Papers

In the 2004 collection Unsolved Problems in Mathematical Systems and Control Theory, Erik Verriest posed the problem of characterizing Riccati stability “without invoking additional matrices.” We give such a characterization through a scalar invariant of the resolvent family. The invariant is defined by covariance balances using at most $n^2+1$ frequency–direction pairs. A finite-dimensional separation argument shows that this covariance radius equals the optimal common ellipsoidal norm of the resolvent family. Combined with the strict bounded real lemma, this yields a necessary and sufficient condition for Riccati stability involving only the Hurwitz property of the first matrix and a single scalar inequality. The invariant reduces to the ordinary spectral radius for one matrix, lies between the pointwise spectral-radius and unscaled small-gain levels of the resolvent family, and coincides with the operator-space spectral radius of Shalit and Shamovich for the natural resolvent function space. The main results have been formally verified in the Lean proof assistant.

Data-driven techniques have shown promising potential for checking behavior of complex systems operating in safety-critical domains against safety and other temporal requirements. This paper studies a class of data-driven techniques that are based on learning a representation of the system from data using non-parametric estimation. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic specifications only using observation samples and without the knowledge of the model, and provides a probabilistic guarantee on the satisfaction of the specification. We first consider finite abstract representations of the system in the form of Markov decision processes (MDPs) and derive asymptotic convergence guarantees between the transition probabilities of the abstract MDP and their estimation using Bernstein's inequality and statistical properties of non-parametric estimators. We then propose theoretical results for estimating the asymptotic upper bound of the Lipschitz constant (LC) of the stochastic system, which can determine the size of the finite abstract MDP for a given precision error. Under appropriate assumptions, our results prove that the asymptotic convergence rate of the estimations is $O(n^{-1/(3+d)})$ for both the transition probabilities and the LC, where $\mathsf d$ is the dimension of the system and $n$ is the data scale. By integrating these results, we can guarantee the asymptotic closeness in formal verification and policy synthesis performed on the original system and its finite abstraction based on the size of the dataset. Multiple case studies are presented to validate the effectiveness of the proposed method.

We study policy optimization for discrete-time robust $\mathcal{H}_\infty$ control with static output-feedback, and present the first feasibility-preserving algorithm with a deterministic, non-asymptotic complexity guarantee. This problem naturally leads to a nonsmooth and nonconvex optimization over the set of stabilizing feedback gains. We first establish several structural properties of the $\mathcal{H}_\infty$ cost. In particular, we show that the cost is weakly convex on every convex subset of a sublevel set. For the state-feedback case, we further establish a weak Polyak–Łojasiewicz inequality, which ensures that every stationary point is globally optimal. Building on these properties, we develop a proximal bundle method for $\mathcal{H}_\infty$ policy optimization. The proposed method can be viewed as an implementable approximation of the proximal point method and uses only function value and subgradient information. We show that all iterates remain stabilizing and establish a deterministic non-asymptotic complexity bound of $\mathcal{O}(\max\{\eta^{-4},\epsilon^{-2}\})$ for finding an $(\eta,\epsilon)$-stationary point. Numerical experiments illustrate our theoretical results.

We study continuous-time full-order dynamic output-feedback $H_\infty$ policy search, a nonconvex and nonsmooth problem. Direct policy search is a central paradigm in reinforcement learning and continuous control, but rigorous guarantees remain scarce in robust output-feedback settings. The $H_\infty$ problem is a canonical benchmark because it captures disturbance attenuation and robustness while exposing the hard nonsmooth geometry of policy-space optimization. We prove that on the exact identity-gauge slice of the extended convex lift, $\varepsilon$-stationarity yields $O(\varepsilon)$-suboptimality on compact exact slices, which in turn yields convergence-rate guarantees for nonsmooth policy-search methods. This result addresses the finite-time optimality-gap question raised by Guo and Hu [2022] in the more general dynamic output-feedback $H_\infty$ policy-search setting. We further use the established value equivalence supplied by extended convex lifting to formulate a nonstrict-feasibility bisection method with one final strict-feasibility recovery step, yielding an explicit $\varepsilon$-optimal stabilizing controller. These results provide a quantitative and algorithmic strengthening of prior qualitative optimality theory for nonsmooth $H_\infty$ policy search.

