Papers

The deployment of multiple transmitters (TXs) in integrated sensing and communication (ISAC) networks necessitates efficient resource sharing to overcome the limitations of orthogonal allocation. While conventional interleaved (CI) pilots combined with non-orthogonal multiple access (NOMA) improve spectral efficiency (SE), they inherently compromise sensing resolution due to spectral sparsity, rendering the CI nulling (CIN) extension a strictly limited remedy. This paper proposes a phase-shifted (PS) pilot design and its novel PS nulling (PSN) variant to integrate a communication TX (CTX) over the PS-ISAC framework. The PSN variant strategically punctures sensing signals at CTX pilot locations to preserve initial channel estimates, enabling a dense data overlay. To resolve the resulting multi-TX interference, joint iterative interference cancellation (IIC) is adapted for non-nulling configurations and sequential IIC is adapted for nulling variants, optimizing for both detection robustness and convergence speed. Simulation results across varying STX densities and modulation orders demonstrate that the phase-shifted frameworks maintain sensing integrity while explicitly reducing receiver-side computational complexities by $18.8\%$ and $21.0\%$ against their respective interleaved baselines.

The wind-induced structural response forecasting capabilities of a novel transformer methodology are examined here. The model also provides a digital twin component for bridge structural health monitoring. Firstly, the approach uses the temporal characteristics of the system to train a forecasting model. Secondly, the vibration predictions are compared to the measured ones to detect large deviations. Finally, the identified cases are used as an early-warning indicator of structural change. The artificial intelligence-based model outperforms approaches for response forecasting as no assumption on wind stationarity or on structural normal vibration behavior is needed. Specifically, wind-excited dynamic behavior suffers from uncertainty related to obtaining poor predictions when the environmental or traffic conditions change. This results in a hard distinction of what constitutes normal vibration behavior. To this end, a framework is rigorously examined on real-world measurements from the Hardanger Bridge monitored by the Norwegian University of Science and Technology. The approach captures accurate structural behavior in realistic conditions, and with respect to the changes in the system excitation. The results, importantly, highlight the potential of transformer-based digital twin components to serve as next-generation tools for resilient infrastructure management, continuous learning, and adaptive monitoring over the system's lifecycle with respect to temporal characteristics.

To meet the requirements for high data rates and ubiquitous connectivity in 6G networks, higher frequencies and larger array apertures are employed to enhance spatial resolution and spectral efficiency. This evolution leads to an expansion of the near-field region, where spherical-wave focusing can significantly enhance received power. However, the pervasive presence of obstacles in near-field environments makes communication in obstructed scenarios a critical challenge, particularly for sensitive high-frequency links with high penetration losses. In this paper, we propose a new waveform, termed the near-field Airy beam, which is tailored to the amplitude and phase characteristics of obstructed near-field channels. By integrating non-uniform amplitude response with non-linear phase profile, the proposed Airy beam forms specific curved trajectories, energy distributions, and focal points, enabling energy concentration at the user even after circumventing obstacles. An Airy beamforming algorithm is also developed for hybrid beamformer architectures. Considering practical conditions with unknown obstacle and user locations, we design an Airy beam codebook and a low-overhead hierarchical search scheme to identify the optimal user-aligned beam. Simulation results demonstrate that in obstructed environments, the near-field Airy beam achieves a received power gain of over 3 dB compared to conventional waveforms like focused and curved beams, closely approaching the theoretical upper bound. Across the mmWave to THz bands and various obstacle dimensions, the proposed beam training scheme consistently outperforms traditional methods in terms of spectral efficiency while maintaining a comparable training overhead.

Conventionally, the concept of moment has been primarily employed in model order reduction to approximate system by matching the moment, which is merely the specific set of steady-state responses. In this paper, we propose a novel design framework that extends this concept from "moment matching" for approximation to "moment assignment" for the active control of steady-state. The key observation is that the closed-loop moment of an interconnected linear system can be decomposed into the open-loop moment and a term linearly parameterized by the moment of the compensator. Based on this observation, we provide necessary and sufficient conditions for the assignability of desired moment and a canonical form of the dynamic compensator, followed by constructive synthesis procedure of compensator. This covers both output regulation and closed-loop interpolation, and further suggests using only the Sylvester equation, rather than regulator equations.

We investigate frequency-switching coherent reception (FSCR), a hardware-efficient technique for offline coherent optical signal characterization in laboratory environments, enabling bandwidth extension without costly and hardware-intensive parallel receiver architectures. By combining signal gating and local-oscillator frequency switching, FSCR captures multiple spectral slices sequentially using a single receiver front-end and oscilloscope. We experimentally demonstrate characterization of signals at symbol rates up to 288 GBaud beyond the receiver bandwidth limit.

