability and contraction analysis, as well as stabilizing and safety-critical control synthesis via convex quadratic programming-based optimization program. Numerical examples demonstrate the effectiveness of the proposed data-driven certification approach for stabilization, contraction, and safe control design.

This tutorial provides a unified view of the emerging area of bilinear learning and control. Using linear systems as a benchmark, it explains what fundamentally changes in the bilinear settings, how recent theory addresses finite-sample learning and control, and how these ideas connect to broader themes in nonlinear control, representation learning, and data-driven decision making. For learning, we emphasize tools that are particularly useful in the bilinear settings, such as one-sided Bernstein's inequality for dependent and heavy-tailed covariates, blocking arguments, and martingale concentration for input-dependent noise. We then apply these tools to obtain finite-sample learning guarantees for fully observed bilinear systems, partially observed bilinear systems, and linear systems with bilinear observations. For control, we discuss quadratic control from bilinear observations, where the classical separation principle fails, and review tractable approaches based on belief-space receding horizon control. We also cover stabilization of bilinear dynamics under state feedback using semi-definite programming, LMI relaxations, sum-of-squares methods, and Koopman-based lifting. We conclude by discussing connections to reinforcement learning and machine learning, and some open problems in combined learning and control of bilinear systems.

Negative-resistance microwave oscillators can simultaneously sustain autonomous oscillations and coherently scatter electromagnetic waves, enabling active reflection beyond conventional linear amplification. Here we demonstrate giant resonant reflection gain from synchronization-induced phase localization in a self-sustained tunnel diode oscillator operating near 2.96 GHz. Weak resonant RF injection drives a transition from a broadband free running state to a phase localized narrowband reflected carrier. The resulting reflected enhancement reaches 83.1dB relative to the injected signal and is accompanied by greater than order of magnitude linewidth collapse, nonlinear injection pulling, and a synchronization bandwidth of 15.84 kHz. Time resolved spectrograms directly resolve injection locking and frequency entrainment, while noisy Stuart Landau simulations reproduce the observed spectral concentration and detuning dependent gain roll off near the Hopf instability. Artificially increasing phase diffusion with broadband bias noise suppresses the reflected enhancement, confirming synchronization-induced quenching of phase fluctuations as the origin of the giant coherent reflection gain.

Robots must complete their tasks and maintain the achieved outcomes while avoiding safety failures at all times. Strict reach-avoid-stay (sRAS) formalizes this requirement: safely reaching a target and remaining there indefinitely after first entry. We propose an sRAS Q-control barrier function (CBF) safety filter for high-dimensional black-box systems under bounded uncertainty. Our construction combines a stay value encoding safe permanent residence in a target subset with a reach-avoid value encoding safe reachability of this subset while avoiding target states from which safe permanent residence cannot be guaranteed. We prove that these values jointly yield a valid robust discrete-time CBF and lift them to state-action Q-functions for runtime intervention. For exact values and under a measure-zero condition, our filter preserves sRAS feasibility from almost every winnable initial state and keeps the system safely within the target after first entry, against all admissible uncertainty realizations. We adopt reachability-based adversarial reinforcement learning for scalable value approximation using only black-box interactions. Notably, neither synthesis nor deployment of our filter requires known dynamics, affine structure, value derivatives, or hand-designed barriers. We validate our framework in quadruped gap jumping in simulation and hardware, where the robot crosses the gap, lands safely, and remains safe afterward. Simulated F1TENTH races further demonstrate safe overtaking and lead retention.

This paper proposes a structured approach to learning linear operators for control systems from data. We address both structural and learning-theoretic aspects of the problem. To derive structural assumptions, we propose using the well-established framework of (semi)groups for evolution equations, as operators in control systems are of the same type. Further, we propose analyzing learning algorithms through the lens of the inverse problems framework. This reveals how a learned model depends on the data via error decompositions, convergence guarantees, and optimal regularization – enabling us to compare existing methods and derive provably advantageous algorithms. In order to obtain these results, we restrict our scope to bounded operators on Hilbert spaces. Although this may appear restrictive, existing approaches often make this assumption implicitly to obtain matrix-like representations. We demonstrate the power of using these frameworks by deriving a convergent estimator for time-varying systems.