The leader-follower formation control problem is investigated for nonlinear multi-agent systems with unknown dynamics, external disturbances, and false data injection (FDI) attacks on actuator channels. The problem is formulated as a zero-sum differential game and solved using the Integral Bellman-Isaacs approach. To address input saturation constraints, a non-quadratic control cost function is incorporated into the optimization problem, leading to a bounded control law. Furthermore, this paper proposes a cost function construction method and develops a critic learning law, which together guarantee the practical fixed-time stability of the system while overcoming the limitations of existing fixed-time reinforcement learning formulations. Finally, the practical fixed-time convergence of both the critic weight estimation error and the leader-referenced formation tracking error to bounded residual sets is rigorously proven. Simulation results demonstrate the effectiveness of the proposed method under external disturbances, FDI attacks, and input constraints.

Incremental contact laws specify the normal contact force through a differential equation carrying an internal state, driven by the indentation and its rate. In some, the force is extinguished at a nonzero indentation, whether by plastic deformation or by an elastic aftereffect, so that a residual deformation remains at the separation. Such laws sit uneasily within rigid body dynamics, which admits no deformation. The tension is tolerable when the indentation is small relative to the bodies, so that it may be carried constitutively rather than geometrically. Even then, the contact law alone does not determine the interaction of the bodies. Because force and indentation no longer vanish together, conditions for the commencement and termination of contact must be supplied separately. So must the fate of the deformation and internal state at separation, neither of which the equations of motion contain. This article formulates the repeated direct collinear impact of two convex bodies under external forces as a hybrid dynamical system. The contact interface is modeled as a massless element carrying the contact law and its state, coupled to the bodies through relative velocity and an interaction force dictated by the contact state. Consequently, all switching and resets are confined to the interface, leaving the geometry and the equations of motion of the bodies unaltered. The principal analytical properties of the resulting formulations are established, among them passivity and completeness; the branching of solutions at the onset and termination of contact is also examined. The framework is demonstrated through numerical simulations.

Consider a parametric ODE control model. A function of the states and parameters is called observable if its value can in principle be reconstructed from input-output data. The observable functions form a field, called the observation field, represented naturally by a set of generators. Even when the model is not fully observable, this field captures the information still accessible from input-output data. We present an algorithm for computing a concise generating set for the observation field of a model with rational dynamics. The algorithm relies on two new results: one allows observable functions to be extracted from the coefficients of repeated Lie derivatives of the outputs, while the other reduces the required orders of differentiation by exploiting identifiable parameter combinations. We implement the resulting algorithm in StructuralIdentifiability$.$jl (https://github.com/SciML/StructuralIdentifiability.jl). For computational efficiency, we employ recent techniques for differential elimination and rational function field simplification. Using models from epidemiology, chemical kinetics, and cancer modeling, we show that the algorithm produces generators with domain-specific interpretations that can inform model analysis and development.

Artificial intelligence (AI)-based radio access network (RAN) controllers are commonly designed for predefined operating scenarios and optimization tasks, limiting their adaptability when network conditions and operator requirements change after deployment. This paper proposes multimodal large language model (MLLM)-guided constrained optimization for RAN intelligent control (MLLM-coRIC), a requirement-adaptive hierarchical Open RAN (O-RAN) framework for joint resource and power allocation. MLLM-coRIC jointly exploits the operator's natural-language specification and radio-frequency (RF)-derived network context as multimodal inputs, enabling a single deployed framework to address different optimization problems without redesigning task-specific algorithms or retraining control policies. At the Non-Real-Time RAN Intelligent Controller (Non-RT RIC), the MLLM performs holistic, longer-timescale reasoning over the operator requirement, predicted network evolution, and measured optimization outcomes to design the numerical control loss. The relative constraint penalties are iteratively refined through a closed-loop process, allowing the optimization criterion to reflect both the intended network behavior and the expected operating context. At the Near-Real-Time RIC (Near-RT RIC), a loss-conditioned hybrid executor translates the synthesized criterion into fast radio actions by combining learned ramp-constrained resource allocation with model-based interference-aware power control. A multi-cell evaluation environment integrating the CARLA urban mobility simulator and the Sionna RT ray-tracing-based wireless propagation simulator is implemented for validation.

