arXiv subjects

Guodong Shi

Publications and source records attributed to Guodong Shi.

At least 19 recordsLinked to original sources

arXiv2026

Distributed Nonlinear Equality-Constrained Optimization via Feedback Linearization and Singular Perturbation

Distributed optimization becomes particularly challenging when nonconvex objectives are combined with nonlinear equality constraints: feasibility is network coupled, while most existing exponentially convergent methods rely on convexity or affine constraints. This paper introduces a feedback-linearization and singular-perturbation framework for two representative problem classes involving, respectively, distributed local nonlinear equality constraints and nonlinear aggregate equality constraints. The framework separates the regulation of consensus and feasibility residuals from optimization along the feasible manifold. Specifically, an ideal feedback-linearized dynamics is constructed whose output behavior can be explicitly assigned, while its zero-output dynamics coincides with the projected gradient flow of the aggregate objective on the feasible manifold. The ideal feedback-linearizing input, however, is determined by a state-dependent, network-coupled algebraic equation and is therefore not directly implementable in a distributed manner. To overcome this obstruction, we replace the nonlocal algebraic solution with a fast residual-tracking dynamics, yielding a singular-perturbation realization that uses only local and neighboring information. Under a local quadratic-growth condition imposed only on the feasible manifold, we establish local exponential convergence of both the ideal and distributed dynamics. For sufficiently strong time-scale separation, the convergence rate of the distributed realization can be chosen arbitrarily close to that of the ideal dynamics. Explicit Euler discretizations are also proved to preserve local exponential convergence. Under stronger manifold regularity conditions, the region of attraction extends to a tubular neighborhood of the feasible manifold and, for affine local equality constraints, to the whole admissible state space.

math.OC↗

arXiv2026

SP-TransientBench: A Real-Captured Single Photon Perception Benchmark

Single-photon LiDAR (SPL) based on single-photon avalanche diode (SPAD) sensing enables time-resolved photon measurements with extreme sensitivity, offering unique potential for active 3D perception in photon-starved scenarios.However, real-world single photon perception remains fundamentally challenging due to unique measurement noise and complex multi-return transient phenomena, which jointly complicate geometric reconstruction and semantic scene understanding. Despite growing interest in SPAD-based sensing, existing studies are largely limited to simulated data or small-scale controlled captures. As a result, systematic evaluation of real-world single photon perception across depth estimation, multi-view reconstruction, and 3D semantic understanding remains underexplored. To bridge this gap, we introduce SP-TransientBench (STB), a real-captured multi-task benchmark for single photon perception. SP-TransientBenc comprises 10 diverse scenes and 10,297 views captured using a solid-state single-photon LiDAR at $256\times192$ resolution. Each view provides full time-of-flight histograms with multi-return behavior,standardized metadata, and calibrated camera poses for multi-view evaluation. We further provide 13-class 3D semantic annotations for selected scenes. By providing dedicated data splits and evaluation protocols for each task, STB enables consistent and reproducible benchmarking of real-world single photon perception across multiple 3D vision problems. The dataset and code will be released upon acceptance.

cs.CV↗

arXiv2026

Provably Guaranteed Polytopic Uncertainty Quantification for SLAM

In safety-critical robotics applications, guaranteed and practical uncertainty quantification (UQ) in perception is vital. Many existing works either offer no formal containment guarantee, rely on restrictive modeling assumptions, or focus only on pose estimation rather than a complete SLAM pipeline. This paper presents provably guaranteed UQ algorithms for 3D-3D landmark-based SLAM. The algorithms consist of three basic UQ modules: forward UQ for mapping, backward UQ for pose tracking, and pose compound. Each module produces a certified uncertainty set; when the input uncertainty bounds are deterministic, the output sets inherit deterministic guarantees, i.e., they provably contain the true poses and landmarks. Specifically, we use polytopes to represent uncertainty sets, enabling tractable computations and a unified treatment of pose uncertainty. To enhance algorithms' practical usability, we incorporate conformal prediction to calibrate measurement uncertainty from data with prescribed probability. Simulations and experiments demonstrate that the proposed algorithms provide both strong theoretical guarantees and practical usability. The code is open-sourced at https://github.com/LIAS-CUHKSZ/Polytopic-SLAM-Uncertainty-Quantification.

