arXiv subjects

Dongjun Wu

Publications and source records attributed to Dongjun Wu.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Unbalanced Optimal Transport: Duality, Reachability, and Computation

We study dynamical unbalanced optimal transport for nonlinear control-affine systems in which the control input affects both the transportation of mass and its growth or decay. This phenomenon arises naturally in controlled transport-reaction systems such as cancer treatment, and distinguishes the problem from standard unbalanced optimal transport, where transport and mass variation are typically independent. To address this problem, we combine classical relaxed-control theory with a weighted superposition principle to obtain an infinite-dimensional linear programming reformulation over weighted trajectories. Under suitable convexity and compactness assumptions, we show that this relaxation is tight. Based on the relaxation, we derive a Kantorovich dual formulation in terms of Hamilton-Jacobi-Bellman inequalities, and establish strong duality over smooth subsolutions. We then utilize the dual formulation to characterize reachability of the system, namely, when a given terminal measure is reachable from a given initial measure. In addition, tractable sufficient conditions for reachability are provided. Finally, we develop an augmented-Lagrangian algorithm based on the dual formulation for numerical computation of the optimal transport plan. The framework is illustrated on a phenotype-structured cancer treatment problem in which therapy simultaneously drives phenotypic adaptation and population growth or death.

math.OC↗

arXiv2026

Stable Dynamical Mass Transportation via port-Hamiltonian Structure

Dynamical optimal mass transportation over nonlinear systems is often hindered by the curse of dimensionality and open-loop implementation. We propose an alternative framework that sacrifices exact optimality in favor of stability, robustness, and scalability. We use a stochastic port-Hamiltonian system as a reference model. Under suitable structural assumptions, we show that its density converges asymptotically to a prescribed steady-state distribution. We then shape a deterministic nonlinear system into a compatible port-Hamiltonian form and add a local density-feedback term so that its closed-loop continuity equation matches the Fokker-Planck-Kolmogorov equation of the reference model. The resulting feedback drives a broad class of initial distributions to the target distribution. Because the density term is local at the particle level, the controller admits decentralized implementation and avoids solving a global finite-horizon transport problem online. Nonlinear examples and simulations illustrate the method. For linear systems with Gaussian targets, we derive necessary and sufficient conditions for stabilizing density feedback and give explicit controller constructions.

math.OC↗

arXiv2026

Wasserstein Contraction of Stochastic Systems on Manifolds: A Differential Approach

Contraction analysis of dynamical systems turns a global convergence problem into a local one. If the variational system is stable in a uniform sense, then all trajectories of the original system converge toward each other. This paper develops a stochastic analogue for continuous-time stochastic systems, where convergence is measured by Wasserstein distance between probability laws. The key step is to employ mean-square differentiation to construct stochastic variational dynamics. Its uniform $L_2$ stability can then be integrated along curves of initial conditions, yielding Wasserstein contraction of the associated probability laws. This yields criteria formulated in terms of differential Lyapunov functions, and on manifolds, it leads to intrinsic Riemannian formulations. A distinctive feature of the stochastic setting is that the coupling of the noises becomes a design freedom. To exploit this freedom, we introduce an orthogonal differential coupling that extends the framework beyond synchronous coupling. The resulting criterion explicitly exposes how the curvature of the state space enters the contraction mechanism and, in the orthonormal-frame case, recovers the classical Ricci-curvature structure. Finally, we apply the framework to stochastic control on a compact manifold. By introducing stochastic control input, we overcome a deterministic obstruction to global stabilization. That is, a system that cannot be globally stabilized through smooth time-invariant deterministic feedback is rendered globally contracting in $W_2$, and its steady state distribution can be made arbitrarily concentrated around a prescribed target equilibrium.

math.OC↗

arXiv2026

DepthPolyp: Pseudo-Depth Guided Lightweight Segmentation for Real-Time Colonoscopy

Accurate polyp segmentation in colonoscopy is essential for early colorectal cancer detection, yet real-world clinical environments pose persistent challenges such as motion blur, specular reflections, and illumination instability. Most existing methods are optimized on clean benchmark images and suffer noticeable performance degradation when deployed in authentic surgical scenarios. We propose DepthPolyp, a lightweight and robust segmentation framework based on pseudo-depth-guided multi-task learning and efficient feature modulation. The architecture combines hierarchical Ghost factorization for compact feature generation, Interleaved Shuffle Fusion for low-cost cross-scale interaction, and Dynamic Group Gating for adaptive group-wise feature weighting. Extensive experiments demonstrate that DepthPolyp achieves strong cross-dataset generalization when trained on degraded data and evaluated on both clean and noisy target domains, consistently outperforming lightweight baselines and remaining competitive with substantially larger models. In real surgical video evaluation on PolypGen, DepthPolyp achieves better segmentation performance than models up to $20\times$ larger while preserving real-time inference speed. With only 3.57M parameters and 0.86 GMACs, the proposed method runs at over 180 FPS on mobile devices, making it well suited for real-time deployment in resource-constrained clinical environments. Code and pretrained weights are available at: https://github.com/ReaganWu/DepthPolyp/

cs.CV↗

arXiv2026

FLICKER: A Fine-Grained Contribution-Aware Accelerator for Real-Time 3D Gaussian Splatting