We present a modular, high-fidelity simulation framework for the development and benchmarking of flight control strategies in fixed-wing aerial robots operating near the ground. Unlike existing simulators that rely on simplified or hover-oriented dynamics, our framework models full 6DoF rigid-body physics, semi-empirical ground-effect aerodynamics, actuator dynamics, sensor noise, and environmental disturbances. This physical realism, combined with modular component design, enables systematic analysis of low-altitude flight behavior under realistic conditions. The simulator supports both CPU and GPU backends via Torch and NVIDIA Warp, enabling high-throughput parallel execution suitable for large-scale reinforcement learning training and optimal control rollouts. A unified interface accommodates a range of controllers (both RL and optical control algorithms) across tasks such as altitude regulation and trajectory tracking. Cross-validation with X-Plane and JSBSim is also supported to facilitate engineering integration and visual fidelity.

A sound runtime admission gate executes only actions it can certify, and certifies only what its observations support. This paper asks how observations should be designed to maximize the set of actions that can be safely admitted, and shows the question is not a re-vocabulary of classical design problems. First, a projection–estimability separation: decomposing a constraint normal as $c=c_{\mathrm{Range}}+c_{\ker}$ relative to an information matrix, two-point discrimination along $c$ becomes arbitrarily reliable as the budget grows whenever $c_{\mathrm{Range}}\neq 0$, while robust admission of an action with normal $c$ is impossible at every budget whenever $c_{\ker}\neq 0$; such mixed directions are generic at any deficient rank, and at full rank the decoupling is bounded by the Kantorovich ratio and diverges with the condition number. Discrimination-optimal designs, being corner solutions of a linear criterion, land in exactly this regime. Second, an active-face equivalence theorem: the permissiveness-optimal design is $L$-optimal for a target matrix generated endogenously by the action faces that become certification bottlenecks, weighted inversely by their remaining slack; single-face collapse recovers $c$-optimal and goal-oriented design exactly, and a Caratheodory argument yields a bottleneck certificate of at most $r(r+1)/2+1$ faces. Around these we assemble exact certifiability per convex contract mode, for which $\kappa\approx 3.29$ is derived rather than calibrated, the $\sqrt{r}$ price of contract-agnostic design, an information-to-slack transfer theorem with a curvature-budget corollary, and a two-part audit in which a design meeting every margin requirement still leaves an action face at a certification cost above ten times its testing cost, in every probe library tested.

Heterogeneous-interface multihop wireless networks (Het-MuNets) are emerging as a promising paradigm for tactical networks and for infrastructure-light applications such as vehicular communications, wireless backhaul, and non-terrestrial connectivity. To exploit the diverse profiles of heterogeneous communication technologies in penetration, interference, and bandwidth, packet-to-interface assignment must be determined on a per-hop basis, making routing and scheduling highly complex. In this work, we develop a unified framework for joint packet routing, link scheduling, and interface assignment in Het-MuNets with multiple concurrent flows. By modeling packet-to-interface assignment as transmission between virtual subnodes, we transform interface assignment into intra-device virtual routing, which is solved jointly with physical routing and scheduling under a unified multi-layer shortest path-biased Backpressure (SP-BP) scheme. Numerical results demonstrate that the proposed framework outperforms SP-BP operating on other baseline graph models and non-backpressure routing schemes in goodput, latency, and packet delivery rate.