cs.RO↗

arXiv2026

Distributed Nesterov Flows for Multi-agent Optimization

Various distributed gradient descent algorithms for multi-agent optimization have incorporated the Nesterov accelerated gradient method, where the use of momentum enhances convergence rates. These algorithms have found broad applications in large-scale machine learning and optimization owing to their simplicity and low communication complexity. In this paper, we establish a continuous-time approximation of distributed Nesterov gradient descent. The convergence properties and convergence rate of the resulting distributed Nesterov flow are analyzed using Lyapunov methods. Building on these insights, we design new parameter choices within the flow, from which we derive flow-inspired discrete-time algorithms for multi-agent optimization. Surprisingly, the resulting algorithms achieve faster convergence compared to existing distributed gradient descent methods: they require fewer iterations to reach the same accuracy for strongly convex functions and exhibit an improved convergence rate for general convex functions without incurring additional communication rounds. Furthermore, we investigate the influence of the network topology on algorithm performance and derive an explicit relationship between the convergence rate and the graph condition number. Numerical simulations are presented to validate the effectiveness of the proposed approach.

eess.SY↗

arXiv2026

Pointwise and dynamic programming control synthesis for finite-level open quantum memory systems

This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and their Heisenberg picture evolution is governed by a quasilinear quantum stochastic differential equation. The latter involves a Hamiltonian whose parameters depend affinely on a classical control signal in the form of a deterministic function of time. The memory performance is quantified by a mean-square deviation of quantum system variables of interest from their initial conditions. We relate this functional to a matrix-valued state of an auxiliary classical control-affine dynamical system. This leads to a pointwise control design where the control signal minimises the time-derivative of the mean-square deviation with an additional quadratic penalty on the control. In an alternative finite-horizon setting with a terminal-integral cost functional, we apply dynamic programming and obtain a quadratically nonlinear Hamilton-Jacobi-Bellman equation, for which a solution is outlined in the form of a recursively computed asymptotic expansion.

math.OC↗

arXiv2026

Explicit Model Predictive Control with Quantum Encryption

This paper studies quantum-encrypted explicit MPC for constrained discrete-time linear systems in a cloud-based architecture. A finite-horizon quadratic MPC problem is solved offline to obtain a piecewise-affine controller. Shared quantum keys generated from Bell pairs and protected by quantum key distribution are used to encrypt the online control evaluation between the sensor and actuator. Based on this architecture, we develop a lightweight encrypted explicit MPC protocol, prove exact recovery of the plaintext control action, and characterize its computational efficiency. Numerical results demonstrate lower online complexity than classical encrypted MPC, while security is discussed in terms of confidentiality of plant data and control inputs.

eess.SY↗

arXiv2026

An Electricity Market with Reactive Power Trading: Incorporating Dynamic Operating Envelopes

Electricity market design that accounts for grid constraints such as voltage and thermal limits at the distribution level can increase opportunities for the grid integration of Distributed Energy Resources (DERs). In this paper, we consider rooftop solar backed by battery storage connected to a distribution grid. We design an electricity market to support customers sharing rooftop generation in excess of their energy demand, where customers earn a profit through peer-to-peer (P2P) energy trading. Our proposed electricity market also incorporates P2P reactive power trading to improve the voltage profile across a distribution feeder. We formulate the electricity market as an optimization-based problem, where voltage and thermal limits across a feeder are managed through the assignment of customer-specific dynamic operating envelopes (DOEs). The electricity market equilibrium is referred to as a competitive equilibrium, which is equivalent to a Nash equilibrium in a standard game. Our proposed market design is benchmarked using the IEEE 13-node test feeder.

