Papers

Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming provides guaranteed upper and lower bounds on stationary moments. However, this formulation suffers from the rapidly growing size of semidefinite constraints due to the combinatorial growth of moments with the number of molecular species. In this paper, we propose a sparsity-exploiting matrix decomposition method for semidefinite constraints in stationary moment bounding problems to reduce the computational cost of the resulting semidefinite programs. Specifically, we characterize the sparsity structure of moment equations, where each reaction involves only a subset of variables determined by its reactants, and exploit this structure to decompose the semidefinite constraints into smaller ones. We demonstrate that the resulting formulation reduces the computational cost of the optimization problem while providing practically useful bounds.

Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on Taylor-series expansion of the equations of motion with the projection-basis adaptation scheme recently proposed by Hollins et al. [2026] for linear model updating. The structural equations of motion, augmented with proportional (Rayleigh) damping and polynomial stiffness nonlinearity, are recast as a first-order autonomous system whose Jacobian possesses complex eigenvectors forming a biorthogonal basis. Taylor operators of second and third order are derived for the nonlinear internal forces and projected onto the reduced eigenvector basis, yielding a low-dimensional nonlinear reduced-order model (ROM). The Cayley transform, generalised from the real orthogonal to the complex unitary group, parametrises the adaptation of the projection basis so that the ROM mode shapes optimally correlate with experimental measurements. The resulting nonlinear model-updating framework is applied to a representative wingbox panel model. Numerical studies demonstrate that the proposed approach captures amplitude-dependent natural frequencies and modal assurance criterion(MAC) values that a purely linear updating scheme cannot reproduce, while recovering the underlying stiffness parameters with improved accuracy.

Precise control of lower limb exoskeletons during sit-to-stand (STS) transitions remains a central challenge in rehabilitation robotics owing to the highly nonlinear, time-varying dynamics of the human-exoskeleton system and the stringent trajectory tracking requirements imposed by clinical safety. This paper presents the systematic design, simulation, and comparative evaluation of three control strategies: a classical Proportional-Integral-Derivative (PID) controller, a Linear Quadratic Regulator (LQR), and a novel Hybrid PID-LQR controller applied to a bilateral lower limb exoskeleton performing the sit-to-stand transition. A high-fidelity, physics-based dynamic model of the exoskeleton is constructed by importing a SolidWorks CAD assembly directly into the MATLAB/Simulink Simscape Multibody environment, preserving accurate geometric and inertial properties of all links. Physiologically representative reference joint trajectories for the hip, knee, and ankle joints are generated using OpenSim musculoskeletal simulation and decomposed into three biomechanical phases: flexion-momentum (0-33%), momentum-transfer (34-66%), and extension (67-100%). The proposed Hybrid PID-LQR controller combines the optimal transient response of LQR with the integral disturbance rejection of PID through a tuned blending coefficient alpha = 0.65. Simulation results demonstrate that the Hybrid PID-LQR achieves RMSE reductions of 72.3% and 70.4% over PID at the hip and knee joints, respectively, reduces settling time by over 90% relative to PID across all joints, and limits overshoot to 2.39%-6.10%, confirming its superiority over both baseline strategies across all evaluated performance metrics and demonstrating strong translational potential for clinical assistive exoskeleton deployment.