Implantable brain-computer interfaces (BCIs) promise transformative societal impact, from restoring lost motor, sensory, and speech function in patients with paralysis, stroke, sclerosis, and sensory deficits to serving as a high-bandwidth conduit between human cognition and machine intelligence. Realizing these visions requires moving from laboratory prototypes to chronic clinical systems that support thousands to millions of electrodes, several millimeters to centimeters deep beneath the brain surface, under strict heating and size limits. Almost every clinically relevant implant therefore operates in a weakly coupled regime, with coupling coefficients of $10^{-3}$ to $10^{-1}$ across centimetres of lossy tissue. In this regime, the wireless channel sets the limits of power-transfer efficiency, communication bandwidth, and energy per bit. We review the recent progress of bidirectional wireless links across inductive, mid-field, RF, ultrasonic, magnetoelectric, optical, UWB, and electro-quasistatic modalities, and benchmark them against the clinical axes of depth, size, and data rate. Within an approximately 10 mW communication budget set by the approximately $1^\circ$C tissue-heating ceiling, narrowband high-Q links are well suited for power transfer and low-speed data, but at 1-10 nJ/b cannot reach the greater than 10 Mbps to tens of Gbps uplinks that thousand- to million-channel interfaces demand, even with aggressive on-implant compression. This calls for sub-10 pJ/b and ultimately sub-1 pJ/b wireless links, where wideband techniques, such as ultra-wideband (UWB) and brain-channel communication (BCC), are suitable. We close with a quantitative framework for analyzing such wireless links and a co-design roadmap across electromagnetics, circuits, packaging, security, and regulation, toward secure, networked, million-channel brain interfaces.

Model-based control design requires sufficiently accurate model of the system-to-be-controlled. This paper addresses the system identification of steering and speed control of a four-wheel-steering agricultural tractor for the purpose of developing path tracking control. To this end, we investigate the steering and speed control systems of the tractor. These are complex systems with digital, mechatronic, and hydraulic components challenging to model based on first principles. We take a data-driven approach to estimating the system models. The resulting model combines the kinematic model of the vehicle, actuators modelled as first-order systems, and estimated values for time constants and transport delays.

We consider a fully connected gossip network of $n$ nodes that track a binary continuous-time Markov source through a strategic sender transmitting updates under a communication budget at a rate that depends on the source state. The receivers exchange packets through gossip and decide whether to follow the sender. We model this interaction as a Stackelberg game and analyze it through a stochastic hybrid systems (SHS) framework. We prove that the sender's budget constraint binds at every interior optimum, reducing its problem to a one-dimensional search on the budget line. When the sender pushes its preferred state at the higher rate, the receivers gossip at the highest available rate. Gossip has no direction of its own and works against the asymmetry in the sender's policy rather than reinforcing it. We prove that an optimistic Stackelberg equilibrium exists, and that it is unique and explicitly characterized whenever a policy on the strategic half of that line is feasible at the gossip cap. Monte Carlo simulations agree with the analytical recursion.

Decarbonising the building sector is central to meeting climate targets, yet existing models rarely capture the interaction between system-level transformation dynamics and heterogeneous individual investment decisions. This work presents AgentHomeID, an agent-based model of building stock evolution in which owner behaviour, techno-economic constraints, and regulatory frameworks are represented explicitly at the level of individual buildings and their owners. The model differentiates owner-occupiers, private landlords, and institutional owners, using willingness-to-pay (WTP) parameters estimated from empirical decision-maker studies, and operates on both representative building archetypes and real building data derived from geographic information systems (GIS). We demonstrate this versatility across three applications. At national scale, scenario analysis for Germany to 2045 shows that removing binding renewable heating requirements substantially raises final energy demand even where envelope refurbishment is unchanged, and that subsidy allocation and investment activity diverge sharply across owner types and income quartiles, with the lowest quartiles persistently underinvesting. At regional scale, bottom-up simulation for a German distribution grid planning region yields spatially concentrated heat pump uptake at NUTS-3 level that differs from aggregated top-down projections in both magnitude and spatial distribution. At urban block level, the same simulations resolve substation-level load heterogeneity and show that integrated system peaks driven by heat pumps, electric vehicles, and photovoltaics do not coincide with individual technology peaks. Across all three scales, owner heterogeneity and local structure materially shape transition pathways, indicating that they should be represented explicitly in models used for policy assessment and infrastructure planning.