Recently, 3D Gaussian Splatting (3DGS) has emerged as a mainstream rendering technique due to its photorealistic quality and low latency. However, processing massive numbers of non-contributing Gaussian points introduces significant computational overhead on resource-limited edge platforms, limiting its deployment in next-generation AR/VR devices. Contribution-based prior skipping alleviates this inefficiency, yet the resulting contribution-testing workload becomes prohibitive for edge execution. In this paper, we present FLICKER, a contribution-aware 3DGS accelerator based on hardware-software co-design. The proposed framework integrates adaptive leader pixels, pixel-rectangle grouping, hierarchical Gaussian testing, and a mixed-precision architecture to enable near pixel-level, contribution-driven rendering with minimal overhead. Experimental results demonstrate up to $1.5\times$ speedup, $2.6\times$ improvement in energy efficiency, and $14%$ area reduction compared with a state-of-the-art accelerator. Compared with a representative edge GPU, FLICKER achieves a $19.8\times$ speedup and $26.7\times$ higher energy efficiency.

cs.AR↗

arXiv2025

Lyapunov and Riccati Equations from a Positive System Perspective

This paper presents a new interpretation of the Lyapunov and Riccati equations from the perspective of positive system theory. We show it is possible to construct positive systems related to these equations, and then certain conclusions -- such as the existence and uniqueness of solutions -- can be drawn from positive systems theory. Specifically, under standard observability assumptions, a strictly positive linear system can be constructed for Lyapunov equations, leading to exponential convergence in Hilbert metric to the Perron-Frobenius vector -- closely related to the solution of the Lyapunov equation. For algebraic Riccati equations, homogeneous strictly positive systems can be constructed, which exhibit more complex dynamical behaviors. While the existence and uniqueness of the solution can still be proven, only asymptotic convergence can be obtained.

math.OC↗

arXiv2025

The Feasibility of Acoustophoresis Multimodal Control

Actuating the acoustic resonance modes of a microfluidic device containing suspended particles (e.g., cells) allows for the manipulation of their individual positions. In this work, we investigate how the number of resonance modes $M$ chosen for actuation and the number of particles $P$ affect the probability of success $S$ of manipulation tasks, denoted Acoustophoretic Control Problems (ACPs). Using simulations, we show that the ratio of locally controllable volume to the state-space volume correlates strongly with $S$. This ratio can be efficiently computed from the pressure field geometry as it does not involve solving a control problem, thus opening possibilities for experimental and numerical device optimization routines. Further, we show numerically that in noise-free 1D systems $S \approx 1 - P/M$, and that in noisy 1D and 2D systems $S$ is accurately predicted by Wendel's Theorem. We also show that the relationship between $M$ and $P$ for a given $S$ is approximately linear, suggesting that as long as $P/M$ is constant, $S$ will remain unchanged. We validate this finding by successfully simulating the control of systems with up to $60$ particles with up to $600$ modes.

physics.app-ph↗

arXiv2025

Consensus of A Class of Nonlinear Systems with Varying Topology: A Hilbert Metric Approach

In this technical note, we introduce a novel approach to studying consensus of continuous-time nonlinear systems with varying topology based on Hilbert metric. We demonstrate that this metric offers significant flexibility in analyzing consensus properties, while effectively handling nonlinearities and time dependencies. Notably, our approach relaxes key technical assumptions from some standard results while yielding stronger conclusions with shorter proofs. This framework provides new insights into nonlinear consensus under varying topology.

math.OC↗

arXiv2025

Controllability Analysis of Multi-Modal Acoustic Particle Manipulation in One-Dimensional Standing Waves

Acoustic manipulation in microfluidic devices enables contactless handling of biological cells for Lab-on-Chip applications. This paper analyzes the controllability of multi-particle systems in a one-dimensional acoustic standing wave system using multi-modal actuation. By modeling the system as a nonlinear control system, we analyze its global and local controllability, quantifying these properties in terms of mode numbers. Our results show that sufficient modes enable dense reachability sets, while mode mixing with 10 modes grants a strict notion of controllability to 80\% of the state space in a two-particle system. These findings offer theoretical insights for designing acoustic manipulation algorithms, supporting efficient control in biomedical applications.