Renewable power-to-ammonia (ReP2A) production offers a promising pathway to decarbonize the power, transport and, chemical sectors, yet its competitiveness remains limited by high costs and fragmented carbon-policy frameworks. In particular, a unified mechanism that links ReP2A producers with fossil-based gray ammonia (GA) competitors in carbon and ammonia markets, while coordinating incentives among renewable generation, hydrogen production, and ammonia synthesis stakeholders in the ReP2A process chain, is still lacking. To address this gap, this paper proposes a hierarchical carbon-driven incentive mechanism (PCIM) that integrates carbon policy with multi-energy market interactions. A two-layer trading framework is developed, where ReP2A and GA compete in carbon allowance (CA) and ammonia markets (outer layer), while electricity and hydrogen transactions coordinate the ReP2A chain (inner layer). The resulting interactions are modeled as a hierarchical equilibrium, where the inner layer is reformulated as a tractable equivalent optimization problem, and the outer layer is solved as a mixed-integer linear program (MILP) derived from Karush-Kuhn-Tucker conditions. Based on equilibrium analysis, the carbon-related revenue of ReP2A is quantified, and a CA allocation mechanism (PCAM) is proposed to ensure individually rationality among stakeholders. Results show that the proposed mechanism reduces carbon emissions by 12.9% with only a 1.8% decrease in sector-wide revenue. Moreover, carbon pricing under the proposed framework redistributes profits between green and gray ammonia without reducing total welfare, and the PCAM further enhances stakeholders' willingness to participate in ReP2A production.

We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a group-structured positive operator-valued measure (POVM) applied to a single copy of a quantum state produces a full-rank, group-averaged density matrix estimator whose eigenbasis and eigenvalue ordering track those of the true density matrix, with a bias toward the symmetrized state, analogous to the classical recovery of covariance eigenstructure from a single observation. We establish a Classical-Quantum Duality Map connecting classical covariance estimation to quantum state tomography, and an Optimality Inheritance Theorem showing that classical group optimality transfers to quantum settings via the Born map within the group-averaged family. SIC-POVMs are identified as AD with the Heisenberg-Weyl group and mutually unbiased bases as AD with the Clifford group, revealing the hierarchy $\mathrm{HW}(d) \subseteq \mathcal{C}(d) \subseteq S_d$ that mirrors the classical $\mathbb{Z}_M \subseteq G_{\min} \subseteq S_M$. The double-commutator eigenvalue theorem gives polynomial-time adaptive POVM selection. A worked qubit example shows the group-averaged estimator from a single computational-basis measurement, averaged over a matched $\mathbb{Z}_2$ group, reaching fidelity 0.99 where standard single-basis tomography gives a rank-1 estimate of fidelity 0.80. Monte Carlo simulations for $d = 2$ to $13$ confirm fidelity above 0.90 from a single outcome while standard fidelity degrades as $\sim 1/d$. The growing ratio reflects collapse of the rank-1 standard estimator, not fewer copies per parameter: the biased single-copy estimator reduces the number of distinct measurement settings, not the per-parameter sampling cost, and a genuine copy reduction holds only under exact symmetry.

We propose regularized approximate message passing (RAMP), a low-complexity algorithm for discrete signal detection in overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas exceeds the number of receive antennas. While the state-of-the-art (SotA) iterative discrete least squares (IDLS) framework achieves near-optimal discrete-aware performance, its iterative matrix inversions impose a prohibitive $\mathcal{O}(M^3)$ complexity. RAMP resolves this by deriving an adaptive, state-dependent scalar denoiser that enforces arbitrary discrete constellation constraints within the approximate message passing (AMP) framework, reducing per-iteration complexity to $\mathcal{O}(NM)$. A robust variant is further proposed by incorporating an $\ell_2$-norm penalty, analogous to a linear minimum mean squared error (LMMSE) estimator, to enhance noise resilience. Simulation results under uncorrelated Rayleigh fading demonstrate that both proposed algorithms closely track their exact IDLS counterparts while avoiding the catastrophic failure of standard AMP in the overloaded regime, achieving steep bit error rate (BER) waterfall curves at a fraction of the computational cost.