Work on the risks of artificial intelligence has focused predominantly on capability risk: the danger that systems become too powerful, too autonomous, or too misaligned with human values. Far less attention has been paid to the organizational level—to whether the institutions building these systems are themselves predisposed to drift toward failure. This paper argues that they are. Regardless of how capable AI systems become, the organizations building them face the same structural dynamics that preceded past major technological disasters. Drawing on case studies of the Space Shuttle Challenger, the Three Mile Island accident, and the Boeing 737 MAX crashes, this paper identifies the common structural mechanisms preceding each failure and maps them onto contemporary AI development. The findings suggest that existing safety infrastructure may provide less protection than it appears, as organizations can complete safety processes in full compliance and still produce catastrophic outcomes. The pre-disaster period of AI development is still underway; the purpose of this paper is to make these dynamics legible while they can still be interrupted.

Autonomous unmanned vehicles are vital to tactical missions, mission-critical public-safety operations like search and rescue and disaster response. However, their reliance on open wireless links and standard Robot Operating System (ROS 2) middleware exposes a broad cyber-physical attack surface. A compromise of these systems can disrupt real-time control loops, leading to mission failure or asset loss in high-stakes environments. This paper presents and empirically evaluates a layered, context-aware cybersecurity framework enforcing Zero-Trust principles for a multi-node robotic fleet over Wi-Fi. The framework integrates an active hardware root of trust (TPM 2.0), centralized in-band and out-of-band SIEM telemetry monitoring (ELK Stack and Kismet), and a non-cryptographic Inter-Packet Delay (IPD) timing watermark. Evaluated on a live ROS 2 mobile testbed under multi-layer exploits (OSI Layers 2-5), results demonstrate that while volume-based filters isolate brute denial-of-service floods, tracking the statistical sample kurtosis (K) of the embedded IPD watermark exposes stealthy Man-in-the-Middle command injections with complete detection accuracy without payload overheads.

Traffic analysts must translate diagnosed bottlenecks into executable interventions without allowing local improvements to degrade network-wide performance. This study presents SimTIO, a simulation-grounded multi-agent large language model framework for composing and selecting traffic interventions under explicit operational constraints. SimTIO first simulates an unmodified SUMO scenario to identify a baseline-frozen set of ten bottleneck edges. A grounded sampler then initializes signal-control, corridor-speed, and demand-preserving routing actions, while three specialist agents use measured simulation feedback to select one-parameter refinements from validator-confirmed mutation catalogs. Compatible actions are combined and re-simulated so that their interaction effects are measured rather than inferred. Final selection minimizes bottleneck time loss while constraining network-wide delay, neighboring-road spillover, throughput loss, and teleport events, with the unmodified scenario retained as a no-operation guard. Across 15 cases covering five U.S. urban networks, three synthetic-demand seeds, and 2,400 origin-destination trips per scenario, SimTIO reduced Top-10 bottleneck time loss by an average of 9.18 percent and network-wide delay by 2.78 percent. It found a feasible improving plan in 86.7 percent of cases, compared with 73.3 percent for grounded random search and 80.0 percent for a deterministic heuristic under the same seven-simulation budget, although the differences in Top-10 improvement were not statistically significant. These results support using LLMs as constrained, feedback-guided local search operators while reserving final decision authority for executable tools, microscopic simulation, and explicit safety constraints.

The operational integrity of autonomous mobile robots relies on the continuous availability of wireless control loops, making them highly attractive targets for adversarial intentional electromagnetic interference. This paper introduces a resilient, cross-layer framework that combines physical-layer spectral perception with network-layer routing optimization to protect middleware stability, such as ROS2, during intentional electromagnetic interference. Utilizing a software-defined radio front-end, the system extracts dynamic spectral descriptors, including spectral entropy and channel occupancy, to inform a Random Forest classifier that establishes adaptive environmental baselines. To ensure uninterrupted data flow, the architecture maintains dual pre-authenticated physical interfaces in a hot-standby configuration, enabling instantaneous failover through automated network routing table updates. Empirical validation on a physical ROS2 mobile robot testbed demonstrates that this adaptive hardware-assisted architecture optimizes communication recovery to an average of 141ms. This sub-second restoration translates directly into a 78.9% reduction in pooled root-mean-square path tracking error compared to software re-association, successfully securing system-level mission integrity.

