Deep learning underpins a wide range of applications in MRI, including reconstruction, artifact removal, and segmentation. However, progress has been driven largely by public datasets focused on brain and knee imaging, shaping how models are trained and evaluated. As a result, careful studies of the reliability of these models across diverse anatomical settings remain limited. In this work, we introduce MosaicMRI, a large and diverse collection of fully sampled raw musculoskeletal (MSK) MR measurements designed for training and evaluating machine-learning-based methods. MosaicMRI is the largest open-source raw MSK MRI dataset to date, comprising 2,671 volumes and 80,156 slices. The dataset offers substantial diversity in volume orientation (e.g., axial, sagittal), imaging contrasts (e.g., PD, T1, T2), anatomies (e.g., spine, knee, hip, ankle, and others), and numbers of acquisition coils. Using VarNet as a baseline for accelerated reconstruction task, we perform a comprehensive set of experiments to study scaling behavior with respect to both model capacity and dataset size. Interestingly, models trained on the combined anatomies significantly outperform anatomy-specific models in low-sample regimes, highlighting the benefits of anatomical diversity and the presence of exploitable cross-anatomical correlations. We further evaluate robustness and cross-anatomy generalization by training models on one anatomy (e.g., spine) and testing them on another (e.g., knee). Notably, we identify groups of body parts (e.g., foot and elbow) that generalize well with each other, and highlight that performance under domain shifts depends on both training set size, anatomy, and protocol-specific factors.

Compact, high-performance components in millimeter-wave (mmWave) communication systems demand new acoustic filter technology at increasingly higher frequencies. Among various promising mmWave platforms, first-order antisymmetric (A1) mode laterally excited bulk acoustic resonators (XBARs) in thin-film lithium niobate (LiNbO3) have perhaps the most impressive linear performance. Despite these advances, there are few reports of nonlinear characterization of LiNbO3 filters at mmWaves. Here, we address this gap by developing a new nonlinear methodology for high-frequency filters. The result is a methodology for performing power-dependent S-parameters and third-order intermodulation (IMD3) measurements. To test our methodology, we fabricated filters on transferred single-crystal LiNbO3 films on sapphire (Al2O3) and silicon (Si) substrates with amorphous silicon (aSi) sacrificial layer. At 21.8 GHz, the filters on Al2O3 demonstrated an insertion loss of 1.48 dB, a 3 dB fractional bandwidth (FBW) of 17.7%, and in-band third-order input intercept points (IIP3) of 50.8 dBm. At 21.6 GHz, the filters on silicon demonstrated an insertion loss of 2.47 dB, a 3 dB FBW of 18.6%, and in-band IIP3 of 46.5 dBm. The nonlinear results conclusively show that thermal stability and passband distortion improved on the Al2O3 substrate, confirming that substrate selection plays a pivotal role in mitigating nonlinearity in acoustic front-end modules.

Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary, possibly non-vanishing, time intervals as an optimization problem. Analysis of the formulation reveals aliasing induced by oscillatory dynamics and the sampling pattern, making an inherent identifiability limit explicit. The analysis also uncovers phase alignment near the true Koopman frequency, which creates a steep loss valley and demands careful optimization. We further show that irregular sampling can break aliasing and lead to phase cancellation. Numerical results demonstrate the efficacy of the proposed method under large regular time intervals compared to generator extended dynamic mode decomposition, and support the idea that irregular sampling can help recover the true Koopman spectrum.

Open-source software for cyber-physical systems (CPS) often lacks robust testing involving robotic platforms, resulting in critical errors that remain undetected. This is especially challenging when multiple modules of CPS software are developed by various open-source contributors. To address this gap, we propose Automated CPS Testing (ACT) that performs automated, continuous testing of open-source software with its robotic platforms, integrated with the open-source infrastructure such as GitHub. We implement an ACT prototype and conduct a case study on an open-source CPS with an educational robotic platform to demonstrate its capabilities.