Despite remarkable progress, automatic speaker verification (ASV) systems typically lack the transparency required for high-accountability applications. Motivated by how human experts perform forensic speaker comparison (FSC), we propose a speaker verification network with phonetic interpretability, PhiNet, designed to enhance both local and global interpretability by leveraging phonetic evidence in decision-making. For users, PhiNet provides detailed phonetic-level comparisons that enable manual inspection of speaker-specific features and facilitate a more critical evaluation of verification outcomes. For developers, it offers explicit reasoning behind verification decisions, simplifying error tracing and informing hyperparameter selection. In our experiments, we demonstrate PhiNet's interpretability with practical examples, including its application in analyzing the impact of different hyperparameters. We conduct both qualitative and quantitative evaluations of the proposed interpretability methods and assess speaker verification performance across multiple benchmark datasets, including VoxCeleb, SITW, and LibriSpeech. Results show that PhiNet achieves performance comparable to traditional black-box ASV models while offering meaningful, interpretable explanations for its decisions, bridging the gap between ASV and forensic analysis.

Uncrewed Aerial Vehicle (UAV) networks require accurate Air-to-Air (A2A) channel models, but most existing work focuses on Air-to-Ground links and leaves the sub-6 GHz A2A channel poorly characterized. We present preliminary 3.4 GHz A2A channel measurements collected with a lightweight, reconfigurable, open-source channel sounder built from USRP B210 software-defined radios and a high-precision GNSS-disciplined oscillator mounted on two UAVs. Measurements were conducted at the AERPAW Lake Wheeler testbed using a spherical flight trajectory around a second drone to capture channel behavior over varying altitudes, elevation angles, and relative headings. From these data, we analyze fundamental channel properties, extract channel impulse responses, model fading behavior as a function of link geometry, and characterize fading statistics including RMS delay spread. The resulting dataset and analysis provide a more realistic basis for the design, emulation, and evaluation of physical-layer and MAC protocols for next-generation UAV communication networks.

We study the monotonicity of the cumulative dose response (cDR) for a class of incoherent feedforward motifs (IFFM) systems with linear intermediate dynamics and nonlinear output dynamics. While the instantaneous dose response (DR) may be nonmonotone with respect to the input, the cDR can still be monotone. To analyze this phenomenon, we derive an integral representation of the sensitivity of cDR with respect to the input and establish general sufficient conditions for both monotonicity and nonmonotonicity. These results reduce the problem to verifying qualitative sign properties along system trajectories. The structural conditions identify eight canonical IFFM models, four of which are analyzed in detail within the proposed framework. In particular, IFFM1 and IFFM3 exhibit monotone cDR despite potentially nonmonotone DR, while IFFM2 is monotone already at the level of DR, which implies monotonicity of cDR. In contrast, IFFM4 exhibits nonmonotone cDR. Numerical simulations indicate that these properties persist beyond the structured initial conditions used in the analysis. Overall, our results provide a unified framework for understanding how system structure shapes monotonicity in cumulative input–output responses.

This paper addresses output-feedback covariance steering for stochastic discrete-time linear time-invariant systems with unknown dynamics. We construct a controllable non-minimal state representation from past inputs and outputs, allowing the problem to be formulated in a standard state-feedback setting. The induced disturbance, however, is temporally correlated, requiring propagation of the state-disturbance cross-covariance. Using persistently exciting offline data, we employ an indirect approach for mean steering and a direct approach for covariance steering. The indirect formulation requires estimation of the mean dynamics, whereas the direct formulation requires estimation of the noise realization. We develop estimation methods suitable for temporally correlated noise and formulate the resulting covariance steering problem as a convex semidefinite program. Numerical simulations demonstrate the effectiveness of the proposed framework.

This paper proposes a new pitch estimator and a novel pitch tracker for speakers. We first decompose the sound signal into subbands using an auditory filterbank, assuming time-frequency sparsity of human speech. Instead of directly selecting the number of subbands according to experience, we propose a novel frequency coverage metric to derive the number of subbands and the center frequencies of the filterbank. The subband signals are then encoded inspired by the computational auditory scene analysis (CASA) approach, and the normalized autocorrelations are calculated for pitch estimation. To suppress spurious errors and track the speaker identity, the temporal continuity constraint is exploited and a Generalized Labeled Multi-Bernoulli (GLMB) filter is adapted for pitch tracking, where we use a novel pitch state transition model based on the Ornstein-Uhlenbeck process, and the measurement driven birth model for adaptive new births of pitch targets. Experimental evaluations with various additive noises demonstrate that the proposed methods have achieved better accuracy compared with several state-of-the-art pitch estimation methods in most studied scenarios. Tests using real recordings in a reverberant room also show that the proposed method is robust against reverberation.