This paper introduces a sample-efficient compositional method for formal safety verification of interconnected monotone systems without requiring explicit models of the local subsystems. Existing data-driven approaches either lack formal safety guarantees or rely on dense Lipschitz-based discretizations of the state space to provide such guarantees, which leads to significant computational overhead and limits scalability. In contrast, we leverage the monotonicity of local subsystems to construct tractable local interval-barrier certificates using only boundary evaluations of each subsystem in a decentralized manner, together with a global condition that guarantees the safety of the overall interconnected system. At the local level, our framework learns interval-barrier certificates using monotone neural networks from boundary samples induced by partitions of the local state and internal-input spaces. At the global level, it composes these local neural interval-barrier certificates using the interconnection structure to certify the safety of the overall system. Furthermore, under appropriate structural assumptions, we reformulate the global safety condition into a scalable form that can be directly incorporated into the neural network loss. This enables the enforcement of overall system safety during local training. The experimental results demonstrate the effectiveness and scalability of the proposed method.

Online residual learning can reduce model mismatch in predictive control, but passive data collection may fail to adequately cover states that become important later in the task. Task-agnostic active learning targets uncertain or informative regions, but information acquired in such regions does not necessarily improve task performance. This paper introduces Task-Oriented Information Acquisition (ToIA), an active-learning criterion for model predictive path integral control (MPPI) with online Gaussian process (GP) residual learning. For each sampled control sequence, ToIA estimates how much an observation obtained early in the rollout would reduce predictive uncertainty at later states on the same rollout, and weights this reduction by the rollout's relevance to the task. The score is evaluated over the existing MPPI rollout batch without sampling future observations or re-optimizing control under hypothetical posterior updates. In simulated off-road navigation across held-out maps with heterogeneous terrain, ToIA improved the goal-reaching success rate over passive GP learning by 19.3 and 27.4 percentage points and outperformed task-agnostic active-learning baselines across dense and sparse online-learning intervals. An ablation study indicates that task relevance is particularly important under sparse model updates. The implementation supports online control at 20 Hz on an NVIDIA RTX 2080 Ti.

We study high-order safety-critical control of quadrotor teams under bounded inputs and pairwise collision-avoidance constraints. Squared-distance barriers may lose thrust effectiveness when the relative displacement is orthogonal to the available thrust directions, while nonsingular constraints may still be jointly infeasible under shared bounds. We characterize both phenomena through pairwise effectiveness and aggregate feasibility measures. A torque-aware dynamic extension exposes attitude torques in a fourth-order barrier and prevents the extended-input row from vanishing under positive thrust. Gaussian processes directly learn the fourth-order HOCBF residual, providing robust margins without differentiating unknown perturbations. Under residual-bound and persistent-feasibility assumptions, the resulting QP guarantees collision avoidance and recovers the nominal input whenever it satisfies the robust safety and actuator constraints.

The increasing complexity of modern power systems, driven by high renewable penetration, load variability, and operational uncertainty, demands fast and reliable solutions to the AC optimal power flow problem (AC-OPF). Traditional optimization methods, though accurate, often struggle with scalability and high computational burdens, making them impractical for real-time use in large networks. This paper introduces PowerModels-ACOPF-AI, a two-stage Bayesian Neural Network (BNN) surrogate designed to predict generator set points, bus voltages, and phase angles with uncertainty. The framework integrates a performance-sensitive on-the-fly learning mechanism that identifies regions of degraded prediction accuracy and dynamically retrains with additional AC-OPF solutions generated by PowerModels.jl. This self-adaptive loop ensures robust performance, enabling the model to maintain accuracy under novel or highly variable operating conditions. Validation on benchmark test systems of different sizes, namely the 30-bus, 200-bus, and 500-bus networks, demonstrates strong generalization capability, efficient handling of stochastic renewable injections, and the ability to provide rapid, uncertainty-aware predictions. Beyond predictive accuracy, the proposed approach offers practical value as both a real-time advisory tool for system operators and a fast initializer for conventional solvers, thus supporting resilient and efficient grid operation in future power systems.

