arXiv subjects

Wenqian Xue

Publications and source records attributed to Wenqian Xue.

6 recordsLinked to original sources

arXiv2026

Energy Generative Modeling: A Lyapunov-based Energy Matching Perspective

Generative models based on static scalar energy functions represent an emerging paradigm in which a single time independent potential drives sample generation through its gradient field, eliminating the need for time conditioning entirely. We unify the training and sampling phases of this paradigm, conventionally treated as separate procedures, within a single framework: density transport on the Wasserstein space, cast as a nonlinear control problem in which the Kullback Leibler (KL) divergence serves as a Lyapunov function. Training and sampling are then two instances of this same master dynamics, differing only in initial condition. Within this autonomous framework we develop two analytic results. First, since the Lyapunov certificate is asymptotic, we derive a finite step stopping criterion for Langevin sampling and prove that no Lyapunov certificate exists for the deterministic gradient flow on the same energy landscape. Second, the reformulation brings the toolkit of nonlinear control theory to bear on static scalar energy generative modeling, that is, we show that additive composition of trained scalar energies retains an explicit Gibbs invariant measure and inherits the closed-loop Lyapunov certificate. Beyond these immediate results, this reformulation bridges static scalar energy generative models with the full toolkit of nonlinear control theory, opening the door to barrier functions for constrained generation and contraction metrics for accelerated sampling. Experiments on synthetic distributions validate the theoretical predictions.

cs.LG↗

arXiv2025

Lyapunov-Based Kolmogorov-Arnold Network (KAN) Adaptive Control

Recent advancements in Lyapunov-based Deep Neural Networks (Lb-DNNs) have demonstrated improved performance over shallow NNs and traditional adaptive control for nonlinear systems with uncertain dynamics. Existing Lb-DNNs rely on multi-layer perceptrons (MLPs), which lack interpretable insights. As a first step towards embedding interpretable insights in the control architecture, this paper develops the first Lyapunov-based Kolmogorov-Arnold Networks (Lb-KAN) adaptive control method for uncertain nonlinear systems. Unlike MLPs with deep-layer matrix multiplications, KANs provide interpretable insights by direct functional decomposition. In this framework, KANs are employed to approximate uncertain dynamics and embedded into the control law, enabling visualizable functional decomposition. The analytical update laws are constructed from a Lyapunov-based analysis for real-time learning without prior data in a KAN architecture. The analysis uses the distinct KAN approximation theorem to formally bound the reconstruction error and its effect on the performance. The update law is derived by incorporating the KAN's learnable parameters into a Jacobian matrix, enabling stable, analytical, real-time adaptation and ensuring asymptotic convergence of tracking errors. Moreover, the Lb-KAN provides a foundation for interpretability characteristics by achieving visualizable functional decomposition. Simulation results demonstrate that the Lb-KAN controller reduces the function approximation error by 20.2% and 18.0% over the baseline Lb-LSTM and Lb-DNN methods, respectively.

eess.SY↗

arXiv2025

Lyapunov-based Adaptive Transformer (LyAT) for Control of Stochastic Nonlinear Systems

This paper presents a novel Lyapunov-based Adaptive Transformer (LyAT) controller for stochastic nonlinear systems. While transformers have shown promise in various control applications due to sequential modeling through self-attention mechanisms, they have not been used within adaptive control architectures that provide stability guarantees. Existing transformer-based approaches for control rely on offline training with fixed weights, resulting in open-loop implementations that lack real-time adaptation capabilities and stability assurances. To address these limitations, a continuous LyAT controller is developed that adaptively estimates drift and diffusion uncertainties in stochastic dynamical systems without requiring offline pre-training. A key innovation is the analytically derived adaptation law constructed from a Lyapunov-based stability analysis, which enables real-time weight updates while guaranteeing probabilistic uniform ultimate boundedness of tracking and parameter estimation errors. Experimental validation on a quadrotor demonstrates the performance of the developed controller.

eess.SY↗

arXiv2024

Fast Deep Predictive Coding Networks for Videos Feature Extraction without Labels

Brain-inspired deep predictive coding networks (DPCNs) effectively model and capture video features through a bi-directional information flow, even without labels. They are based on an overcomplete description of video scenes, and one of the bottlenecks has been the lack of effective sparsification techniques to find discriminative and robust dictionaries. FISTA has been the best alternative. This paper proposes a DPCN with a fast inference of internal model variables (states and causes) that achieves high sparsity and accuracy of feature clustering. The proposed unsupervised learning procedure, inspired by adaptive dynamic programming with a majorization-minimization framework, and its convergence are rigorously analyzed. Experiments in the data sets CIFAR-10, Super Mario Bros video game, and Coil-100 validate the approach, which outperforms previous versions of DPCNs on learning rate, sparsity ratio, and feature clustering accuracy. Because of DCPN's solid foundation and explainability, this advance opens the door for general applications in object recognition in video without labels.

cs.CV↗

arXiv2023

Provable Reinforcement Learning for Networked Control Systems with Stochastic Packet Disordering

This paper formulates a stochastic optimal control problem for linear networked control systems featuring stochastic packet disordering with a unique stabilizing solution certified. The problem is solved by proposing reinforcement learning algorithms. A measurement method is first presented to deal with PD and calculate the newest control input. The NCSs with stochastic PD are modeled as stochastic NCSs. Then, given a cost function, a modified algebraic Riccati equation is derived within the formulation. We propose offline policy iteration and value iteration algorithms to solve the MARE associated with provable convergence. These two algorithms require knowledge of NCS dynamics and PD probabilities. To release that, we further design online model-free off-policy and Q-learning algorithms with an online estimation method for PD probability. Both model-free algorithms solve the optimal control problem using real-time system states, control inputs, and PD probability estimates. Simulation results verify the proposed formulation and algorithms at last.

eess.SY↗

arXiv2023

Data-Driven Inverse Reinforcement Learning for Expert-Learner Zero-Sum Games

In this paper, we formulate inverse reinforcement learning (IRL) as an expert-learner interaction whereby the optimal performance intent of an expert or target agent is unknown to a learner agent. The learner observes the states and controls of the expert and hence seeks to reconstruct the expert's cost function intent and thus mimics the expert's optimal response. Next, we add non-cooperative disturbances that seek to disrupt the learning and stability of the learner agent. This leads to the formulation of a new interaction we call zero-sum game IRL. We develop a framework to solve the zero-sum game IRL problem that is a modified extension of RL policy iteration (PI) to allow unknown expert performance intentions to be computed and non-cooperative disturbances to be rejected. The framework has two parts: a value function and control action update based on an extension of PI, and a cost function update based on standard inverse optimal control. Then, we eventually develop an off-policy IRL algorithm that does not require knowledge of the expert and learner agent dynamics and performs single-loop learning. Rigorous proofs and analyses are given. Finally, simulation experiments are presented to show the effectiveness of the new approach.

cs.LG↗