The performance of constructive interference precoding (CIP) for multi-user multi-antenna (MU-MIMO) systems is governed by the structure of the constructive interference (CI) regions, yet this is overlooked in conventional constellation design. This work proposes the region-based constellation (RBC) model to lay the foundation for CIP constellation design. An RBC directly defines the mapping between messages and their feasible regions, instead of deriving them from an existing constellation. To provide insight for RBC design, we study the limitations of quadrature-amplitude-modulation (QAM)-based CIP. Analytical results show that the restrictive CI regions of QAM symbols are systematically misaligned with the objective-minimising sign pattern, resulting in a significant gap to the theoretical performance limit. From the perspective of improving sign alignment, two novel RBC schemes with non-convex feasible regions are proposed, namely mirrored-ends QAM (ME-QAM) and real-extended ME-QAM. A low-complexity algorithm is also developed for the resulting mixed-integer quadratic program, achieving a complexity comparable to QAM-based CIP. Simulation results with constellation sizes $\{16,64\}$ demonstrate up to $4$~dB signal-to-noise-ratio gain of the proposed schemes over QAM-based CIP. The proposed RBC model is also applicable to other systems with non-bijective modulation, representing a promising direction for future research.

User-defined keyword spotting (KWS) without resorting to domain-specific pre-labeled training data is of fundamental importance in building adaptable and personalized voice interfaces. However, such systems are still faced with arduous challenges, including constrained computational resources and limited annotated training data. Existing methods also struggle to distinguish acoustically similar keywords, often leading to a pesky false alarm rate (FAR) in real-world deployments. To mitigate these limitations, we put forward MALEFA, a novel lightweight zero-shot KWS framework that jointly learns utterance- and phoneme-level alignments via cross-attention and a multi-granularity contrastive learning objective. Evaluations on four public benchmark datasets show that MALEFA achieves a high accuracy of 90%, significantly reducing FAR to 0.007% on the AMI dataset. Beyond its strong performance, MALEFA demonstrates high computational efficiency and can readily support real-time deployment on resource-constrained devices.

The integration of photovoltaic (PV) systems, stationary energy storage systems (ESSs), and electric vehicles (EVs) alongside demand response (DR) programmes in industrial parks presents opportunities to reduce costs and improve renewable energy utilisation. Coordinating these resources is challenging because office and production zones have distinct operational objectives, and battery ageing costs are often ignored. This paper proposes a DR-based energy management framework that jointly optimises grid interaction costs, thermal comfort, EV departure state-of-charge requirements, carbon emissions, and battery ageing. We model heterogeneous load characteristics using a dynamic energy distribution ratio and incorporate dispatch-level ageing models for both ESS and EV batteries. The problem is formulated as a Markov decision process (MDP) and solved with a deep deterministic policy gradient (DDPG) algorithm. High-fidelity simulations using data from a practical industrial park in China show the framework maintains indoor comfort while significantly reducing total operating costs, yielding savings of 44.58% and 40.68% compared with a rule-based DR strategy and a conventional time-of-use arbitrage approach, respectively.

Surgical video segmentation is fundamental to computer-assisted surgery. In practice, surgeons need to dynamically specify targets throughout extended procedures, using heterogeneous cues such as visual selections, textual expressions, or audio instructions. However, existing Promptable Video Object Segmentation (PVOS) methods are typically restricted to a single prompt modality and rely on coupled frameworks that cause optimization interference between target initialization and tracking. Moreover, these methods produce hallucinated predictions when the target is absent and suffer from accumulated mask drift without failure recovery. To address these challenges, we present UniSurgSAM, a unified PVOS model enabling reliable surgical video segmentation through visual, textual, or audio prompts. Specifically, UniSurgSAM employs a decoupled two-stage framework that independently optimizes initialization and tracking to resolve the optimization interference. Within this framework, we introduce three key designs for reliability: presence-aware decoding that models target absence to suppress hallucinations; boundary-aware long-term tracking that prevents mask drift over extended sequences; and adaptive state transition that closes the loop between stages for failure recovery. Furthermore, we establish a multi-modal and multi-granular benchmark from four public surgical datasets with precise instance-level masklets. Extensive experiments demonstrate that UniSurgSAM achieves state-of-the-art performance in real time across all prompt modalities and granularities, providing a practical foundation for computer-assisted surgery. Code and datasets will be available at https://jinlab-imvr.github.io/UniSurgSAM.