eess.SY↗

arXiv2026

How Entanglement Reshapes the Geometry of Quantum Differential Privacy

Quantum differential privacy provides a rigorous framework for quantifying privacy guarantees in quantum information processing. While classical correlations are typically regarded as adversarial to privacy, the role of their quantum analogue, entanglement, is not well understood. In this work, we investigate how quantum entanglement fundamentally shapes quantum local differential privacy (QLDP). We consider a bipartite quantum system whose input state has a prescribed level of entanglement, characterized by a lower bound on the entanglement entropy. Each subsystem is then processed by a local quantum mechanism and measured using local operations only, ensuring that no additional entanglement is generated during the process. Our main result reveals a sharp phase-transition phenomenon in the relation between entanglement and QLDP: below a mechanism-dependent entropy threshold, the optimal privacy leakage level mirrors that of unentangled inputs; beyond this threshold, the exact privacy leakage is strictly smaller than its unentangled value and admits an explicitly computable upper bound that strictly decreases with the entropy. This bound can also certify that some non-private mechanisms become private under sufficiently strong entanglement constraints. The phase-transition phenomenon gives rise to a nonlinear dependence of the certified privacy-leakage upper bound on the entanglement entropy, even though the underlying quantum mechanisms and measurements are linear. We show that the transition is governed by the intrinsic non-convex geometry of the set of entanglement-constrained quantum states, which we parametrize as a smooth manifold and analyze via Riemannian optimization. Our findings demonstrate that entanglement serves as a genuine privacy-enhancing resource, offering a geometric and operational foundation for designing robust privacy-preserving quantum protocols.

cs.IT↗

arXiv2026

Differential Privacy on Affine Manifolds: Geometrically Confined Privacy in Linear Dynamical Systems

In this paper, we present a comprehensive framework for differential privacy over affine manifolds and validate its usefulness in the contexts of differentially private cloud-based control and average consensus. We consider differential privacy mechanisms for linear queries when the input data are constrained to lie on affine manifolds, a structural property that is assumed to be available as prior knowledge to adversaries. In this setting, the definition of neighborhood adjacency must be formulated with respect to the intrinsic geometry of the manifolds. We demonstrate that such affine-manifold constraints can fundamentally alter the attainable privacy levels relative to the unconstrained case. In particular, we derive necessary and sufficient conditions under which differential privacy can be realized via structured noise injection mechanisms, wherein correlated Gaussian or Laplace noise distributions, rather than i.i.d. perturbations, are calibrated to the dataset. Based on these characterizations, we develop explicit noise calibration procedures that guarantee the tight realization of any prescribed privacy budget with a matching noise magnitude. Finally, we show that the proposed framework admits direct applications to linear dynamical systems ranging from differentially private cloud-based control to privacy-preserving average consensus, all of which naturally involve affine-manifold constraints. The established theoretical results are illustrated through numerical examples.

eess.SY↗

arXiv2026

Blended Dynamics and Emergence in Open Quantum Networks

In this paper, we develop a blended dynamics framework for open quantum networks with diffusive couplings. The network consists of qubits interconnected through Hamiltonian couplings, environmental dissipation, and consensus-like diffusive interactions. Such networks commonly arise in spontaneous emission processes and non-Hermitian quantum computing, and their evolution follows a Lindblad master equation. Blended dynamics theory is well established in the classical setting as a tool for analyzing emergent behaviors in heterogeneous networks with diffusive couplings. Its key insight is to blend the local dynamics rather than the trajectories of individual nodes. Perturbation analysis then shows that, under sufficiently strong coupling, all node trajectories tend to stay close to those of the blended system over time. We first show that this theory extends naturally to the reduced-state dynamics of quantum networks, revealing classical-like clustering phenomena in which qubits converge to a shared equilibrium or a common trajectory determined by the quantum blended reduced-state dynamics. We then extend the analysis to qubit coherent states using quantum Laplacians and induced graphs, proving orbit attraction of the network density operator toward the quantum blended coherent dynamics, establishing the emergence of intrinsically quantum and dynamically clustering behaviors. Finally, numerical examples validate the theoretical results.

quant-ph↗

arXiv2025

Measurement-based Initial Point Smoothing and Control Approach to Quantum Memory Systems

This paper is concerned with a quantum memory system for storing quantum information in the form of its initial dynamic variables in the presence of environmental noise. In order to compensate for the deviation from the initial conditions, the classical parameters of the system Hamiltonian are affected by the actuator output of a measurement-based classical controller. The latter uses an observation process produced by a measuring apparatus from the quantum output field of the memory system. The underlying system is modelled as an open quantum harmonic oscillator whose Heisenberg evolution is governed by linear Hudson-Parthasarathy quantum stochastic differential equations. The controller is organised as a classical linear time-varying system, so that the resulting closed-loop system has quantum and classical dynamic variables. We apply linear-quadratic-Gaussian control and fixed-point smoothing at the level of the first two moments and consider controllers with a separation structure which involve a continuously updated estimate for the initial quantum variables. The initial-point smoother is used for actuator signal formation so as to minimise the sum of a mean-square deviation of the quantum memory system variables at a given time horizon from their initial values and an integral quadratic penalty on the control signal.