Foundation models, including large language models (LLMs), are increasingly used for human-in-the-loop (HITL) cyber-physical systems (CPS) because foundation model-based AI agents can potentially interact with both the physical environments and human users. However, the unpredictable behavior of human users and AI agents, in addition to the dynamically changing physical environments, leads to uncontrollable nondeterminism. To address this urgent challenge of enabling agentic AI-powered HITL CPS, we propose a reactor-model-of-computation (MoC)-based approach, realized by the open-source Lingua Franca (LF) framework. We also carry out a concrete case study using the agentic driving coach as an application of HITL CPS. By evaluating the LF-based agentic HITL CPS, we identify practical challenges in reintroducing determinism into such agentic HITL CPS and present pathways to address them.

This paper studies cyber attacks against informativity-based analysis in data-driven control. Focusing on strong observability, we consider an adversary who post-processes finite time-series data by an invertible linear transformation acting on the data matrices. We show that such transformations are capable of embedding malicious states into the invariant subspace explained by the transformed dataset. We provide a constructive attack method and derive feasibility conditions that characterize when such transformations exist. Moreover, we formulate an optimization problem to obtain the minimum-norm attack that quantifies the smallest data distortion required to destroy informativity. Numerical examples demonstrate that small and structured transformations can invalidate informativity certificates.

Frequency-selective wireless power transfer provides a feasible route to enable independent actuation and control of multiple untethered robots in a common workspace; however, the scalability remains unquantified, particularly the maximum number of resonators that can be reliably addressed within a given frequency bandwidth. To address this, we formulate the relationship between resonator quality factor (Q-factor) and the number of individually addressable inductor-capacitor (LC) resonant energy harvesters within a fixed radio-frequency (RF) spectrum, and we convert selectively activated harvested energy into mechanical motion. We theoretically proved and experimentally demonstrated that scalability depends primarily on the Q-factor. For this proof-of-concept study, we define effective series resistance as a function of frequency allocating bandwidths to discrete actuators. We provide design equations for scaling untethered magnetic actuation with Q-factor optimization. Resonator networks spanning bandwidths from 100kHz to 1MHz were analyzed to quantify how increasing the number of resonators affects independent addressability. We validated the approach experimentally by fabricating three centimeter-scale untethered actuators that selectively trigger the motion of mechanical beams at 734kHz, 785kHz, and 855kHz. We also characterized the generated mechanical force and the activation bandwidth of each actuator, confirming that no unintended cross-triggering occurred.

Microscale manipulation has advanced substantially in controlled locomotion and targeted transport, yet many biomedical applications require precise and adaptive interaction with biological micro-objects. At these scales, manipulation is realized through three main classes of platforms: embodied microrobots that physically interact as mobile agents, field-mediated systems that generate contactless trapping or manipulation forces, and externally actuated end-effectors that interact through remotely driven physical tools. Unlike macroscale manipulators, these systems function in fluidic, confined, and surface-dominated environments characterized by negligible inertia, dominant interfacial forces, and soft, heterogeneous, and fragile targets. Consequently, classical assumptions of dexterous manipulation, including rigid-body contact, stable grasping, and rich proprioceptive feedback, become difficult to maintain. This review introduces micro-dexterity as a framework for analyzing biological micromanipulation through the coupled roles of embodiment, perception, and control. We examine how classical manipulation primitives, including pushing, reorientation, grasping, and cooperative manipulation, are reformulated at the microscale; compare the architectures that enable them, from contact-based micromanipulators to contactless field-mediated systems and cooperative multi-agent platforms; and review the perception and control strategies required for task execution. We identify the current dexterity gap between laboratory demonstrations and clinically relevant biological manipulation, and outline key challenges for future translation.