Model predictive path integral (MPPI) is a sampling-based method for solving complex model predictive control (MPC) problems, but its real-time implementation is challenged by computational and sample requirements that grow with the prediction horizon, as well as sensitivity to manually tuned sampling parameters. To address these issues, we propose Step-MPPI, a framework that learns a sampling distribution and MPPI parameters for efficient single-step lookahead MPPI. Specifically, a neural network parameterizes the MPPI sampling mean and covariance at each time step, while the single-step cost weights and temperature are jointly learned in a self-supervised manner over long horizons using the MPC cost, constraint penalties, and maximum-entropy regularization. By embedding long-horizon objectives into the learned cost and sampling policy, Step-MPPI achieves the foresight of multi-step optimization with the millisecond-level latency of single-step lookahead. We demonstrate its efficiency across challenging tasks involving high-dimensional systems and/or long control horizons.

Speech-based depression detection has shown promise as an objective diagnostic tool, yet the cross-linguistic robustness of acoustic markers and their neurobiological underpinnings remain underexplored. This study extends Cross-Data Multilevel Attention (CDMA) framework, initially validated on Italian, to investigate these dimensions using a Chinese Mandarin dataset with Electroencephalography (EEG) recordings. We systematically fuse read speech with spontaneous speech across different emotional valences (positive, neutral, negative) to investigate whether emotional arousal is a more critical factor than valence polarity in enhancing detection performance in speech. Additionally, we establish the first neurophysiological validation for a speech-based depression model by correlating its predictions with neural oscillatory patterns during emotional face processing. Our results demonstrate strong cross-linguistic generalizability of the CDMA framework, achieving state-of-the-art performance (F1-score up to 89.6%) on the Chinese dataset, which is comparable to the previous Italian validation. Critically, emotionally valenced speech (both positive and negative) significantly outperformed neutral speech. This comparable performance between positive and negative tasks supports the emotional arousal hypothesis. Most importantly, EEG analysis revealed significant correlations between the model's speech-derived depression estimates and neural oscillatory patterns (theta and alpha bands), demonstrating alignment with established neural markers of emotional dysregulation in depression. This alignment, combined with the model's cross-linguistic robustness, not only supports that the CDMA framework's approach is a universally applicable and neurobiologically validated strategy but also establishes a novel paradigm for the neurophysiological validation of computational mental health models.

In Earth remote sensing, spatial-frequency domain visibility samples are inversely transformed into spatial-domain brightness temperature (BT) images through the signal processing pipeline of synthetic aperture interferometric radiometers (SAIR). However, L-band radio-frequency interference (RFI) contaminates the measured visibilities and severely degrades BT image quality, thereby impairing geophysical parameter retrieval. To address this issue, we propose VFDM, a Visibility-Function Diffusion Model based on Denoising Diffusion Probabilistic Models (DDPM), to mitigate RFI in the spatial-frequency domain while preserving fine-scale structures consistent with natural scene statistics. Furthermore, we construct a comprehensive dataset comprising more than ten thousand pairs of RFI-free natural scene visibility sample sets and their corresponding simulated contaminated counterparts, categorized by varying RFI intensities, numbers, and distributions. Finally, comprehensive experiments on both simulated and real-world data demonstrate the effectiveness and robustness of the proposed VFDM-based approach.

Many speaker localization methods can be found in the literature. However, speaker localization under strong reverberation still remains a major challenge in the real-world applications. This paper proposes two algorithms for localizing speakers using microphone array recordings of reverberated sounds. To separate concurrent speakers, the first algorithm decomposes microphone signals spectrotemporally into subbands via an auditory filterbank. To suppress reverberation, we propose a novel speech onset detection approach derived from the speech signal and impulse response models, and further propose to formulate the multi-channel cross-correlation coefficient (MCCC) of encoded speech onsets in each subband. The subband results are combined to estimate the directions-of-arrival (DOAs) of speakers. The second algorithm extends the generalized cross-correlation - phase transform (GCC-PHAT) method by using redundant information of multiple microphones to address the reverberation problem. The proposed methods have been evaluated under adverse conditions using not only simulated signals (reverberation time $T_{60}$ of up to $1$s) but also recordings in a real reverberant room ($T_{60} \approx 0.65$s). Comparing with some state-of-the-art localization methods, experimental results confirm that the proposed methods can reliably locate static and moving speakers, in presence of reverberation.

