arXiv subjects

Qi Gong

Publications and source records attributed to Qi Gong.

18 recordsLinked to original sources

arXiv2026

Modeling Large-Scale Adversarial Swarm Engagements using Optimal Control

We study optimal control of large-scale autonomous systems under adversarial conditions in which agents may be probabilistically destroyed during an engagement. Because attrition changes the population that generates the spatial interaction dynamics, treating survival and motion independently can produce physically inconsistent solutions. We formulate a stochastic variable-population benchmark and examine three deterministic approximations that propagate agent survival probabilities from relative geometry. The models are applied to defense of a high-value unit against an attacking swarm and solved using direct optimal-control methods. Monte Carlo realizations of the stochastic benchmark show that deterministic models can reproduce engagement outcomes when attrition is coupled to spatial influence, whereas a decoupled formulation can exploit effectively destroyed defenders that continue to repel attackers, a failure mode we term ``ghost herding.'' Large-scale simulations and defender-number sweeps further show that this modeling choice can substantially alter predicted high-value-unit survival and inferred defensive resource requirements. The results provide a tractable framework for attrition-aware trajectory optimization and resource--survival analysis in adversarial autonomous systems.

math.OC↗

arXiv2026

Tell Me What I Missed: Interacting with GPT during Recalling of One-Time Witnessed Events

LLM-assisted technologies are increasingly used to support cognitive processing and information interpretation, yet their role in aiding memory recall, and how people choose to engage with them, remains underexplored. We studied participants who watched a short robbery video (approximating a one-time eyewitness scenario) and composed recall statements using either a default GPT or a guided GPT prompted with a standardized eyewitness protocol. Results show that, in the default condition, participants who believed they had a clearer understanding of the event were more likely to trust GPT's output, whereas in the guided condition, participants showed stronger alignment between subjective clarity and actual recall. Additionally, participants evaluated the legitimacy of the individuals in the incident differently across conditions. Interaction analysis further revealed that default-GPT users spontaneously developed diverse strategies, including building on existing recollections, requesting potentially missing details, and treating GPT as a recall coach. This work shows how GPT-user interplay can subconsciously shape beliefs and perceptions of remembered events.

cs.HC↗

arXiv2025

"If I were in Space": Understanding and Adapting to Social Isolation through Designing Collaborative Narratives

Social isolation can lead to pervasive health issues like anxiety and loneliness. Previous work focused on physical interventions like exercise and teleconferencing, but overlooked the narrative potential of adaptive strategies. To address this, we designed a collaborative online storytelling experience in social VR, enabling participants in isolation to design an imaginary space journey as a metaphor for quarantine, in order to learn about their isolation adaptation strategies in the process. Eighteen individuals participated during real quarantine undertaken a virtual role-play experience, designing their own spaceship rooms and engaging in collaborative activities that revealed creative adaptative strategies. Qualitative analyses of participant designs, transcripts, and interactions revealed how they coped with isolation, and how the engagement unexpectedly influenced their adaptation process. This study shows how designing playful narrative experiences, rather than solution-driven approaches, can serve as probes to surface how people navigate social isolation.

cs.HC↗

arXiv2025

HiPreNets: High-Precision Neural Networks through Progressive Training

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to hyperparameters make consistent performance improvement difficult, and traditional approaches prioritize minimizing mean squared error while overlooking the $L^{\infty}$ norm error that is critical in safety-sensitive applications. To address these challenges, we present HiPreNets, a progressive framework for training high-precision neural networks through sequential residual refinements. Starting from an initial network, each stage trains a refinement network on the normalized residuals of the ensemble so far, systematically reducing both average and worst-case error. A key theme throughout the framework is concentrating training effort on high-error regions of the input domain, which we pursue through complementary techniques including loss function design, adaptive data sampling, localized patching, and boundary-aware training. We validate the framework on benchmark regression problems from the Feynman dataset, where it consistently outperforms standard fully connected networks and reported Kolmogorov-Arnold Networks results, with accuracy approaching machine precision depending on select problems. We further apply the framework to learning the flow map of a 20-dimensional power system ODE, which appears to be the highest dimensional problem studied using this class of multistage methods, achieving substantial reductions in both RMSE and $L^{\infty}$ norm error while enabling a surrogate that predicts system state $238\times$ faster than direct numerical simulation.