We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $\pi\propto\mu e^{\tau r}$, where $r$ is the reward, $\tau>0$ the inverse temperature, and $\mu$ denotes the pretrained model's terminal density for fine-tuning or the constant $1$ for sampling. We shift the paradigm from isolated losses to iterative optimization over canonical models: population minimizers of standard conditional matching for terminal densities. Under compatible smooth-realization assumptions, canonical velocities form a manifold diffeomorphic to the density manifold. Transporting the Fisher-Rao metric and mixture connection to this manifold, we show that the reverse-KL Hessian equals the metric, so the Newton direction coincides with the negative Fisher-Rao gradient. At terminal density $\rho$, each stage takes a tangential step generated by the regularized reward $r-\frac1\tau\log(\rho/\mu)$, followed by terminal-density-preserving canonicalization. This canonical retraction yields an exact finite-stepsize density characterization. For the ideal iteration, we prove strict reverse-KL descent away from the target for $0 < \eta \le \tau$, global convergence under mild conditions, and local quadratic convergence for full steps ($\eta=\tau$). Covariance and gradient forms, each with forward or reverse regression-pair constructions, yield sample-wise tangential-update losses with the same population minimizer, without importance sampling or full-trajectory backpropagation. We develop approximate updates and define critical-point consistency as vanishing tangential displacement if and only if $\rho=\pi$. We recover representative methods as exact realizations, critical-point-consistent approximations, or objective-altering variants, enabling modular algorithm design. Our work advances the theory and algorithms of reinforcement learning for generative models.

Grid studies often represent data-center flexibility as a fixed percentage of load, although no public production trace has shown how much eligible load persists across event durations or co-moves across clusters. We reconstruct 4,439 hourly power observations from a 185-day trace of 155,410 GPUs and derive a workload-semantic flexibility envelope. The fleet's time-averaged Monte Carlo median facility demand is 55.8 MW, while immediate eligible curtailment averages 3.55 MW after retaining allocated-GPU idle power: 12.1% of workload power and 6.35% of median facility power. Under full realization of that eligibility, 95%-available relief falls from 2.51 MW for one hour to 2.32 MW for four hours and 1.95 MW for 24 hours; a common realizable fraction q scales every value exactly by q. A mean-calibrated scalar overstates these quantities by 17%, 25%, and 47%, while a scalar tail-calibrated at four hours understates the one-hour product by 6% and overstates the 24-hour product by 17%; the share that reproduces the surface varies by a factor of 1.6 across durations and reliability levels. Aggregating 13 clusters raises four-hour firmness from 0.38 to 0.66, but cross-cluster covariance limits the gain. The production scheduler exposes almost no additional delay-based capacity: newly deferrable arrivals average 0.008 MW and have zero 95%-available capacity. These results replace an assumed flexibility percentage with duration, reliability, portfolio, and realizability terms that can be written into interconnection and demand-response contracts.

The dataset described in this article was constructed using the results of laser Doppler vibrometry experiments conducted on an aluminum plate having four bolts. The database captures the variation in the vibration characteristics of the plate as a function of changes in tightening torque on the bolts. In total, there were 18 different states for the tightening torque, ranging from a situation where all bolts are tightened to all bolts being loose. Other possible combinations include states with varying torque applied to just one bolt, and those involving multiple loose bolts. Data consist of 1,836 files exported from Polytec PSV-500, categorized as amplitude and phase data, for frequency ranges spanning 1 Hz to 51,200 Hz at intervals of 1 Hz. The identified zones were analyzed at 51 scan points for all states of torque. Supporting documents included specifications of the test plate, scan point and torque state information, selected resonance peaks tables, measured frequencies for seven resonance groups, correlation values for all FRF, visualizations, and code scripts.

This paper develops a calibrated transient forecasting surrogate model for generator digital twin (DT) decision support that evaluates planned active- and reactive power load commands before they are applied. The proposed event-conditioned Hankel Dynamic Mode Decomposition with Control (Hankel-DMDc) model combines delay-coordinate lifting, command-event memory features, and an event-weighted Hankel basis so that sparse load-transition dynamics influence the reduced representation and fitted dynamics. This design targets intervals where voltage/frequency deviations and recovery behavior determine whether a candidate load command keeps the system within acceptable limits. To provide operator-facing confidence information, a split-conformal calibration layer is applied to the frozen surrogate model to form event-conditioned joint prediction bands for voltage and frequency. The experimental results show event-window root-mean-square errors of 1.058 V and 0.155 Hz. For a nominal 90% target, the bands attain 90.17% pointwise joint voltage-frequency coverage, with mean band widths of 3.55 V and 0.566 Hz. A 50-s open-loop rollout is computed in 181 ms on a single CPU core, approximately 280 times faster than real time, with forecast accuracy evaluated over horizons up to 5 s. These results demonstrate a computationally efficient advisory framework for generator DTs that combines transient prediction with calibrated uncertainty.