Industrial control applications require detecting system anomalies as accurately and quickly as possible to enable prompt maintenance. In this context, it is common to consider several possible plant models, each linked to a different anomaly. The log-likelihood ratio method can then be used to identify the most accurate model and thereby classify which anomaly, if any, has occurred. Although the method has been applied to a wide variety of systems, there is no formal analysis of what makes anomalies more or less prone to detection. In this paper, we investigate a real-time anomaly detector based on the log-likelihood ratio and provide a theoretical characterization of its error rate when it is applied to linear Gaussian systems. We showcase the performance of this algorithm and the characterization obtained, and demonstrate how the latter can be leveraged for observer design.

In this paper we address the problem of detecting differences or anomalies in a dynamical system, based on historical data of nominal operations. This problem encompasses quality control, where newly manufactured systems are tested against desired nominal operations, and the detection of changes in the dynamics due to degradation or repairs. We propose a model free approach based on Gaussian processes (GPs). The idea is to train offline a GP based on nominal data, which is then deployed online to detect whether measurements of the system state are compatible with nominal operations or if they deviate. Detecting this deviation is made more challenging by the presence of process and measurement noise, which might obfuscate deviations in the dynamics. The detection then is based on a threshold that ensures a specific false positive rate. We showcase the promising performance of the proposed method with two systems, and highlight several interesting future research questions.

Cell-free massive multiple-input multiple-output is a potential candidate for future networks with pervasive connectivity by utilizing coherent joint transmission and distributed antenna arrays. This paper studies the exploitation of full-duplex communication for a distributed antenna array. Specifically, we derive a closed-form expression for the uplink and downlink ergodic spectral efficiency (SE) for a network where the APs can flexibly operate in either the full-duplex or half-duplex mode with linear processing and Rayleigh fading channels. A long-term total SE maximization problem is formulated subject to a network operation model and individual SE requirements with limited power budget. Due to the intrinsic nonconvexity and infeasible circumstances where some UEs might not be able to achieve the rate requirements, we adapt differential evolution to design a low computational complexity algorithm that can attain good power allocation and network operation mode in polynomial time. Numerical results demonstrate the effectiveness of our system design and proposed algorithm over state-of-the-art benchmarks with satisfactory service to the majority of UEs, although several ones may be unscheduled under harsh conditions.

The enhanced Gaussian noise (EGN) model is widely used for estimating the nonlinear interference (NLI) power accumulated in coherent fiber-optic transmission systems. Given a fixed fiber link, under the assumption that transmitted symbols are independently and identically distributed (i.i.d.), the EGN model establishes that the NLI power depends on time-invariant signal statistics, i.e., the second-, fourth-, and sixth-order moments of the symbols, which are determined by the modulation format and its probability distribution. However, recent advances in coded modulation have sought to mitigate NLI by introducing controlled temporal correlations among transmitted symbols, thereby violating the i.i.d. assumption underlying the EGN model. Among these correlations, symbol energy correlations are believed to exert the most significant influence on NLI. This work presents a rigorous mathematical derivation of a memory extension of the EGN model that explicitly accounts for symbol energy correlations, referred to as the MEGN model. The proposed MEGN model is validated through both numerical simulations and transmission experiments. Normalized average NLI power estimations with less than 5% errors across a wide range of symbol rates and transmission distances are reported. The model also provides a theoretical framework for analyzing and optimizing optical transmission systems employing temporally correlated modulation schemes.

This paper proposes a novel Distributed Unknown Input Observer (DUIO) framework for state estimation in large-scale systems subject to local unknown inputs. We consider systems where outputs are measured by a network of spatially distributed sensors and inputs are introduced through multiple dispersed channels. In this framework, each local node utilizes only its local input and output measurements to estimate the maximal locally reconstructible state. Subsequently, nodes collaboratively reconstruct the whole system state via a distributed optimization algorithm that fuses these partial estimates. We provide a rigorous analysis showing that the estimation error is bounded, with the error bound explicitly dependent on the number of communication iterations per time step and strongly convexity constant determined by the system parameters. Furthermore, to counteract curvature anisotropy induced by poor conditioned system geometry, we embed a normalization step into the distributed optimization procedure. Simulation results demonstrate the effectiveness of the proposed framework and the performance improvements yielded by the normalization procedure.