cs.LG↗

arXiv2022

Neural Network Optimal Feedback Control with Guaranteed Local Stability

Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well understood. In particular, some neural networks with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel neural network architectures, which we show guarantee local asymptotic stability while retaining the approximation capacity to learn the optimal feedback policy semi-globally. The proposed architectures are compared against standard neural network feedback controllers through numerical simulations of two high-dimensional nonlinear optimal control problems: stabilization of an unstable Burgers-type partial differential equation, and altitude and course tracking for an unmanned aerial vehicle. The simulations demonstrate that standard neural networks can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stabilizing and can achieve near-optimal performance.

math.OC↗

arXiv2022

An Actor Critic Method for Free Terminal Time Optimal Control

Optimal control problems with free terminal time present many challenges including nonsmooth and discontinuous control laws, irregular value functions, many local optima, and the curse of dimensionality. To overcome these issues, we propose an adaptation of the model-based actor-critic paradigm from the field of Reinforcement Learning via an exponential transformation to learn an approximate feedback control and value function pair. We demonstrate the algorithm's effectiveness on prototypical examples featuring each of the main pathological issues present in problems of this type.

math.OC↗

arXiv2021

Neural network optimal feedback control with enhanced closed loop stability

Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In this paper we use numerical simulations to demonstrate that typical test accuracy metrics do not effectively capture the ability of an NN controller to stabilize a system. In particular, some NNs with high test accuracy can fail to stabilize the dynamics. To address this we propose two NN architectures which locally approximate a linear quadratic regulator (LQR). Numerical simulations confirm our intuition that the proposed architectures reliably produce stabilizing feedback controllers without sacrificing optimality. In addition, we introduce a preliminary theoretical result describing some stability properties of such NN-controlled systems.

math.OC↗

arXiv2021

Defense Against Adversarial Swarms with Parameter Uncertainty

This paper addresses the problem of optimal defense of a High Value Unit against a large-scale swarm attack. We show that the problem can be cast in the framework of uncertain parameter optimal control and derive a consistency result for the dual problem of this framework. We show that the dual can be computed numerically and apply these numerical results to derive optimal defender strategies against a 100 agent swarm attack.

math.OC↗

arXiv2021

Modeling and Control of Large-Scale Adversarial Swarm Engagements

We theoretically and numerically study the problem of optimal control of large-scale autonomous systems under explicitly adversarial conditions, including probabilistic destruction of agents during the simulation. Large-scale autonomous systems often include an adversarial component, where different agents or groups of agents explicitly compete with one another. An important component of these systems that is not included in current theory or modeling frameworks is random destruction of agents in time. In this case, the modeling and optimal control framework should consider the attrition of agents as well as their position. We propose and test three numerical modeling schemes, where survival probabilities of all agents are smoothly and continuously decreased in time, based on the relative positions of all agents during the simulation. In particular, we apply these schemes to the case of agents defending a high-value unit from an attacking swarm. We show that these models can be successfully used to model this situation, provided that attrition and spatial dynamics are coupled. Our results have relevance to an entire class of adversarial autonomy situations, where the positions of agents and their survival probabilities are both important.

math.OC↗

arXiv2021

Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional problems often rely on specific, restrictive problem structures, or are valid only locally around some nominal trajectory. In this paper, we propose a data-driven method to approximate semi-global solutions to HJB equations for general high-dimensional nonlinear systems and compute candidate optimal feedback controls in real-time. To accomplish this, we model solutions to HJB equations with neural networks (NNs) trained on data generated without discretizing the state space. Training is made more effective and data-efficient by leveraging the known physics of the problem and using the partially-trained NN to aid in adaptive data generation. We demonstrate the effectiveness of our method by learning solutions to HJB equations corresponding to the attitude control of a six-dimensional nonlinear rigid body, and nonlinear systems of dimension up to 30 arising from the stabilization of a Burgers'-type partial differential equation. The trained NNs are then used for real-time feedback control of these systems.

math.OC↗

arXiv2020

Neural Network Approximations of Compositional Functions With Applications to Dynamical Systems

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many published results in recent years. Towards the goal of revealing the underlying reason why neural networks are capable of solving some high dimensional problems, we develop an algebraic framework and an approximation theory for compositional functions and their neural network approximations. The theoretical foundation is developed in a way so that it supports the error analysis for not only functions as input-output relations, but also numerical algorithms. This capability is critical because it enables the analysis of approximation errors for problems for which analytic solutions are not available, such as differential equations and optimal control. We identify a set of key features of compositional functions and the relationship between the features and the complexity of neural networks. In addition to function approximations, we prove several formulae of error upper bounds for neural networks that approximate the solutions to differential equations, optimization, and optimal control.