Whole-body control (WBC) has demonstrated significant advantages in complex interactive movements of high-dimensional robotic systems. However, when a robot is required to handle dynamic multi-contact combinations along a single kinematic chain-such as pushing open a door with its elbow while grasping an object-it faces major obstacles in terms of complex contact representation and joint configuration coupling. To address this, we propose a new control approach that explicitly manages arbitrary contact combinations, aiming to endow robots with whole-body interactive capabilities. We develop a morphology-constrained WBC network (MorphoGuard)-which is trained on a self-constructed dual-arm physical and simulation platform. A series of model recommendation experiments are designed to systematically investigate the impact of backbone architecture, fusion strategy, and model scale on network performance. To evaluate the control performance, we adopt a multi-object interaction task as the benchmark, requiring the model to simultaneously manipulate multiple target objects to specified positions. Experimental results show that the proposed method achieves a contact point management error of approximately 1 cm, demonstrating its effectiveness in whole-body interactive control.

This paper addresses the spatiotemporal mismatch in multi-agent distribution tracking within time-varying environments. While recent advancements in Density-Driven Optimal Control (D$^2$OC) have enabled finite-time distribution matching using Optimal Transport theory, existing formulations primarily assume a stationary reference density. In dynamic scenarios, such as tracking evolving wildfires or moving plumes, this assumption leads to a structural tracking lag where the agent configuration inevitably falls behind the shifting reference flow. To resolve this, we propose a feedforward-augmented D$^2$OC framework that explicitly incorporates the reference velocity field, modeled via the continuity equation, into the control law. We provide a formal mathematical quantification of the induced tracking lag and analytically prove that the proposed predictive mechanism effectively reduces the cumulative tracking error. Furthermore, an analytical ultimate bound for the local Wasserstein distance is established under discretization errors and transport jitter. Theoretical analysis and numerical results demonstrate that our approach significantly mitigates tracking latency, ensuring robust and high-fidelity tracking performance in rapidly changing environments.

Multi-person 3D reconstruction is pivotal for real-world interaction analysis, yet remains challenging due to severe occlusions and depth ambiguity. Current approaches typically rely on single-modality inputs, which inherently lack geometric guidance. Furthermore, these methods often reconstruct subjects in isolation, neglecting the collective group context essential for resolving ambiguities in crowded scenes. To address these limitations, we propose Contrastive Multi-modal Hypergraph Reasoning to synergize semantic, geometric, and pose cues for crowd reconstruction. We first initialize robust node representations by combining RGB features, geometric priors, and occlusion-aware incomplete poses. Additionally, we introduce a pelvis depth indicator as a global spatial anchor, aligning visual features with a metric-scale-agnostic depth ordering. Subsequently, we construct a shared-topology hypergraph that moves beyond pairwise constraints to model higher-order crowd dynamics. To improve feature fusion, we design a hypergraph-based contrastive learning scheme that jointly enhances intra-modal discriminability and enforces cross-modal orthogonality. This mechanism enables the network to propagate global context effectively, allowing it to infer missing information even under severe occlusion. Extensive experiments on the Panoptic and GigaCrowd benchmarks confirm that our method achieves new state-of-the-art performance. Code and pre-trained models are available at https://github.com/SunMH-try/CoMHR.

Human 3D vision involves two distinct stages: an Experience Module, where stereo depth is extracted relative to fixation, and an Inference Module, where this experience is interpreted to estimate 3D scene properties. Paradoxically, although stereo vision does not provide us with absolute distance information, it nonetheless affects our inferences about distance. We propose the Inference Module exploits a natural scene statistic: near scenes produce vivid disparity gradients, while far scenes appear comparatively flat. QualiaNet implements this two-stage architecture computationally: disparity maps simulating human stereo experience are passed to a CNN trained to estimate distance. The network can recover distance from disparity gradients alone, validating this approach.