quant-ph↗

arXiv2025

Quantum Encrypted Control of Networked Systems

Encrypted control has been extensively studied to ensure the confidentiality of system states and control inputs for networked control systems. This paper presents a computationally efficient encrypted control framework for networked systems enabled by quantum communication. A quantum channel between sensors and actuators is used to generate identical secret keys, whose security is further enhanced through quantum key distribution. These keys enable lightweight encryption and decryption while preserving confidentiality and control accuracy. We develop a novel encryption-decryption architecture for state-feedback control of linear systems based on quantum keys, and characterize the impact of quantum state errors on closed-loop stability. In particular, we establish the existence of a critical threshold on intrinsic quantum noise below which stability is guaranteed. In contrast to classical encrypted control schemes, which may collapse under a single key-bit error, the proposed quantum encrypted control exhibits strong robustness to key imperfections. We further adopt quantization techniques to address the scenarios with limited communication bits in practical situations, and implement privacy protection for quantum keys based on a stochastic quantizer. These results demonstrate that integrating quantum technologies into control systems in a nontrivial and principled manner, even at their current level of maturity, can yield substantial performance gains in reducing computational complexity and improving resilience to key errors while ensuring security against multiple eavesdropping sources.

quant-ph↗

arXiv2025

Quantum memory optimisation using finite-horizon, decoherence time and discounted mean-square performance criteria

This paper is concerned with open quantum memory systems for approximately retaining quantum information, such as initial dynamic variables or quantum states to be stored over a bounded time interval. In the Heisenberg picture of quantum dynamics, the deviation of the system variables from their initial values lends itself to closed-form computation in terms of tractable moment dynamics for open quantum harmonic oscillators and finite-level quantum systems governed by linear or quasi-linear Hudson-Parthasarathy quantum stochastic differential equations, respectively. This tractability is used in a recently proposed optimality criterion for varying the system parameters so as to maximise the memory decoherence time when the mean-square deviation achieves a given critical threshold. The memory decoherence time maximisation approach is extended beyond the previously considered low-threshold asymptotic approximation and to Schr\"{o}dinger type mean-square deviation functionals for the reduced system state governed by the Lindblad master equation. We link this approach with the minimisation of the mean-square deviation functionals at a finite time horizon and with their discounted version which quantifies the averaged performance of the quantum system as a temporary memory under a Poisson flow of storage requests.

quant-ph↗

arXiv2025

Peer-to-Peer Energy Markets With Uniform Pricing: A Dynamic Operating Envelope Approach

The recent widespread adoption of rooftop solar backed by battery storage is enabling energy customers to both produce and consume electricity (i.e., prosumers of electricity). To facilitate prosumer participation in the electric grid, new market mechanisms are required. In this paper, we design peer-to-peer energy markets where prosumers trade their excess energy with peers to gain profit while satisfying the overall balance in electricity supply and demand. We first consider a market structure, considering the case where voltage and/or thermal constraints are binding. When such grid constraints are binding, market clearing prices can vary across locations. However, heterogeneous prices may be considered by regulators to lack fairness. To ensure uniform pricing, we design two peer-to-peer energy markets with dynamic operating envelopes (DOEs). DOEs enable us to decompose global voltage and thermal constraints across the power grid into local constraints for each prosumer, resulting in uniform prices across the grid. By means of numerical simulations on an IEEE 13-node feeder, we benchmark the proposed market-based approaches in the presence of binding voltage constraints.

eess.SY↗

arXiv2025

Toward Robust Single-Photon Perception for Robots: A Condition-Aware Active Learning Approach