cs.LG↗

arXiv2020

QRnet: optimal regulator design with LQR-augmented neural networks

In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman equations arising in optimal feedback control. Concretely, we augment linear quadratic regulators with neural networks to handle nonlinearities. We train the augmented models on data generated without discretizing the state space, enabling application to high-dimensional problems. We use the proposed method to design a candidate optimal regulator for an unstable Burgers' equation, and through this example, demonstrate improved robustness and accuracy compared to existing neural network formulations.

math.OC↗

arXiv2020

Algorithms of Data Development For Deep Learning and Feedback Design

Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton-Jacobi-Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time applications of optimal control. A critical part of this design method is to generate data for training the neural network and validating its accuracy. In this paper, we provide a survey of existing algorithms that can be used to generate data. All the algorithms surveyed in this paper are causality-free, i.e., the solution at a point is computed without using the value of the function at any other points. At the end of the paper, an illustrative example of optimal feedback design using deep learning is given.

math.DS↗

arXiv2019

Density Propagation with Characteristics-based Deep Learning

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few uncertain variables or require large amounts of simulation data. In this paper, we propose a data-driven method for approximating joint probability density functions (PDFs) of nonlinear dynamic systems with initial condition and parameter uncertainty. Our approach leverages on the power of deep learning to deal with high-dimensional inputs, but we overcome the need for huge quantities of training data by encoding PDF evolution equations directly into the optimization problem. We demonstrate the potential of the proposed method by applying it to evaluate the robustness of a feedback controller for a six-dimensional rigid body with parameter uncertainty.

math.DS↗

arXiv2019

A new scalable algorithm for computational optimal control under uncertainty

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random parameters or processes. The objective is to provide a validated new computational capability for optimal control which will be achieved more efficiently than current state-of-the-art methods. The new framework utilizes direct single or multi-shooting discretization, and is based on efficient vectorized gradient computation with adaptable memory management. The algorithm is demonstrated to be scalable to high-dimensional nonlinear control systems with random initial condition and unknown parameters.

math.NA↗

arXiv2018

A Pseudospectral Approach to High Index DAE Optimal Control Problems

Historically, solving optimal control problems with high index differential algebraic equations (DAEs) has been considered extremely hard. Computational experience with Runge-Kutta (RK) methods confirms the difficulties. High index DAE problems occur quite naturally in many practical engineering applications. Over the last two decades, a vast number of real-world problems have been solved routinely using pseudospectral (PS) optimal control techniques. In view of this, we solve a "provably hard," index-three problem using the PS method implemented in DIDO, a state-of-the-art MATLAB optimal control toolbox. In contrast to RK-type solution techniques, no laborious index-reduction process was used to generate the PS solution. The PS solution is independently verified and validated using standard industry practices. It turns out that proper PS methods can indeed be used to "directly" solve high index DAE optimal control problems. In view of this, it is proposed that a new theory of difficulty for DAEs be put forth.

math.OC↗

arXiv2016

A Stochastic Model of Order Book Dynamics using Bouncing Geometric Brownian Motions

We consider a limit order book, where buyers and sellers register to trade a security at specific prices. The largest price buyers on the book are willing to offer is called the market bid price, and the smallest price sellers on the book are willing to accept is called the market ask price. Market ask price is always greater than market bid price, and these prices move upwards and downwards due to new arrivals, market trades, and cancellations. We model these two price processes as "bouncing geometric Brownian motions (GBMs)", which are defined as exponentials of two mutually reflected Brownian motions. We then modify these bouncing GBMs to construct a discrete time stochastic process of trading times and trading prices, which is parameterized by a positive parameter $δ$. Under this model, it is shown that the inter-trading times are inverse Gaussian distributed, and the logarithmic returns between consecutive trading times follow a normal inverse Gaussian distribution. Our main results show that the logarithmic trading price process is a renewal reward process, and under a suitable scaling, this process converges to a standard Brownian motion as $δ\to 0$. We also prove that the modified ask and bid processes approach the original bouncing GBMs as $δ\to0$. Finally, we derive a simple and effective prediction formula for trading prices, and illustrate the effectiveness of the prediction formula with an example using real stock price data.

q-fin.TR↗

arXiv2014

Diffusion Models for Double-ended Queues with Renewal Arrival Processes

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits.

math.PR↗