Computing the effective resistance between nodes in finite discrete resistor grids is a classical problem in circuit analysis with applications in VLSI power delivery network analysis, graph theory, and network science. Recent advances, particularly the infinity mirror technique, provide an elegant physical interpretation for boundary conditions in finite grids. Building upon this foundation, this paper presents a closed-form analytical expression that avoids numerical truncation or polynomial fitting. Our theoretical development proceeds in two steps. First, we derive an exact analytical primitive for the singular integral term $R_2$ within the integral operator $\Omega_\alpha$. Second, we transform the doubly infinite mirror series into a compact expression using the Jacobi theta function $\vartheta_1$. This transformation achieves machine precision with only a few terms. However, under high anisotropy, the pure analytical approximation exhibits a distinct "cross-shaped" residual error. To address this, we introduce a hybrid engineering remediation: a dynamic numerical cache that performs localized grid integration (LGI), combining $O(1)$ speed with exact near-field accuracy. Numerical experiments demonstrate mean relative errors below 0.04% compared to SPICE simulations, eliminating axis-localized error artifacts. To facilitate further research, the implementation of our proposed 2D resistor grid calculator is available at: https://github.com/SeaTheDestiny/2D-Resistor-Grid-Calculator.git.

Reinforcement learning (RL) and model predictive control (MPC) offer complementary strengths, yet existing MPC-RL frameworks commonly rely on gradient-based optimization and therefore cannot handle the non-differentiable dynamics and objectives common in RL. We propose Soft MPCritic, an MPC-RL framework that learns a soft value function and uses sampling-based planning both for online control and for generating value targets. Specifically, Soft MPCritic instantiates MPC with model predictive path integral control (MPPI) and learns a terminal Q-function through fitted value iteration. Because the value targets are computed by the same planner used for control, the learned value function is aligned with the planner and implicitly extends its effective horizon. To keep target generation tractable, we introduce an amortized warm-start strategy that reuses the open-loop action sequences planned during online control to initialize batched MPPI computations of value targets, reducing computational cost without sacrificing solution quality. For robustness to model error, Soft MPCritic plans over scenarios drawn from an ensemble of dynamics models trained for next-step prediction. On both classical and constrained control tasks, Soft MPCritic learns effective policies with non-differentiable objectives, particularly where finite-horizon MPPI alone falls short. Soft MPCritic thus offers a practical blueprint for synthesizing MPC policies directly from black-box objectives, without differentiable surrogates.

Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the operator. Yet, existing techniques are largely restricted to Euclidean settings. To bridge this gap, this paper presents an approach for computing principal angles and vectors to enable Koopman subspace pruning within a Reproducing Kernel Hilbert Space (RKHS) geometry. We first outline an exact computational routine, which is subsequently scaled for large datasets using randomized Nystrom approximations. Based on these foundations, we introduce the Kernel-SPV and Approximate Kernel-SPV algorithms for targeted subspace refinement via principal vectors. Simulation results validate our approach.

This paper proposes a discrete-time event-triggered extremum seeking control scheme for real-time optimization of nonlinear systems. Unlike conventional discrete-time implementations relying on periodic updates, the proposed approach updates the control input only when a state-dependent triggering condition is satisfied, reducing unnecessary actuation and communication. The resulting closed-loop system combines extremum seeking with an event-triggering mechanism that adaptively determines the input update instants. Using discrete-time averaging and Lyapunov analysis, we establish practical convergence of the trajectories to a neighborhood of the unknown extremum point and show exponential stability of the associated average dynamics. The proposed method preserves the optimization capability of classical extremum seeking while significantly reducing the number of input updates. Simulation results illustrate the effectiveness of the approach for resource-aware real-time optimization.

In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.

Modern real-time systems require accurate characterization of task timing behavior to ensure predictable performance, particularly on complex hardware architectures. Existing methods, such as worst-case execution time analysis, often fail to capture the fine-grained timing behaviors of a task under varying resource contexts (e.g., an allocation of cache, memory bandwidth, and CPU frequency), which is necessary to achieve efficient resource utilization. In this paper, we introduce a novel generative profiling approach that synthesizes context-dependent, fine-grained timing profiles for real-time tasks, including those for unmeasured resource allocations. Our approach leverages a nonparametric, conditional multi-marginal Schrödinger Bridge (MSB) formulation to generate accurate execution profiles for unseen resource contexts, with maximum likelihood guarantees. We demonstrate the efficiency and effectiveness of our approach through real-world benchmarks, and showcase its practical utility in a representative case study of adaptive multicore resource allocation for real-time systems.