Robotic additive manufacturing (AM) extends material-extrusion printing beyond gantry kinematics but makes process planning robot-dependent. A slicer-generated plan that appears favorable in part coordinates can become infeasible or robotically unfavorable on a manipulator because slicer-process decisions and part orientation determine the generated path, while part orientation and workspace placement affect its kinematic realization. Existing AM tools, large language model (LLM)-based decision-support methods, and digital-shadow systems do not provide integrated pre-execution evaluation of these coupled decisions. This paper presents agentic robotic additive manufacturing (A-RAM), an agent-specialist-tool framework that converts user intent and a part file into traceable, execution-ready plans. The LLM interprets manufacturing objectives and constraints, identifies prescribed and searchable planning variables, and encodes this reasoning in a schema-constrained request; a deterministic Planning Agent instantiates the corresponding search workflow, while domain tools compute quantitative evidence for slicing, placement, inverse kinematics, trajectory timing, Joint-6 jerk, and extrusion. The framework is evaluated on a six-axis robotic-arm AM cell through three case studies covering expert-specified planning, goal-only planning, objective-dependent infill screening, and geometry-dependent orientation-placement selection. Across the evaluated candidate sets, selected plans achieve up to 53.5% lower maximum Joint-6 jerk and 48.3% lower mean absolute Joint-6 jerk than the least favorable valid candidates, while objective-specific infill screening yields motion-plan completion times up to 40.1% shorter and extrusion paths up to 12.7% shorter than the corresponding least favorable screened patterns.

This paper proposes a high-fidelity hyperscale data center load modeling framework that disaggregates facility demand into IT and non-IT components and represents load behavior at second- and minute-level resolutions. Building upon this foundation, a comprehensive multi-phase optimization framework is developed for the planning and resilient design of BESS for BTM data center microgrids. The framework deploys BESS on the load side to act as a dynamic buffer between stochastic demand and generation assets. By smoothing the load spikes and excursions before they are observed by gas turbines, the load-side BESS reduces operational stress and limits conditions that can contribute to SSTI issues, shaft fatigue, system trips, equipment damage, and forced outages. Simultaneously, generation-side BESS resources are optimally sized to provide spinning reserves and enhance system resilience. The proposed methodology co-optimizes BESS with solar, wind, natural gas fuel cells, simple-cycle gas turbines, and combined-cycle gas turbines while incorporating operational, reliability, resiliency, and technology-specific constraints. Simulation results demonstrate the proposed methodology's ability to identify cost-effective, resilient, and operationally feasible designs that satisfy the demanding reliability requirements and energy market challenges of next-generation hyperscale data centers while providing planning insights for investors, developers, and system operators.

We stabilize the linearized 2-D Poiseuille channel flow at arbitrary Reynolds numbers, and assign the decay of every wavenumber to any user-prescribed rate. The actuation is as in Vazquez–Krstic (IEEE TAC, 2007), VK'07 below: the two velocity components at only one wall. This is the first Fredholm backstepping design for a Navier–Stokes system. In VK'07 the wall-normal input renders the plant spatially causal, after which the tangential input closes a Volterra backstepping loop. Here the normal input carries a finite-rank feedback of arbitrarily small gain, whose sole role, in the sense of Heymann's lemma (TAC, 1968), is to give the plant simple spectrum and make every mode controllable from the tangential velocity. The tangential input then applies a stabilizing feedback, obtained through an invertible Fredholm transform to a Stokes target PDE, shifted left by an arbitrary decay. No simplicity of eigenvalues of the Orr–Sommerfeld operator is assumed and the exclusions of plant coefficient values that have accompanied Fredholm backstepping are removed. We state the comparison with the Volterra design without embellishment: the Fredholm architecture is powerful, but its gain is spectral where VK'07 is closed-form, the simpler of the two, and one from which the Fredholm approach takes its model, its actuation, and its target. What is demonstrated here is the reach of the Fredholm method on its most demanding plant to date. The feedback is tested at Reynolds number $30000$, with the dominant part of the closed-loop spectrum assigned so that it amounts to slowing the flow about twentyfold.