As the penetration of inverter-based resources (IBRs) increases in microgrids, they are increasingly expected to play a greater role in load frequency control (LFC). Model predictive control (MPC) is attractive for LFC because it incorporates system dynamics and operational constraints. However, most MPC-based LFC formulations rely on fixed reserve headroom based on forecasted renewable availability or storage systems. Under short-term renewable intermittency, IBR headroom is stochastic and time-varying, causing optimal control commands to exceed the physically deliverable regulation capability and cause stochastic saturation. This control-actuator mismatch degrades LFC performance. Accordingly, this study develops two headroom-aware strategies for PV-dominated microgrids. First, stochastic headroom constrained MPC (SHCMPC) incorporates headroom predictions through time-varying input constraints to enforce control feasibility. Second, stochastic adaptive MPC (SAMPC) embeds headroom awareness into the MPC objective function by adaptively penalizing control actions based on predicted headroom, reducing reliance on units with limited headroom without hard time-varying constraints. Simulation results show that stochastic saturation degrades conventional MPC-based LFC, particularly under tight reserve margins. Both strategies improve regulation performance. SHCMPC eliminates saturation events, while SAMPC achieves substantial saturation mitigation with lower computational effort, offering a computationally efficient alternative for real-time LFC under stochastic renewable availability.

Building automation systems generate rich sensor data yet remain insight-poor because heterogeneous point naming, missing metadata, and fragmented documentation obstruct their operational use. This systematic review analyses and codes 66 peer-reviewed studies on large language models (LLMs) for HVAC operations published between 2023 and March 2026. Each study is classified across five application families and three LLM method families and assessed for evidence realism, deployment readiness, and the responsibility boundary between the LLM and physical HVAC decisions. The corpus is concentrated in building energy modelling (BEM, 32 of 66 papers), while load forecasting remains too sparse for subfield-level conclusions. Only four studies reach pilot-level evidence, and none reports sustained operational deployment. No study was classified as ready-now for industry adoption; three were near-term and 63 research-only. Nevertheless, several bounded, human-in-the-loop uses merit near-term trials, including point-name normalisation, document-grounded operator support, BEM workflow assistance, and advisory interfaces around physics-based controllers. Conventional machine learning (ML), model predictive control (MPC), reinforcement learning (RL) and ontology-based tools remain more adopted for high-frequency control, short-horizon numerical forecasting, and well-posed ontology mapping, while autonomous agentic operation and unvalidated occupant proxies remain research-stage. Current evidence therefore supports LLMs primarily as semantic and workflow layers rather than autonomous HVAC controllers. Future work should prioritise field-validated benchmarks, orchestration evaluation under operational constraints, and LLM-MPC/RL architectures with bounded latency and verifiable safety properties.

Data assimilation estimates the evolving state of a dynamical system by combining model forecasts with observations. While many conventional methods assume point-valued measurements, practical sensing systems may instead provide coarse information such as binary, ordinal, inequality, or interval-valued reports. Interval Data Assimilation (IDA) provides a principled framework for assimilating such information, but assumes that the observations to be assimilated are specified in advance. In many sensing settings, however, both where to query and what inequality to ask can be chosen, while only a limited number of queries can be issued. This raises a new observation-design problem: how should informative inequality queries be selected from the forecast uncertainty before their responses are known? We propose Active Query Design for Interval Data Assimilation (AQD-IDA), which uses the forecast ensemble to design binary threshold queries prior to the IDA update. AQD-IDA treats both the observation target and the threshold defining the inequality as design variables, thereby allowing the assimilation system to determine not only where to observe but also what question to ask. We develop query-selection criteria that account for forecast uncertainty, redundancy among queries, and anticipated reduction in posterior uncertainty. Experiments on Lorenz–96 and a spherical quasi-geostrophic model show that adaptive query design improves assimilation accuracy under a fixed binary-query budget, with joint observation-target–threshold selection outperforming fixed or separately designed queries. These results demonstrate that actively designing the information supplied to data assimilation can substantially increase the value of coarse observations.