LiDAR-based perception plays a fundamental role in modern robotic systems for environment understanding and navigation. Single-photon LiDAR (SPL) extends conventional LiDAR by enabling photon-efficient 3D sensing under challenging conditions such as long-range operation, low-albedo targets, and limited signal returns. However, developing SPL perception models for real-world robotic applications remains difficult because annotated SPL data are costly to obtain and model performance can vary substantially across imaging conditions. In this paper, we present the first active learning framework tailored to the SPL sensing modality rather than a specific downstream task. Our method introduces a physics-grounded, imaging condition-aware sampling strategy that uses synthetic SPL variants to characterize how candidate samples respond to changes in sensing conditions. By jointly modeling prediction uncertainty, sample diversity, and sensitivity to photon-level imaging variations, the proposed approach prioritizes samples that are informative for improving labeling efficiency and robustness. Extensive experiments on synthetic and real-world SPL datasets demonstrate that our method substantially reduces annotation requirements while maintaining strong performance across image-level and dense prediction settings. On synthetic data, our approach achieves 97% classification accuracy using only 1.5% labeled samples. On real-world data, it maintains 90% accuracy with 8.2% labeled samples, outperforming the strongest baseline by 6%. Segmentation results further show that the same condition-aware acquisition principle improves annotation efficiency and robustness across imaging conditions. These results establish a modality-aware active learning strategy for data-efficient SPL perception, with the potential to extend to a broader range of downstream tasks.

eess.IV↗

arXiv2025

Bias-Eliminated PnP for Stereo Visual Odometry: Provably Consistent and Large-Scale Localization

In this paper, we first present a bias-eliminated weighted (Bias-Eli-W) perspective-n-point (PnP) estimator for stereo visual odometry (VO) with provable consistency. Specifically, leveraging statistical theory, we develop an asymptotically unbiased and $\sqrt {n}$-consistent PnP estimator that accounts for varying 3D triangulation uncertainties, ensuring that the relative pose estimate converges to the ground truth as the number of features increases. Next, on the stereo VO pipeline side, we propose a framework that continuously triangulates contemporary features for tracking new frames, effectively decoupling temporal dependencies between pose and 3D point errors. We integrate the Bias-Eli-W PnP estimator into the proposed stereo VO pipeline, creating a synergistic effect that enhances the suppression of pose estimation errors. We validate the performance of our method on the KITTI and Oxford RobotCar datasets. Experimental results demonstrate that our method: 1) achieves significant improvements in both relative pose error and absolute trajectory error in large-scale environments; 2) provides reliable localization under erratic and unpredictable robot motions. The successful implementation of the Bias-Eli-W PnP in stereo VO indicates the importance of information screening in robotic estimation tasks with high-uncertainty measurements, shedding light on diverse applications where PnP is a key ingredient.

cs.RO↗

arXiv2025

Decoherence time maximization and partial isolation for open quantum harmonic oscillator memory networks

This paper considers a network of open quantum harmonic oscillators which interact with their neighbours through direct energy and field-mediated couplings and also with external quantum fields. The position-momentum dynamic variables of the network are governed by linear quantum stochastic differential equations associated with the nodes of a graph whose edges specify the interconnection of the component oscillators. Such systems can be employed as Heisenberg picture quantum memories with an engineered ability to approximately retain initial conditions over a bounded time interval. We use the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation for a subset (or linear combinations) of network variables from their initial values. This approach is applied to maximizing a high-fidelity asymptotic approximation of the decoherence time over the direct energy coupling parameters of the network. The resulting optimality condition is a set of linear equations for blocks of a sparse matrix associated with the edges of the direct energy coupling graph of the network. We also discuss a setting where the quantum network has a subset of dynamic variables which are affected by the external fields only indirectly, through a complementary ``shielding'' system. This holds under a rank condition on the network-field coupling matrix and can be achieved through an appropriate field-mediated coupling between the component oscillators. The partially isolated subnetwork has a longer decoherence time in the high-fidelity limit, thus providing a particularly relevant candidate for a quantum memory.

quant-ph↗

arXiv2025

Linear Convergence of Distributed Compressed Optimization with Equality Constraints

In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a distributed saddle-point algorithm is proposed by employing distributed filters to derive errors of the transmitted states for spatio-temporal compression purposes. It is shown that the resulting distributed compressed algorithm achieves linear convergence. Furthermore, the algorithm is generalized to the case where each agent holds a portion of the global equality constraint, i.e., the constraints across agents are coupled. By introducing an additional design freedom, the global equality constraint is shown to be equivalent to the one where each agent holds an equality constraint, for which the proposed distributed compressed saddle-point algorithm can be adapted to achieve linear convergence. Numerical simulations are adopted to validate the effectiveness of the proposed algorithms.

eess.SY↗