Understanding the efficient transport of fluid droplets in confined geometries has been a domain of interest for industrial applications in recent times. In the present work, we focus on designing control strategies that optimally steer droplet motion. Here, we apply optimal control framework to the droplet transport problem in a microchannel based on lubrication theory that minimizes viscous dissipation. Two complementary modeling routes are adopted: a reduced-order ordinary differential equation (ODE) model optimized via Pontryagin's Maximum Principle, and a full nonlinear partial differential equation (PDE) model optimized using a Covariance Matrix Adaptation-Evolutionary Strategy. By parameterizing target displacement, droplet size, and capillary number, we uncover two distinct optimal transport regimes: a "translate-relax" strategy for short distances and a "compact-translate-relax" strategy for longer targets. In continuum mechanics, the competition between surface forces and cumulative viscous dissipation decides the optimal transport strategies. We further show that the displacement range over which the reduced-order controller transfers to the continuum model is governed by capillary stiffness. We finally address closed-loop stability by adapting a control Lyapunov function (CLF) framework to the reduced-order dynamics. We demonstrate that the terminal cost which penalizes deviation from the target, serves as a cost-compatible CLF on the physical domain, and prove that the CLF-compatible feedback exponentially stabilizes the target state.

This paper develops a guidance framework for cooperative transportation of a rigid payload by two uncrewed aerial vehicles (UAVs) to stationary and maneuvering landing platforms. A virtual equivalent-agent representation is first introduced to describe the translational motion of the rigidly coupled UAV-payload system, allowing the transportation problem to be formulated in terms of relative range and line-of-sight dynamics with respect to the landing platform. A geometric analysis establishes the terminal feasibility conditions for payload delivery. In particular, an arbitrary prescribed approach angle can be achieved for a stationary platform, whereas successful delivery to a maneuvering platform with zero relative velocity requires terminal velocity and heading angle synchronization and consequently a zero landing angle. Leveraging this framework, a robust fixed-time sliding mode guidance strategy is developed to regulate both relative range and line-of-sight dynamics. A separate link-orientation controller and control allocation scheme is presented to map virtual equivalent agent commands to the individual UAV's control inputs. The proposed strategy guarantees convergence to the desired landing configuration within a uniformly bounded time, independent of initial engagement geometries, while explicitly accommodating uncertainties arising from target maneuvers. Numerical simulations demonstrate accurate delivery under different terminal approach angles and platform maneuvers, while processor-in-the-loop implementation on a Raspberry Pi demonstrates that the guidance algorithm satisfies the real-time computational requirements. Nonetheless, a comparative analysis shows that the proposed framework achieves better tracking accuracy and faster sliding surface convergence while requiring significantly less control energy from each UAV.

This paper addresses leader-follower formation control using only relative bearing and velocity measurements. Bearing-based leader-follower control strategies commonly use fixed control gains, for which the guaranteed convergence rates explicitly depend on the persistence of excitation (PE) properties of the desired formations. We propose a time-varying matrix gain that evolves according to the bearing information available to each follower and decouples the convergence rate from the PE bound. We establish the well-posedness and uniform boundedness of the proposed gain for bearing-persistently exciting formations, and characterize the exponential convergence rate through a tunable design parameter. The proposed control design is further extended to leader-follower formations with double-integrator dynamics. Simulations illustrate the resulting convergence properties compared with fixed gain designs.