Current limitations in wireless modeling and radio frequency (RF)-based AI are primarily driven by a lack of high-quality, measurement-based datasets that connect RF signals to their physical environments. RF heatmaps, the typical form of such data, are high-dimensional and complex but lack the geometric and semantic context needed for interpretation, constraining the development of supervised machine learning models. To address this bottleneck, we propose a new class of multimodal datasets that combines RF measurements with auxiliary modalities like high-resolution cameras and lidar to bridge the gap between RF signals and their physical causes. The proposed data collection will span diverse indoor and outdoor environments, featuring both static and dynamic scenarios, including human activities ranging from walking to subtle gestures. By achieving precise spatial and temporal co-registration and creating digital replicas for voxel-level annotation, this dataset will enable transformative AI research. Key tasks include the forward problem of predicting RF heatmaps from visual data to revolutionize wireless system design, and the inverse problem of inferring scene semantics from RF signals, creating a new form of RF-based perception.

This paper revisits linear precoding, namely match-filter (MF) and zero-forcing (ZF), in a semantic multiple-input multiple-output (MIMO) system empowered by generative AI. The aim is to examine whether interference, channel state information (CSI) accuracy, and scalability limitations in conventional MIMO systems remain critical. Theoretical analysis, which is based on the generative inference model and Lipschitz continuous assumptions, reveals reduced sensitivity to interference and channel imperfections, as well as performance inferiority in high-SINR regimes compared to conventional MIMO systems. Simulation results validate the analysis and show that MF achieves semantic performance comparable to ZF under both perfect and imperfect CSI. These findings suggest that semantic MIMO relaxes the needs for aggressive interference mitigation and highly accurate CSI, while improving scalability with reduced computational and implementation complexity.

We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint reflecting the temporal structure of the system. We formulate this problem as a Schr"odinger Bridge, which seeks the coupling closest - in Kullback-Leibler divergence - to a given prior while enforcing both marginal and causality constraints. For the case of Gaussian marginals and general time-dependent quadratic cost functions, we derive a fully tractable characterization of the Sinkhorn iterations that converges to the optimal solution. Beyond its theoretical contribution, the proposed framework provides a principled foundation for applying causal optimal transport methods to system identification from distributional data.

We establish two concentration inequalities for nonlinear stochastic system under time-varying contraction conditions. The key to our approach is an energy function termed Averaged Moment Generating Function (AMGF). By combining it with incremental stability analysis, we develop a concentration inequality that bounds the deviation between the stochastic system state and its deterministic counterpart. As this inequality is restricted to single time instance, we further combine AMGF with martingale-based methods to derive a concentration inequality that bounds the fluctuation of the entire stochastic trajectory. Additionally, by synthesizing the two results, we significantly improve the trajectory-level concentration inequality for strongly contractive systems. Given the probability level $1-\delta$, the derived inequalities ensure an $\mO(\sqrt{\log(1/\delta))}$ bound on the deviation of stochastic trajectories, which is tight under our assumptions. Our results are exemplified through a case study on stochastic safe control.

Control barrier function (CBF)-based safety filters provide a systematic way to enforce state constraints, but they can significantly alter the closed-loop dynamics induced by a nominal, stabilizing controller. In particular, the resulting safety-filtered system may exhibit undesirable behaviors including limit cycles, unbounded trajectories, and undesired equilibria. This paper develops a policy optimization framework to maximally enhance the stability properties of safety-filtered controllers. Focusing on linear systems with linear nominal controllers, we jointly parameterize the nominal feedback gain and safety-filter components, and optimize them using trajectory-based objectives computed from closed-loop rollouts. To ensure that the nominal controller remains stabilizing throughout training, we encode Lyapunov-based stability conditions as smooth scalar constraints and enforce them using robust safe gradient flow. This guarantees feasibility of the stability constraints along the optimization iterates and therefore avoids instability during training. Numerical experiments on obstacle-avoidance problems show that the proposed approach can remove asymptotically stable undesired equilibria and improve convergence behavior while maintaining forward invariance of the safe set.

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system on a reproducing kernel Hilbert space (RKHS), the storage function and supply rate functions are expressed as kernel quadratic forms, through which the dissipative inequality is expressed as a linear operator inequality. The RKHS is specified by a linear–radial kernel, which inherently encode the information of equilibrium point, thus ensuring that all functions in the RKHS are locally at least linear around the origin and that kernel quadratic forms are locally at least quadratic, which expressively generalize conventional quadratic forms including sum-of-squares polynomials. Based on the kernel matrices of the sampled data, the dissipativity estimation can be posed as a finite-dimensional convex optimization problem, and a statistical learning bound can be derived on the kernel quadratic form for the probabilistic approximate correctness of dissipativity estimation.