This paper investigates the impact of practical features of the emerging antenna array technology of Dynamic Metasurface Antennas (DMAs) when used for wideband sensing. By adopting a realistic DMA response model capturing frequency selective magnetic polarizability, finite resonant frequency tuning, and waveguide phase and leakage effects, we first present a compact observation model for user localization and multiple scattering points sensing through DMA-based analog combining of Orthogonal Frequency Division Multiplexing (OFDM) pilots transmitted in the uplink direction. Building on this model, we derive the Fisher Information Matrix (FIM), the equivalent FIM, and the corresponding Cramer-Rao Bounds (CRBs) for the relevant spatitemporal parameters estimation. The analysis reveals that frequency selectivity reduces the effective information bandwidth and distorts the DMA-based reception manifold, while waveguide attenuation decreases both the coherent combining gain and the effective aperture, thereby degrading estimation accuracy. Numerical results validate the analysis and confirm the resulting inflation in the delay, angle, and position error bounds.

This work explores controllability and the control effort required for lithium-ion batteries. Battery packs have become a critical technology in both personal and professional applications as a means to store large amounts of energy. Management of cells in a pack becomes increasingly difficult though, with charging and discharging operations requiring more complex strategies due to parameter variations between the cells. There are numerous studies which develop effective estimation and control schemes to reduce the impact of the imbalances present in battery packs, but the receptiveness of the individual cells to these schemes is much less explored. This paper performs a nonlinear controllability analysis for experimentally parameterized cells. A connection is shown between the condition number of a battery's controllability matrix and the amount of control effort that battery will require. This reveals that if a cell's dynamics are poorly mathematically conditioned, it will require more time or higher power to control than one that is not. The controllability condition number of each cell's model is then determined both with new and aged parameters, and a sensitivity analysis shows that the cells' conditioning is equally impacted by all parameters. This offers insight into the increased control effort required for a battery as it ages and the culprit of said increase. The results of this analysis are then used to determine the best conditioned assemblies for a batch of cells with a mix of new and second-life parameters.

Traditionally, industrial control systems (ICS) were designed without security in mind, prioritizing availability and real-time communication. As these systems increasingly become targets of powerful adversaries, security can no longer be neglected. Driven by flexibility and automation needs, ICS are transitioning from wired to 5G communication, introducing new attack surfaces and a less reliable communication medium, thereby exacerbating existing security challenges. Given their critical role in society, a comprehensive evaluation of their security is imperative. To this end, we introduce SWICS, a fully virtual testbed simulating an ICS in a realistic 5G environment, and study how this transition affects security under varying channel conditions. Our results show three key findings: under optimal channel conditions, industrial 5G networks can achieve resilience comparable to wired systems, while degraded channel conditions can amplify traditional attacks, threaten system stability, and undermine detection mechanisms based on predictable traffic patterns. We further demonstrate the inherent limits of securing 5G channels for ICS through eavesdropping and jamming on the open-air interface. Our work highlights the interplay between security and 5G channel conditions, showing that traditional security controls may no longer be sufficient and motivating further research.

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management sciences (OR/MS), which have long offered conceptual and methodological foundations for sequential decision-making under uncertainty. At the same time, recent advances in deep learning, including feedforward neural networks, LSTMs, transformers, and deep reinforcement learning, have expanded the scope of data-driven modeling and opened new possibilities for large-scale decision systems. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision-making under uncertainty. Its central premise is that deep learning is valuable not as a replacement for optimization, but as a complement to it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the structural rigor needed to represent constraints, recourse, and uncertainty. The tutorial reviews key decision-making foundations, connects them to the major neural architectures in modern AI, and discusses leading approaches to integrating learning and optimization. It also highlights emerging impact in domains such as supply chains, healthcare and epidemic response, agriculture, energy, and autonomous operations. More broadly, it frames these developments as part of a wider transition from predictive AI toward decision-capable AI and highlights the role of OR/MS in shaping the next generation of integrated learning--optimization systems.