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent $X$ rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

This note establishes a geometric foundation for trajectory-manifold representations of deterministic nonlinear systems in a behavioral setting motivated by data-enabled predictive control. For a discrete-time system $x_{k+1}=f(x_k,u_k)$ with measured state and a $C^r$ transition map, $r\geq 1$, we consider the terminal-state-augmented finite-horizon behavior consisting of all admissible state-input trajectories over a prediction horizon $N$. We prove that this behavior is a $C^r$ embedded submanifold of the ambient trajectory space with intrinsic dimension $n+Nm$, where $n$ and $m$ are the state and input dimensions. Moreover, the rollout map from the admissible initial-state and input coordinates $(x_0,\mathbf u)$ is a $C^r$ diffeomorphism onto the behavior manifold, providing explicit global smooth coordinates. This yields a canonical exact encoder–decoder representation and implies that any exact differentiable latent representation of the full behavior must have latent dimension at least $n+Nm$. The geometric result does not require controllability, stabilizability, or invertibility of the dynamics. Corresponding results are given for zero-order-hold sampled continuous-time systems and fixed-step numerical transition maps. These results provide the deterministic geometric foundation for subsequent data-driven approximation and predictive-control development.

This paper establishes the necessary and sufficient conditions for asymptotic stability of the time-varying Kalman filter applied to a linear time invariant system with semidefinite initial state covariance and positive definite process and measurement noise. Rather than analyze the discrete Riccati equation as in the classic literature, the equivalent state smoothing optimization problem is stated and all results are established using properties of this optimization problem. A Lyapunov-like function, termed a modified $Q$-function is derived and used for this analysis. This optimization approach removes the need for the classic but cumbersome Riccati iteration algebra and provides better generalization and application for nonlinear systems.

As data center (DC) loads increasingly penetrate the power grid, there is an urgent need for grid operators to provide clear dynamic specifications to DC owners to ensure safe grid operation. To this end, we study two salient behaviors of large language model (LLM) training loads: abrupt ramps at job initiation and termination, which induce transient frequency excursions, and sustained periodic oscillations during training, which result in oscillatory steady-state behavior. For ramping loads, we show that nodal rotor frequencies can be accurately approximated by the center-of-inertia (COI) frequency and derive analytical expressions for its nadir and rate of change of frequency (RoCoF). These expressions determine allowable combinations of ramp times and steady-state load demands satisfying prescribed frequency limits. For oscillatory loads, we derive spectral specifications on their Fourier coefficients and show that the admissible coefficient set can be approximated by a polytope. We further obtain a compact representation via its maximum-volume inscribed ellipsoid, which we show is axis-aligned. Numerical tests on the WECC 179-bus system demonstrate that the resulting specifications remain valid for higher-order nonlinear dynamics. The proposed framework provides actionable specifications for regulating the dynamic behavior of large DC loads and informing load-shaping mechanisms within the data center ecosystem.

Large Language Models (LLMs) are now routinely trained using synthetic data, since high-quality human data has been exhausted by the ever increasing needs of larger and larger models. However, recursive training on synthetic data frequently induces model collapse, a degenerative feedback loop where models progressively forget the true underlying data distribution. Training on a mixture of synthetic and fresh human data is a logical countermeasure and can prevent model collapse. However, it is an open question as to what is the exact minimum required ratio of human-to-synthetic data to maintain training stability. In this paper, we establish rigorous theoretical guarantees on the minimum rate of human data required to prevent model collapse. Although previous work established a formal lower bound for this ratio, such bound can be vacuous for very high dimensions, as the analysis relies on the usual Euclidean metric in R^n and is not adapted to the space of categorical probability distributions. Instead, in this paper we explicitly leverage the information-geometric structure of the probability simplex by analyzing the dynamics of the process under the Fisher-Rao metric. We derive quantitative contraction and invariance bounds that are stable and do not become trivial as the dimensions increase. Thus, we show that the effective required data ratio to prevent model collapse is different than previously implied.

This paper addresses the problem of designing time-optimal control profiles for point-to-point control of a gantry crane moving in a two dimensional plane. It is assumed that the hoisting motor completes the hoisting maneuver at a constant rate and completes its transition in the same time that it takes for the cart to reach its terminal position. This results in a linear time-varying model and a closed form solution to the time-optimal control problem is shown to be parameterized with Bessel functions. A comprehensive analysis of the structure of the time-optimal control profile is studied by examining the switching function which illustrates the mechanism of introduction and decimation of switches in the bang-off-bang control profile. The variation of the number of switches in the optimal control profile is presented and a non-intuitive control profile structure is noted, one which initiates with a stationary cart, while the hoisting cable length is changed prior to the initiation of motion of the cart. To address the issue of uncertainties in the initial cable length, a model with the sensitivity of the system states with respect to the initial cable length is used to augment the system model and is used for the design of robust time-optimal controllers. Experimental results validate the time-optimal and robust time-optimal control profiles.