We establish that temporal averaging over multiple observations is the degenerate case of algebraic group action with the trivial group $G=\{e\}$. A General Replacement Theorem proves that a group-averaged estimator from one snapshot achieves equivalent subspace decomposition to multi-snapshot covariance estimation. The Trivial Group Embedding Theorem proves that the sample covariance is the accumulation of trivial-group estimates, with variance governed by a $(G,L)$ continuum as $1/(|G|\cdot L)$. The processing gain $10\log_{10}(M)$ dB equals the classical beamforming gain, establishing that this gain is a property of group order, not sensor count. The DFT, DCT, and KLT are unified as group-matched special cases. We conjecture a General Algebraic Averaging Theorem extending these results to arbitrary statistics, with variance governed by the effective group order $d_{\mathrm{eff}}$. Monte Carlo experiments on the first four sample moments across five group types confirm the conjecture to four-digit precision. The framework exploits the $structure$ of information (representation-theoretic symmetry of the data object) rather than the content, complementing Shannon's theory. Five applications are demonstrated: single-snapshot MUSIC, massive MIMO, single-pulse waveform classification, graph signal processing, and analysis of transformer LLMs. Techniques for blind group matching are described.

Spiking Neural Networks (SNNs) offer a promising solution for energy-efficient edge intelligence; however, their hardware deployment is constrained by memory overhead, inefficient scaling operations, and limited parallelism. This work proposes L-SPINE, a low-precision SIMD-enabled spiking neural compute engine for efficient edge inference. The architecture features a unified multi-precision datapath supporting 2-bit, 4-bit, and 8-bit operations, leveraging a multiplier-less shift-add model for neuron dynamics and synaptic accumulation. Implemented on an AMD VC707 FPGA, the proposed neuron requires only 459 LUTs and 408 FFs, achieving a critical delay of 0.39 ns and 4.2 mW power. At the system level, L-SPINE achieves 46.37K LUTs, 30.4K FFs, 2.38 ms latency, and 0.54 W power. Compared to CPU and GPU platforms, it reduces inference latency from seconds to milliseconds, achieving an up to three orders-of-magnitude improvement in energy efficiency. Quantisation analysis shows that INT2/INT4 configurations significantly reduce memory footprint with minimal accuracy loss. These results establish L-SPINE as a scalable and efficient solution for real-time edge SNN deployment.

With the growing demand for large-scale and high-quality data in edge intelligence systems, mobile robots are increasingly deployed to collect data proactively, particularly in complex environments. However, existing robot-assisted data collection methods face significant challenges in achieving reliable and efficient performance, especially in non-line-of-sight (NLoS) environments. This paper proposes a communication-and-learning dual-driven (CLD) autonomous navigation scheme that incorporates region-aware propagation characteristics and a non-point-mass robot representation. This scheme enables simultaneous optimization of navigation, communication, and learning performance. An efficient algorithm based on majorization-minimization (MM) is proposed to solve the non-convex and non-smooth CLD problem. Simulation results demonstrate that the proposed scheme achieves superior performance in collision-avoidance navigation, data collection, and model training compared to benchmark methods. It is also shown that CLD can adapt to different scenarios by flexibly adjusting the weight factor among navigation, communication and learning objectives.

Grid-connected inverters are required to operate stably under a wide range of grid conditions. However, conventional grid-following (GFL) control may suffer from instability under weak-grid conditions, while grid-forming (GFM) control may exhibit unstable oscillations under strong-grid conditions. To address these issues, a hybrid voltage-current control method is proposed in this article. A voltage control is introduced on the d-axis, while a current control is adopted on the q-axis, enabling the inverter to exhibit voltage-source characteristics on the d-axis and current-source characteristics on the q-axis. In this way, the proposed control integrates the characteristics of both conventional GFL and GFM control. A full-order model is established to analyze the port characteristics and small-signal stability of the systems. Finally, the effectiveness of the proposed control strategy is validated through simulations and experiments on a 1.5 kW inverter experimental platform. The results show that the proposed control maintains stable operation under different grid conditions with varying short-circuit ratios (SCRs).