eess.SY↗

arXiv2025

Nonlinear Dynamical Unbalanced Optimal Transport: Relaxation and Duality

In this paper, we introduce a generalized dynamical unbalanced optimal transport framework by incorporating limited control input and mass dissipation, addressing limitations in conventional optimal transport for control applications. We derive a convex dual of the problem using dual optimal control techniques developed before and during the 1990s, transforming the non-convex optimization into a more tractable form.At the core of this formulation is the smooth sub-solutions to an HJB equation. A first-order algorithm based on the dual formulation is proposed to solve the problem numerically.

math.OC↗

arXiv2024

Duality-based Dynamical Optimal Transport of Discrete Time Systems

We study dynamical optimal transport of discrete time systems (dDOT) with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting algorithm is proposed for numerical implementation. While solving partial differential equations is often required in the continuous time case, a salient feature of our algorithm is that it avoids equation solving entirely. Furthermore, it is typical to solve a convex optimization problem at each grid point in continuous time settings, the discrete case reduces this to a straightforward maximization. Additionally, the proposed algorithm is highly amenable to parallelization. For linear systems with Gaussian marginals, we provide a semi-definite programming formulation based on our theory. Finally, we validate the approach with a simulation example.

math.OC↗

arXiv2024

The use of a humanoid robot for older people with dementia in aged care facilities

This paper presents an interdisciplinary PhD project using a humanoid robot to encourage interactive activities for people with dementia living in two aged care facilities. The aim of the project was to develop software and use technologies to achieve successful robot-led engagement with older people with dementia. This paper outlines the qualitative findings from the project's feasibility stage. The researcher's observations, the participants' attitudes and the feedback from carers are presented and discussed.

cs.RO↗

arXiv2024

Optimal Mass Transport of Nonlinear Systems under Input and Density Constraints

We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based on the Douglas-Rachford algorithm. Some preliminary simulation results are presented to demonstrate the effectiveness of our approaches.

math.OC↗

arXiv2024

Control contraction metrics on Lie groups

In this paper, we extend the control contraction metrics (CCM) approach, which was originally proposed for the universal tracking control of nonlinear systems, to those that evolves on Lie groups. Our idea is to view the manifold as a constrained set that is embedded in Euclidean space, and then propose the sufficient conditions for the existence of a CCM and the associated controller design. Notably, we demonstrate that the search for CCM on Lie groups can be reformulated as convex conditions. The results extend the applicability of the CCM approach and provide a framework for analyzing the behavior of control systems with Lie group structures.

eess.SY↗

arXiv2023

Stability Analysis of Trajectories on Manifolds with Applications to Observer and Controller Design

This paper examines the local exponential stability (LES) of trajectories for nonlinear systems on Riemannian manifolds. We present necessary and sufficient conditions for LES of a trajectory on a Riemannian manifold by analyzing the complete lift of the system along the given trajectory. These conditions are coordinate-free which reveal fundamental relationships between exponential stability and incremental stability in a local sense. We then apply these results to design tracking controllers and observers for Euler-Lagrangian systems on manifolds; a notable advantage of our design is that it visibly reveals the effect of curvature on system dynamics and hence suggests compensation terms in the controller and observer. Additionally, we revisit some well-known intrinsic observer problems using our proposed method, which largely simplifies the analysis compared to existing results.

math.OC↗

arXiv2022

Regret Analysis for Risk-aware Linear Quadratic Control

This paper investigates the regret associated with the Distributionally Robust Control (DRC) strategies used to address multistage optimization problems where the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. We quantify the price (distributional regret) that one ends up paying for not knowing the exact probability distribution of the stochastic system uncertainty while aiming to control it using the DRC strategies. The conservatism of the DRC strategies for being robust to worst-case uncertainty distribution in the considered ambiguity set comes at the price of lack of knowledge about the true distribution in the set. We use the worst case Conditional Value-at-Risk to define the distributional regret and the regret bound was found to be increasing with tighter risk level. The motive of this paper is to promote the design of new control algorithms aiming to minimize the distributional regret.

math.OC↗

arXiv2022

Further Geometric and Lyapunov Characterizations of Incrementally Stable Systems on Finsler Manifolds

In this paper, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the complete lift of the system. Based on this, two Lyapunov characterizations of incrementally stable systems are derived, namely, converse contraction theorems, and revelation of the connection between incremental stability and stability of an equilibrium point, in which the second result recovers and extends the classical Krasovskii's method.

eess.SY↗

arXiv2020

Intrinsic Construction of Lyapunov Functions on Riemannian Manifold

For systems evolving on a Riemannian manifold, we propose converse Lyapunov theorems for asymptotic and exponential stability. The novelty of the proposed approach is that is does not rely on local Euclidean coordinate, and is thus valid on a wider domain than the immediate vicinity of the considered equilibrium. We also show how the constructions can be useful for robustness analysis.

eess.SY↗