Region-of-attraction (ROA) certificates for polynomial systems become expensive as state dimension and degree grow: direct sum-of-squares (SOS) formulations require combinatorially growing monomial bases. Quadratization represents a polynomial vector field exactly on an invariant manifold of a quadratic system, allowing a quadratic Lyapunov function to certify the ROA. For a fixed lift, stabilizer gains shape the off-manifold extension and transverse dynamics, while representation gauges change the matrix representation but not the vector field. Both affect the spectral-norm certificate, yet prior work fixes the gain by a feasibility heuristic before optimizing the gauge. We formulate optimal dissipative quadratization (ODQ), jointly designing gains and gauges for a fixed monomial lift, reference extension, stabilizer factorization, and Lyapunov weight $Q=I$. Gains lie in a prescribed compact Hurwitz box. At each gain, an exact semidefinite program globally minimizes the spectral-norm bound over the gauge. Residual-aware bounds yield a certified closed Lyapunov sublevel set, accounting for the floating-point Lyapunov residual. Under our stated assumptions, every accumulation point of the idealized outer search is box-Clarke stationary. A finite run returns the best independently verified candidate; global optimality of the gain search is not claimed. On a planar quintic, optimizing the gain increases the certified area by a factor of $2.238$ over a matched zero-gain gauge. Across 16 heterogeneous polynomial systems with stabilizer freedom, ODQ improves on both fixed-gain lifted baselines. All 36 ODQ runs on the relay benchmark complete, and all 27 repeat-level comparisons across nine fully paired cases favor ODQ over an SOS baseline with a fixed quadratic Lyapunov function in both the fixed-direction proxy and construction time. Broader comparisons with direct SOS methods remain mixed.

Two-stage stochastic Mixed-Integer Linear Programs are a canonical modeling tool to optimize power system operations under uncertainty, yet their extensive-form counterparts scale linearly with the number of scenarios and quickly become computationally prohibitive under day-ahead time constraints. We propose an Input Convex Neural Network architecture to learn a convex surrogate of the second-stage value function, enabling fast first-stage optimization while preserving convexity by construction. We couple the surrogate with a Neural-Benders correction loop that refines the first-stage solution a posteriori, recovering the exact optimum whether the network overestimates or underestimates the recourse cost, and certifying solution quality independently of surrogate accuracy. We evaluate the method on IEEE Stochastic Unit Commitment benchmarks (case9-case118) under both continuous and integer recourse. The proposed approach achieves solutions with zero optimality gap on the $K$-scenario instance across all test cases and scenario dimensions $K \in \{10, 50, 100\}$, with speedups up to $214\times$ over the Extensive Form in the integer setting. Solve times are stable across scenario realizations and compatible with day-ahead time windows on the tested benchmark instances.

The O-RAN control plane is becoming agentic: autonomous AI agents, deployed as rApps by different vendors, independently close control loops over shared radio resources. We demonstrate on a live O-RAN system that this independence is unsafe. Two agents with individually correct objectives, one protecting a latency SLA and one maximizing utilization for energy efficiency, jointly drive recurring opposing excursions of the shared resource partition that neither produces alone. Existing conflict-mitigation mechanisms presume a statically known application population and cannot govern agents whose behavior emerges at run time. We present AURA, a lightweight arbitration layer that admits agent actions only when they satisfy feasibility invariants, per-variable dwell times, and a deadband, and we prove the arbitrated system converges to a feasible operating point. Implemented on an OpenAirInterface (OAI) testbed with measured one-way latency and throughput, AURA reduces recurring shared-state excursions by more than an order of magnitude (from 8.4 to 0.4 PRB amplitude) and virtually eliminates cross-slice throughput starvation (from 40-55% to 0.3%), while leaving the protected slice's own latency compliance unchanged, a trade-off the convergence guarantee makes explicit.