We study online task allocation for multi-robot, multi-queue systems with asymmetric stochastic arrivals and switching delays. We formulate the problem in discrete time: each location can host at most one robot per slot, servicing a task consumes one slot, switching between locations incurs a one-slot travel delay, and arrivals at locations are independent Bernoulli processes with heterogeneous rates. Building on our previous structural result that optimal policies are of exhaustive type, we formulate a discounted-cost Markov decision process and develop an exhaustive-assignment actor-critic policy architecture that enforces exhaustive service by construction and learns only the next-queue allocation for idle robots. Unlike the exhaustive-serve-longest (ESL) queue rule, whose optimality is known only under symmetry, the proposed policy adapts to asymmetry in arrival rates. Across different server-location ratios, loads, and asymmetric arrival profiles, the proposed policy consistently achieves lower discounted holding cost and smaller mean queue length than the ESL baseline, while remaining near-optimal on instances where an optimal benchmark is available. These results show that structure-aware actor-critic methods provide an effective approach for real-time multi-robot scheduling.

Plug-and-play (PnP) methods are widely used for solving imaging inverse problems by incorporating a denoiser into optimization algorithms. Score-based diffusion models (SBDMs) have recently demonstrated strong generative performance through a denoiser trained across a wide range of noise levels. Despite their shared reliance on denoisers, it remains unclear how to systematically use SBDMs as priors within the PnP framework without relying on reverse diffusion sampling. In this paper, we establish a score-based interpretation of PnP that justifies using pretrained SBDMs directly within PnP algorithms. Building on this connection, we introduce a stochastic generative PnP (SGPnP) framework that injects noise to better leverage the expressive generative SBDM priors, thereby improving robustness in severely ill-posed inverse problems. We provide a new theory showing that this noise injection induces optimization on a Gaussian-smoothed objective and promotes escape from strict saddle points. Experiments on challenging inverse tasks, such as multi-coil MRI reconstruction and large-mask natural image inpainting, demonstrate consistent improvement over conventional PnP methods and achieve performance competitive with diffusion-based solvers.

Wavefront sensing involves estimating the phase and intensity of light, enabling a wide range of imaging applications, from adaptive optics and astronomy to biomedical imaging. Since conventional image sensors can only measure the spatial intensity distribution, phase retrieval arises as the central problem in wavefront sensing. Conventional interferometric approaches like phase-shifting interferometry (PSI) can recover phase information, but they rely on a stable reference beam that is difficult to realize in practical settings. To overcome this limitation, we propose a novel self-reference framework that relies on interference between shifted copies of the incoming wave; this results in pairwise phase differences between shifted pixels. We formulate an analytical solution for the complete phase retrieval based on the propagation of these differences across a connected graph. Furthermore, we provide a theoretical analysis of optimal measurement patterns, proving that co-prime shifts guarantee a connected graph and bound worst-case error accumulation, yielding a provably robust method. Extensive simulations demonstrate that complete phase profiles can be recovered from as few as eight shifted measurements, outperforming several existing approaches. Finally, we validate our framework using a hardware prototype, demonstrating real experiments for optical phase profile recovery, auto-refocusing, and imaging through scattering media.