Many wireless systems divide the baseband processing between two locations, interconnected by a fronthaul. This paper examines the impact of fronthaul quantization on multiple-input multiple-output (MIMO) systems. Starting from a Bussgang-based analysis of quantized single-input single-output (SISO) channels, we extend the framework to MIMO and derive a capacity lower bound under fronthaul quantization, where the receive combining is performed before the quantization. To maximize the sum rate, we propose a joint bit and power allocation (JBP-Alloc) scheme that efficiently distributes fronthaul bits and transmit power across active data streams. Asymptotic analysis shows that uniform bit allocation becomes optimal at high SNR. Numerical results confirm that JBP-Alloc outperforms uniform allocation and quantization-unaware water-filling, and achieves the same performance as Greedy bit allocation but with substantially lower computational complexity.

Reinforcement learning (RL) can be a powerful alternative to classical control methods when standard model-based control is insufficient, e.g., when deriving a suitable model is intractable or impossible. In many cases, however, the choice between model-based and RL-based control is not obvious. Due to the high computational costs of training RL agents, RL-based control should be limited to cases where it is expected to yield superior results compared to model-based control. To the best of our knowledge, there exists no approach to quantify the benefit of RL-based control that does not require RL training. In this work, we present a computationally efficient, purely simulation-based litmus test predicting whether RL-based control is superior to model-based control. Our test evaluates the suitability of the given model for model-based control by analyzing the impact of model uncertainties on the control problem. For this, we use reachset-conformant model identification combined with simulation-based analysis. This is followed by a learnability evaluation of the uncertainties based on correlation analysis. This two-part analysis enables an informed decision on the suitability of RL for a control problem without training an RL agent. We apply our test to several benchmarks, demonstrating its applicability to a wide range of control problems and highlight the potential to save computational resources.

Ensuring operational safety is critical for human-to-humanoid motion imitation. This paper presents a vision-based framework that enables a humanoid robot to imitate human movements while avoiding collisions. Human skeletal keypoints are captured by a single camera and converted into joint angles for motion retargeting. Safety is enforced through a Control Barrier Function (CBF) layer formulated as a Quadratic Program (QP), which filters imitation commands to prevent both self-collisions and human-robot collisions. Simulation results validate the effectiveness of the proposed framework for real-time collision-aware motion imitation.

Our objective is to study the performance and robustness of the model-free strategy for controlling the oxygen stoichiometry of a fuel cell air supply system with a proton exchange membrane. After reviewing the literature on modeling and control of this process, the model-free approach appears to be a good candidate because, on the one hand, it allows straightforward real-time adaptation to track operating points and, on the other hand, it requires a low computational burden, which is attractive for industrial applications. Numerical simulations for two scenarios (constant and variable oxygen stoichiometry) with two current profiles reveal satisfactory performance of the model-free control law. The robustness is addressed by considering significant variations in the parameters of the proton exchange membrane air supply system.

Integrated sensing and communication (ISAC) systems rely on communication waveforms to perform sensing tasks, thus making their sensing performance strongly dependent on the level of communication symbol knowledge available to the sensing receivers. However, the existing literature fails to capture this dependency, often relying on full symbol knowledge assumptions. In this paper, we present a Cramer Rao bound (CRB) analysis of a bistatic ISAC network with heterogeneous uplink and downlink illumination and structured clutter. We consider different symbol knowledge regimes by modeling unknown communication symbols as nuisance parameters. Assuming a temporal evolution of the communication channel, we derive a correlation aware channel estimator and an expression for the UEs uplink spectral efficiency (SE). Numerical results show the CRB degradation induced by clutter and symbol uncertainty and how this can affect resource allocation policies. We also show the performance gain of our channel estimator relative to conventional block fading architectures.