We study latency-optimal file assignment in geo-distributed storage systems modeled as weighted graphs, where edge weights represent communication delays and each node stores one (possibly coded) file. Our goal is to minimize the average time required to retrieve an original file, taken uniformly over all nodes and files. We show that for every fixed number of files $k \geq 3$, computing a latency-minimizing assignment is NP-hard via a reduction from the domatic number problem. On the positive side, we identify natural network topologies that admit uncoded, structured optimal assignments in which, for every node, one can choose its $k$ closest nodes, including itself, so that they store distinct original files. We prove that every weighted tree, certain weighted cycles, and unit-weight graphs with sufficiently large minimum degree admit such assignments. For these graph classes, we provide efficient algorithms to construct latency-optimal file assignments.

Robotic hands vary widely in anatomical fidelity and mechanical complexity, and these structural choices influence the coordination of joint motions and the difficulty of controlling the system. A unified framework is presented in which the kinematic and actuation stages are analysed separately and in composition, through the conditioning of the task Jacobian, the actuation matrix, and their product. It is applied to two hands representing opposing design philosophies, the Shadow Dexterous Hand and the Anatomically Correct, Biomechatronic Hand, along four morphological aspects: joint axis geometry, actuator-to-DOF ratio, coupling architecture, and authority distribution. All parameters are derived from the hands' canonical digital representations. Anatomical fidelity carries no uniform advantage: oblique axes improve thumb conditioning but leave the long fingers worse conditioned than the orthogonal-axis design, while the branching tendon network improves the effective control mapping at every long finger and worsens it significantly at the thumb, where actuator authority is concentrated on thumb opposition. Predictions derived from these metrics are evaluated against reinforcement learning experiments using PPO, DDPG+HER, and TQC+HER, across three different tasks.

We consider safety-critical control problems involving multiple requirements with different priorities and uncertainty in their evaluation. We represent these requirements using risk-aware rulebooks, where each requirement is assigned a risk measure and an acceptable threshold, and a priority relation is defined among the requirements. Each requirement induces a risk-evaluation function that maps a policy to the risk associated with its violation. We formulate risk-aware optimal control with rulebooks as a lexicographic optimization problem over excess risks and develop an anytime filtering and branch-and-bound algorithm that progressively tightens the certified optimality gap while characterizing the corresponding set of policies at each priority level. The algorithm returns a policy together with these gaps, which bound its suboptimality. We prove that these gaps are valid for any finite computational budget and, under additional assumptions, converge to zero as the computational budget increases. We evaluate the algorithm on a synthetic benchmark with a known optimum and a realistic highway-merging simulation with CVaR-based collision, rear-braking, headway, and comfort rules.

Flexible loads can enhance power system stability by providing reserves, but their limited energy capacity and uncertain availability distinguish them from conventional generators. To accommodate these characteristics, the Danish Transmission System Operator (TSO) recently introduced new reserve market rules that incorporate energy constraints and relax reliability requirements. In this context, the optimal reserve quantification becomes a joint chance-constrained reserve quantification problem, which is difficult to solve. In this paper, we derive two analytical reformulations of this problem: an exact one when a reserve direction dominates and an approximate one, otherwise. Furthermore, when flexible loads must collectively satisfy a reliability requirement, we introduce the concept of an optimal portfolio of flexible loads: adding loads with similar expected values but different stochastic behaviors to an existing portfolio may change the total portfolio's reserves. To support this idea, we theoretically study the marginal increase in reserves resulting from adding a load. Numerical results show that our analytical reformulations closely match the exact formulation, with a mean absolute error of 2.5%. Case studies further demonstrate the existence of optimal load groupings and our ability to predict the portfolio in which a load's marginal value is highest, leveraging our theoretical analysis.