A virtual power plant (VPP) is operated by an aggregator that acts as a market intermediary, aggregating consumers to participate in wholesale power markets. By setting incentive prices, the aggregator induces consumers to sell energy and profits by providing this aggregated energy to the market. This supply is enabled by consumers' flexibility to adjust electricity consumption in response to market conditions. However, heterogeneity in flexibility means that profit-maximizing VPP pricing can create inequalities in participation and benefit allocation across consumers. In this paper, we develop a fairness-aware pricing framework to analyze how different fairness notions reshape system performance, measured by consumer Nash welfare, total consumer utility, and social welfare. We consider three fairness criteria: energy fairness, which ensures equitable energy provision; price fairness, which ensures similar incentive prices; and utility fairness, which ensures comparable levels of consumer utility. We model the aggregator-consumer interaction as a Stackelberg game and derive consumers' optimal responses to incentive prices. Using a stylized model, we show that profit-only pricing systematically disadvantages less flexible consumers. We further show that energy fairness can either improve or worsen all performance measures, and gains across most measures arise only at moderate fairness levels. Surprisingly, price fairness never benefits less flexible consumers, even when it reduces price disparities. By contrast, utility fairness protects less flexible consumers without benefiting more flexible ones. We validate our findings using data from an experiment in Norway under a tiered pricing scheme. Our results provide regulators and VPP operators with a systematic map linking fairness definitions and enforcement levels to operational and welfare outcomes.

Control barrier functions (CBFs) provide a principled framework for enforcing safety in control systems – yet the certified safe operating region in practice is often conservative, especially under input bounds. In many applications, multiple smaller safe sets can be certified independently, e.g., around distinct equilibria with different stabilizing controllers. This paper proposes a framework for uniting such regions into a single certified safe set using combinatorial CBFs. We refine the combinatorial CBF framework by introducing an auxiliary variable that enables logical compositions of individual CBFs. In the proposed framework, we show that such compositions yield a generalized combinatorial CBF under a condition termed conjunctive compatibility. Building on this result, we extend the framework to enable the aggregation of multiple implicit safe sets generated by the backup CBF framework. We show that the resulting CBF-based quadratic program yields a continuous safety filter over the aggregated safe region. The approach is demonstrated on two spacecraft safety problems, safe attitude control and safe station keeping, where multiple certified safe regions are combined to expand the operational envelope.

Aligning physiological parameter labels with large-scale photoplethysmographic (PPG) data for deep learning is challenging and resource-intensive. While self-supervised representation learning (SSRL) can handle limited annotated data, the challenge lies in learning robust shared representations from vast unlabeled data and integrating contextual cues to learn distinctive representations. To alleviate these challenges, a generative SSRL framework TS2TC is proposed to utilize the temporal, spectrogram, and temporal-spectrogram mixed domains to explore and incorporate the unique features of PPG for universal and noninvasive physiological parameter estimation. A pretext task named Cross-Temporal Fusion Generative Anchor (CTFGA) is designed, modeling temporal dependencies and reconstructing independent segments at a coarse level to provide robust global feature extraction and local contextual representation. The framework includes sub-signals from PPG with diverse frequency scales and order derivatives reflecting hemodynamics to facilitate learning shared representations at varying semantic levels. Secondly, a cognitive-inspired dual-process transfer (DPT) strategy is formulated, consisting of prior-dependent autonomous processes and posterior observation reasoning processes, to leverage the independent and integrated advantages of shared and specific representations. TS2TC introduces a bilinear temporal-spectrogram fusion method in the mixed domain, aligning latent representations from different domains and establishing fine-grained contextual interactions across multiple sources of information. Extensive experiments on physiological parameter estimation tasks showed that the joint performance of CTFGA and DPT outperforms standard generative learning significantly. TS2TC achieved an average 2.49% improvement in RMSE over state-of-the-art estimation methods with only 10% training data.

This paper presents cooperative protocols for multi-agent systems with agents having a finite state-space. Both scalar single-integrator consensus and general LTI system synchronization are considered. Systems having a finite state-space describe agents with minimal memory capacity processing only a finite alphabet. Such systems are remarkably resilient to communication noise. The crucial problem, however, is to construct the admissible communication topology, which is NP-hard. We address this by efficiently exploring the subsets of admissible graph matrices and propose two new algorithms to generate them. Simulations validate the proposed approach.