The integration of first-principles models with learning-based components, i.e., model augmentation, has gained increasing attention, as it offers higher model accuracy and faster convergence properties compared to black-box approaches, while generating physically interpretable models. Recently, a unified formulation has been proposed that generalizes existing model augmentation structures, utilizing linear fractional representations (LFRs). However, several potential benefits of the approach remain underexplored. In this work, we address three key limitations. First, the added flexibility of LFRs also introduces possible algebraic loops, i.e., a problem of well-posedness. To address this challenge, we propose a constraint-free direct parametrization of the model structure with a well-posedness guarantee. Second, we introduce a constraint-free parametrization that ensures stability of the overall model augmentation structure via contraction. Third, we adopt an efficient identification pipeline capable of handling non-smooth cost functions, such as group-lasso regularization, which facilitates automatic model order selection and discovery of the required augmentation configuration. These contributions are demonstrated on various simulation and benchmark identification examples.

We present a framework for bridging the gap between sensor attack detection and recovery in cyber-physical systems. The proposed framework models modern-day, complex perception pipelines as bipartite graphs, which combined with anomaly detector alerts defines a Bayesian network for inferring compromised sensors. An active probing strategy exploits system nonlinearities to maximize distinguishability between attack hypotheses, while compromised sensors are selectively disabled to maintain reliable state estimation. We propose a threshold-based probing strategy and show its effectiveness via a simplified partially observable Markov decision process (POMDP) formulation. Experiments on an inverted pendulum under single and multi-sensor attacks show that our method significantly outperforms outlier-robust and prediction-based baselines, especially under prolonged attacks.

The dominant paradigm for building LLM based agents is the Agent Loop, an iterative cycle where a single language model decides what to do next by reading an ever growing context window. This paradigm has three structural weaknesses: implicit dependencies between steps, unbounded recovery loops, and mutable execution history that complicates debugging. We characterize the Agent Loop as a single ready unit scheduler: at any moment, at most one executable unit is active, and the choice of which unit to activate comes from opaque LLM inference rather than an inspectable policy. This perspective places Agent Loops and graph based execution engines on a single semantic continuum. We propose SGH, Structured Graph Harness, which lifts control flow from implicit context into an explicit static DAG. SGH makes three commitments: execution plans are immutable within a plan version, planning execution and recovery are separated into three layers, and recovery follows a strict escalation protocol. These choices trade some expressiveness for controllability, verifiability, and implementability. Our contributions are fourfold: a scheduler unified framework that applies classical scheduling theory to LLM agent execution and identifies challenges introduced by non deterministic LLM nodes; a trade off analysis of controllability, expressiveness, and implementability across 70 surveyed systems; a formal specification including a node state machine with termination and soundness guarantees; and an attributable experimental framework with a seven group design for future validation. This is a position paper and design proposal. We provide a theoretical framework, design analysis, and experimental protocol, not a production implementation or empirical results.

We address density control problems for large-scale multi-agent systems in leader-follower settings, where a group of controllable leaders must steer a population of followers toward a desired spatial distribution. Unlike prior work, we explicitly account for follower-follower interactions, capturing realistic behaviors such as flocking and collision avoidance. Within a macroscopic framework based on partial differential equations governing the density dynamics, we derive (i) necessary and sufficient feasibility conditions linking the target distribution to interaction strength, diffusion, and leader mass, and (ii) a feedback control law guaranteeing local stability with an explicit estimate of the basin of attraction. Our analysis reveals sharp feasibility thresholds, phase transitions beyond which no control effort can achieve the desired configuration. Numerical simulations in one- and two-dimensional domains validate the theoretical results at the macroscopic level, and agent-based simulations on finite populations confirm the practical deployability of the proposed framework.

Incentive design problems consider a system planner who steers self-interested agents toward a socially optimal Nash equilibrium by issuing incentives in the presence of information asymmetry, that is, uncertainty about the agents' cost functions. A common approach formulates the problem as a Mathematical Program with Equilibrium Constraints (MPEC) and optimizes incentives using hypergradients-the total derivatives of the planner's objective with respect to incentives. However, computing or approximating the hypergradients typically requires full or partial knowledge of equilibrium sensitivities to incentives, which is generally unavailable under information asymmetry. In this paper, we propose a hypergradient-free incentive law, called the social-gradient flow, for incentive design when the planner's social cost depends on the agents' joint actions. We prove that the social cost gradient is always a descent direction for the planner's objective, irrespective of the agent cost landscape. In the idealized setting where equilibrium responses are observable, the social-gradient flow converges to the unique socially optimal incentive. When equilibria are not directly observable, the social-gradient flow emerges as the slow-timescale limit of a two-timescale interaction, in which agents' strategies evolve on a faster timescale. It is established that the joint strategy-incentive dynamics converge to the social optimum for any agent learning rule that asymptotically tracks the equilibrium. Theoretical results are also validated via numerical experiments.

State estimation constitutes a core task in monitoring, supervision, and control of dynamic systems. This paper proposes a data-driven framework for the design of state observers for descriptor systems. Necessary and sufficient conditions for the existence of a standard state observer are derived purely from data under mild assumptions. When the system is subject to unknown inputs, we further extend the framework to the data-driven design method for full-order unknown input observer (UIO). Notably, for both the standard state observer and the UIO, we establish the mathematical equivalence between the proposed data-driven existence conditions and classical model-based ones. Moreover, the data-driven approach is applied to the design of extended state observers, enabling simultaneous estimation of system states and disturbances via system augmentation. Numerical simulations validate the effectiveness of the proposed methods.

We propose a simple yet effective divide-and-discard (DD) approach to guaranteed state estimation for nonlinear discrete-time systems. Our method iteratively subdivides interval enclosures of the state and propagates them forward in time using a mean-value enclosure. The central idea is to rely on repeated refinement of simple sets rather than on more complex set representations, yielding an observer that is straightforward to implement and easy to integrate into existing frameworks. Our divide-and-discard strategy exploits that many sets can be discarded early and limits the number of maintained sets, resulting in low computational cost with complexity that scales only quadratically in the state dimension. The proposed method is evaluated on nonlinear benchmark problems previously used to compare guaranteed observers, where it outperforms state-of-the-art approaches in terms of both computational efficiency and enclosure tightness.

The rapid growth of the low-altitude economy (LAE) is making aerial systems an important part of future digital infrastructure. Although major advances have been achieved in unmanned aerial vehicle (UAV) platforms, communications, and autonomous control, environmental perception remains a key bottleneck to reliable and scalable LAE operations. Existing sensing modalities, such as optical, LiDAR, and millimeter-wave radar, are limited by visibility, sensing range, and environmental conditions, resulting in fragmented situational awareness. This article argues that addressing these limitations requires a shift from platform-centric sensing to a shared, environment-aware sensing infrastructure. In this context, synthetic aperture radar (SAR) offers a distinct advantage by enabling all-weather, wide-area perception. We show that SAR can support UAV operations through global environmental awareness, enhance task-level sensing, and enable cooperative sensing across satellites, high-altitude platforms, UAVs, and ground systems. Building on this perspective, we present a system-level view of SAR-enabled LAE, highlighting key transformations from fragmented to infrastructure-centric sensing, from reactive to predictive operation, and from device-centric to environment-aware networking. We further discuss enabling architectures, including multi-platform sensing hierarchies, integration with integrated sensing and communication (ISAC), and the role of artificial intelligence and digital twins, along with the key challenges toward real-world deployment. By positioning SAR as a shared sensing foundation rather than a standalone modality, this article provides new insights into the design of scalable, reliable, and intelligent LAE systems.