Multimodal emotion recognition in conversations aims to infer utterance-level emotions by jointly modeling textual, acoustic, and visual cues within context. Despite recent progress, key challenges remain, including redundant cross-modal information, imperfect semantic alignment, and insufficient modeling of high-order speaker interactions. To address these issues, we propose a framework that combines dual-space feature disentanglement with dual-branch graph learning. A shared encoder and modality-specific encoders are used to separate modality-invariant and modality-specific representations. The invariant features are modeled by a Fourier graph neural network to capture global consistency and complementary patterns, with a frequency-domain contrastive objective to enhance discriminability. In parallel, a speaker-aware hypergraph is constructed over modality-specific features to model high-order interactions, along with a speaker-consistency constraint to maintain coherent semantics. Finally, the two branches are fused for utterance-level emotion prediction. Experiments on IEMOCAP and MELD demonstrate that the proposed method achieves superior performance over strong baselines, validating its effectiveness.

In environments with uncertainties or undesirable influences, control systems can require additional energy to achieve their task while remaining resilient to these influences. In this paper, we present an energetic resilience metric that quantifies the maximal additional energy used by a system under undesired effects, while satisfying complex specifications encoded through temporal logic. We prove that this metric satisfies properties that enable its computation even for compositions of these specifications, thus allowing considerations of sequential reachability and safety tasks. For specifications related to finite-horizon reachability and safety, we describe how synthesizing a control input and computing this metric reduces to solving efficient quadratic programs. Two case studies on a fighter-jet model and a planar mobile robot illustrate how the synthesized control inputs satisfy given specifications despite undesired and potentially adversarial effects. Further, we demonstrate how the energetic resilience metric varies with the initial state as well as the magnitude of undesired effects.

Homogeneous polynomial dynamical systems (HPDSs), which can be equivalently represented by tensors, are essential for modeling higher-order networked systems, including ecological networks, chemical reactions, and multi-agent robotic systems. However, identifying such systems from data is challenging due to the rapid growth in the number of parameters with increasing system dimension and polynomial degree. In this article, we adopt compact and scalable representations of HPDSs leveraging low-rank tensor decompositions, including tensor train, hierarchical Tucker, and canonical polyadic decompositions. These representations exploit the intrinsic multilinear structure of HPDSs and substantially reduce the dimensionality of the parameter space. Rather than identifying the full dynamic tensor, we develop a data-driven framework that directly learns the underlying factor tensors or matrices in the associated decompositions from time-series data. The resulting identification problem is solved using alternating least-squares algorithms tailored to each tensor decomposition, achieving both accuracy and computational efficiency. We further analyze the robustness of the proposed framework in the presence of measurement noise and characterize data informativity. Finally, we demonstrate the effectiveness of our framework with numerical examples.

This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of features and a parametric description of the distribution of the noise, a computationally efficient method is described that estimates both the surface and the noise distribution parameters. In the provided examples, polynomial and sinusoidal basis functions were used. However, any chosen basis that satisfies the outlined conditions mentioned in the paper can be approximated as a combination of trigonometric, exponential, and/or polynomial terms, making the presented approach highly generalizable. The proposed algorithm exhibits linear computational complexity in the number of samples. Our approach requires no hyperparameter tuning or data preprocessing and effectively handles data in dimensions beyond 2D and 3D. The theoretical results demonstrating the convergence of the proposed algorithm have been provided. To highlight the performance of the proposed method, comprehensive numerical results are conducted, evaluating our method against state-of-the-art algorithms, including Poisson Reconstruction and the Neural Network-based Encoder-X, on 2D and 3D shapes. The results demonstrate the superiority of our method under the same conditions.

An unconstrained optimal control policy is completely decentralized if computing actuation for each subsystem only requires information directly available to its own subcontroller. Parameters that admit a completely decentralized optimal controller have been characterized in a variety of systems, but attempts to physically explain the phenomenon have been limited. As a step toward a general characterization of complete decentralization, this paper presents conditions for complete decentralization of Linear Quadratic Regulators for several simple cases and physically interprets these conditions with illustrative examples. These simple cases are then leveraged to characterize complete decentralization of more complex systems.

Sensor spoofing analysis in cyber-physical systems is predominantly confined to linear state spaces, where an attack's persistence implies the existence of an integrator somewhere in the loop. We extend this insight to a commutativity condition on Lie groups, where noncommutative dynamics can distort sensor attacks, exposing nominally stealthy attacks by complex maneuvers. We present a geometric framework characterizing when a sensor attack can transfer across operating conditions, preserving both its physical impact and stealthiness. We prove that successful transfer requires the attack to commute with the flow (a Lie bracket condition), isolating transferable attacks to an invariant subspace. For small deviations from transferable attacks, our decomposition theorem reveals a fundamental asymmetry: the flow's Adjoint action distorts the physical impact of the bracket-violating component. Furthermore, even if the attack's impact isn't distorted, the subsequent residual could be. Finally, we demonstrate how turning maneuvers on a Dubins unicycle collapse the transferable subspace to a single direction, verifying that imperfect attacks remain within theoretical detection bounds.

The progression of modern power systems towards converter-rich operations calls for new models and analytics in steady-state voltage stability assessment. The classic modeling assumption of the generators as stiff voltage sources no longer holds. Instead, the voltage- and current-limited behaviors of converters need to be considered. In this paper, we develop a Wirtinger derivative-based formulation for the power flow Jacobian and derive an explicit sufficient condition for its singularity. Compared to existing works, we extend the explicit sufficient singularity condition to incorporate all bus types instead of only slack and PQ types. We prove that the singularity of the alternative Jacobian coincides with that of the conventional one. A bus-wise voltage stability index, denoted $C_{\mathrm{W}}$, is derived from diagonal dominance conditions. The condition $\min_i C_{W,i}$ being greater than one certifies the nonsingularity of the Jacobian and provides a fast, non-iterative stability margin. Case studies in standard IEEE test systems show that the proposed index yields less conservative and more localized assessments than classical indices such as the L-index, the $K_{\mathrm{R}}$ index, and the SCR index.

Control barrier functions (CBFs) provide an effective framework for enforcing safety in dynamical systems with scalar constraints. However, many safety constraints are more naturally expressed as matrix-valued conditions, such as positive definiteness or eigenvalue bounds - scalar formulations introduce potential nonsmoothness that complicates analysis. Matrix control barrier functions (MCBFs) address this limitation by directly enforcing matrix-valued safety constraints. Yet for constraints where the control input does not appear in the first derivative, high-order formulations are required. While such extensions are well understood in the scalar case, they remain largely unexplored in the matrix case. This paper develops high-order matrix control barrier functions (HOMCBFs) and establishes conditions ensuring well-posedness and feasibility of the associated constraints, enabling enforcement of matrix-valued safety constraints for systems with high-order dynamics. We further show that, using an optimal-decay HOMCBF formulation, forward invariance can be ensured while requiring control only over the minimum eigenspace. The framework is demonstrated on a double-integrator localization problem by enforcing positive definiteness of the information matrix.

Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose solution is a mapping from task description (e.g., cost or dynamics functions) to optimal control law (e.g., feedback policy). We approximate these solution operators using a permutation-invariant neural operator architecture. Across a range of parametric optimal control environments and a locomotion benchmark, a single operator trained via behavioral cloning accurately approximates the solution operator and generalizes to unseen tasks, out-of-distribution settings, and varying amounts of task observations. We further show that the branch-trunk structure of our neural operator architecture enables efficient and flexible adaptation to new tasks. We develop structured adaptation strategies ranging from lightweight updates to full-network fine-tuning, achieving strong performance across different data and compute settings. Finally, we introduce meta-trained operator variants that optimize the initialization for few-shot adaptation. These methods enable rapid task adaptation with limited data and consistently outperform a popular meta-learning baseline. Together, our results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation.