arXiv subjects

Zachary I. Bell

Publications and source records attributed to Zachary I. Bell.

At least 19 recordsLinked to original sources

arXiv2026

Safe Output-Feedback Adaptive Optimal Control of Input-Constrained Control-Affine Nonlinear Systems

In this paper, a novel online, safe output-feedback, critic-only, adaptive optimal control framework is developed for safety-critical control of partially observable systems. The developed framework ensures system stability and safety, regardless of the lack of full-state measurements, while learning and implementing a near-optimal controller. The approach leverages linear matrix inequality-based observer design methods to efficiently search for observer gains for effective state estimation. Then, approximate dynamic programming is used to develop an approximate controller that uses simulated experiences to guarantee the safety and stability of the closed-loop system. Safety is enforced by adding a recentered robust Lyapunov-like barrier function to the cost function that effectively enforces safety constraints, even in the presence of state estimation errors. Lyapunov-based stability analysis is used to guarantee uniform ultimate boundedness of the trajectories of the closed-loop system and ensure safety. Simulation studies are performed to demonstrate the effectiveness of the developed method through two real-world safety-critical scenarios, specifically one ensuring that the state trajectories of a given system remain within a given set, and the other ensuring that the system avoids an obstacle.

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arXiv2025

A Switched Systems Approach to Image-Based Feature Tracking for Autonomous Satellite Inspection

This paper presents an information-based guidance and control architecture for an autonomous deputy spacecraft tasked with inspecting a chief satellite in orbit. The primary objective is for the deputy spacecraft to maximize information gain while tracking features on the chief satellite. The deputy spacecraft needs to respect various constraints such as illumination, field-of-view (FOV), fuel limitations, and avoidance regions. Additionally, the absence of GPS information poses a significant challenge for relative localization within the space environment. To learn the structure of the chief satellite while achieving relative self-localization and maximizing the information gain, this paper integrates a memory regression extension (MRE)-based distance observer with an information-maximizing adaptive controller. The distance observer utilizes feedback from a camera. A switched systems approach is used to determine the minimum dwell time required for a feature to remain within the FOV of the camera to ensure accurate estimation. A k-means clustering algorithm acts as a high-level planner to intermittently generate goal locations that guide the deputy spacecraft toward the nearest cluster of uninspected points on the chief satellite, subject to illumination and FOV constraints. A Lyapunov-based stability analysis is conducted to analyze the developed architecture, and simulation results validate the theoretical results of the paper.

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arXiv2025

Safe Output-Feedback Adaptive Optimal Control of Affine Nonlinear Systems

In this paper, we develop a safe control synthesis method that integrates state estimation and parameter estimation within an adaptive optimal control (AOC) and control barrier function (CBF)-based control architecture. The developed approach decouples safety objectives from the learning objectives using a CBF-based guarding controller where the CBFs are robustified to account for the lack of full-state measurements. The coupling of this guarding controller with the AOC-based stabilizing control guarantees safety and regulation despite the lack of full state measurement. The paper leverages recent advancements in deep neural network-based adaptive observers to ensure safety in the presence of state estimation errors. Safety and convergence guarantees are provided using a Lyapunov-based analysis, and the effectiveness of the developed controller is demonstrated through simulation under mild excitation conditions.

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arXiv2025

A Taylor Series Approach to Correction of Input Errors in Gaussian Process Regression

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject to zero-mean noise. However, several real-world applications such as mobile sensors have imperfect localization, leading to inputs with biased errors. These biases can typically be estimated through measurements collected over time using, for example, Kalman filters. To avoid recomputation of the entire GP model when better estimates of the inputs used in the training data become available, we introduce a technique for updating a trained GP model to incorporate updated estimates of the inputs. By leveraging the differentiability of the mean and covariance functions derived from the squared exponential kernel, a second-order correction algorithm is developed to update the trained GP models. Precomputed Jacobians and Hessians of kernels enable real-time refinement of the mean and covariance predictions. The efficacy of the developed approach is demonstrated using two simulation studies, with error analyses revealing improvements in both predictive accuracy and uncertainty quantification.

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arXiv2025

Distributed Asynchronous Time-Varying Quadratic Programming with Asynchronous Objective Sampling

Existing works on multi-agent time-varying optimization allow agents to asynchronously communicate and/or compute, but do not allow asynchronous sampling of objectives. Sampling can be difficult to synchronize, and we therefore present a multi-agent optimization framework that allows asynchrony in sampling, communications, and computations for time-varying quadratic programs. We show that agents have bounded error when tracking the solution to the asynchronously sampled problem, which solves an open problem for quadratic programs. Simulations validate these results.

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arXiv2025

System Identification and Control Using Lyapunov-Based Deep Neural Networks without Persistent Excitation: A Concurrent Learning Approach

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the challenge of identifying the system dynamics using the DNN. This paper presents the first result on simultaneous trajectory tracking and online system identification using a DNN-based controller, without requiring persistent excitation. Two new concurrent learning adaptation laws are constructed for the weights of all the layers of the DNN, achieving convergence of the DNN's parameter estimates to a neighborhood of their ideal values, provided the DNN's Jacobian satisfies a finite-time excitation condition. A Lyapunov-based stability analysis is conducted to ensure convergence of the tracking error, weight estimation errors, and observer errors to a neighborhood of the origin. Simulations performed on a range of systems and trajectories, with the same initial and operating conditions, demonstrated 40.5% to 73.6% improvement in function approximation performance compared to the baseline, while maintaining a similar tracking error and control effort. Simulations evaluating function approximation capabilities on data points outside of the trajectory resulted in 58.88% and 74.75% improvement in function approximation compared to the baseline.

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arXiv2025

Improved Dwell-times for Switched Nonlinear Systems using Memory Regression Extension

This paper presents a switched systems approach for extending the dwell-time of an autonomous agent during GPS-denied operation by leveraging memory regressor extension (MRE) techniques. To maintain accurate trajectory tracking despite unknown dynamics and environmental disturbances, the agent periodically acquires access to GPS, allowing it to correct accumulated state estimation errors. The motivation for this work arises from the limitations of existing switched system approaches, where increasing estimation errors during GPS-denied intervals and overly conservative dwell-time conditions restrict the operational efficiency of the agent. By leveraging MRE techniques during GPS-available intervals, the developed method refines the estimates of unknown system parameters, thereby enabling longer and more reliable operation in GPS-denied environments. A Lyapunov-based switched-system stability analysis establishes that improved parameter estimates obtained through concurrent learning allow extended operation in GPS-denied intervals without compromising closed-loop system stability. Simulation results validate the theoretical findings, demonstrating dwell-time extensions and enhanced trajectory tracking performance.

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arXiv2025

Uncertainty-Aware Guidance for Target Tracking subject to Intermittent Measurements using Motion Model Learning

This paper presents a novel guidance law for target tracking applications where the target motion model is unknown and sensor measurements are intermittent due to unknown environmental conditions and low measurement update rate. In this work, the target motion model is represented by a transformer neural network and trained by previous target position measurements. This transformer motion model serves as the prediction step in a particle filter for target state estimation and uncertainty quantification. The particle filter estimation uncertainty is utilized in the information-driven guidance law to compute a path for the mobile agent to travel to a position with maximum expected entropy reduction (EER). The computation of EER is performed in real-time by approximating the information gain from the predicted particle distributions relative to the current distribution. Simulation and hardware experiments are performed with a quadcopter agent and TurtleBot target to demonstrate that the presented guidance law outperforms two other baseline guidance methods.

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arXiv2025

Lyapunov-Based Graph Neural Networks for Adaptive Control of Multi-Agent Systems

Graph neural networks (GNNs) have a message-passing framework in which vector messages are exchanged between graph nodes and updated using feedforward layers. The inclusion of distributed message-passing in the GNN architecture makes them ideally suited for distributed control and coordination tasks. Existing results develop GNN-based controllers to address a variety of multi-agent control problems while compensating for modeling uncertainties in the systems. However, these results use GNNs that are pre-trained offline. This paper provides the first result on GNNs with stability-driven online weight updates to address the multi-agent target tracking problem. Specifically, new Lyapunov-based distributed GNN and graph attention network (GAT)-based controllers are developed to adaptively estimate unknown target dynamics and address the second-order target tracking problem. A Lyapunov-based stability analysis is provided to guarantee exponential convergence of the target state estimates and agent states to a neighborhood of the target state. Numerical simulations show a 20.8% and 48.1% position tracking error performance improvement by the GNN and GAT architectures over a baseline DNN architecture, respectively.

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arXiv2025

Gaussian Process-Based Scalar Field Estimation in GPS-Denied Environments

This paper presents a methodology for an autonomous agent to map an unknown scalar field in GPS-denied regions. To reduce localization errors, the agent alternates between GPS-enabled and GPS-denied areas while collecting measurements. User-defined error bounds determine the dwell time in each region. A switching trajectory is then designed to ensure field measurements in GPS-denied regions remain within the specified error limits. A Lyapunov-based stability analysis guarantees bounded error trajectories while tracking the desired path. The effectiveness of the proposed methodology is demonstrated through simulations, with an error analysis comparing the GP-predicted scalar field model to the actual field.

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arXiv2025

The Safe Trusted Autonomy for Responsible Space Program

The Safe Trusted Autonomy for Responsible Space (STARS) program aims to advance autonomy technologies for space by leveraging machine learning technologies while mitigating barriers to trust, such as uncertainty, opaqueness, brittleness, and inflexibility. This paper presents the achievements and lessons learned from the STARS program in integrating reinforcement learning-based multi-satellite control, run time assurance approaches, and flexible human-autonomy teaming interfaces, into a new integrated testing environment for collaborative autonomous satellite systems. The primary results describe analysis of the reinforcement learning multi-satellite control and run time assurance algorithms. These algorithms are integrated into a prototype human-autonomy interface using best practices from human-autonomy trust literature, however detailed analysis of the effectiveness is left to future work. References are provided with additional detailed results of individual experiments.

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arXiv2024

Heterogeneous Roles against Assignment Based Policies in Two vs Two Target Defense Game

In this paper, we consider a target defense game in which the attacker team seeks to reach a high-value target while the defender team seeks to prevent that by capturing them away from the target. To address the curse of dimensionality, a popular approach to solve such team-vs-team game is to decompose it into a set of one-vs-one games. Such an approximation assumes independence between teammates assigned to different one-vs-one games, ignoring the possibility of a richer set of cooperative behaviors, ultimately leading to suboptimality. In this paper, we provide teammate-aware strategies for the attacker team and show that they can outperform the assignment-based strategy, if the defenders still employ an assignment-based strategy. More specifically, the attacker strategy involves heterogeneous roles where one attacker actively intercepts a defender to help its teammate reach the target. We provide sufficient conditions under which such a strategy benefits the attackers, and we validate the results using numerical simulations.

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arXiv2024

Scalar Field Mapping with Adaptive High-Intensity Region Avoidance

This research is motivated by a scenario where a group of UAVs is assigned to map an unknown scalar field, with the imperative of maintaining a safe distance from the sources of the field to evade detection or damage. The location of the sources is unknown a priori, so the UAVs rely on measurements of the field intensity to gauge safety. The UAVs estimate the unknown scalar field using Gaussian process (GP) regression and use the estimate to generate a map of high-intensity regions using Hough transform (HT), updated online based on the field measurements. A convergence analysis shows the boundedness of the error between the actual scalar field and the learned scalar field. The effectiveness of the method is evaluated through simulations, showcasing its ability to accurately learn scalar fields with multiple high-intensity regions while reducing the number of measurements taken inside the high-intensity regions.

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arXiv2024

Network Preference Dynamics using Lattice Theory

Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information about other agents. Exploiting the ordered algebraic structure of preferences, we introduce a message-passing algorithm for heterogeneous agents distributed over a network to update their preferences based on aggregations of the preferences of their neighbors in a graph. We demonstrate the existence of equilibrium points of the resulting global dynamical system of local preference updates and provide a sufficient condition for trajectories to converge to equilibria: stable preferences. Finally, we present numerical simulations demonstrating our preliminary results.

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arXiv2024

An adaptive optimal control approach to monocular depth observability maximization

This paper presents an integral concurrent learning (ICL)-based observer for a monocular camera to accurately estimate the Euclidean distance to features on a stationary object, under the restriction that state information is unavailable. Using distance estimates, an infinite horizon optimal regulation problem is solved, which aims to regulate the camera to a goal location while maximizing feature observability. Lyapunov-based stability analysis is used to guarantee exponential convergence of depth estimates and input-to-state stability of the goal location relative to the camera. The effectiveness of the proposed approach is verified in simulation, and a table illustrating improved observability is provided.

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arXiv2024

Defending a Static Target Point with a Slow Defender

This paper studies a target-defense game played between a slow defender and a fast attacker. The attacker wins the game if it reaches the target while avoiding the defender's capture disk. The defender wins the game by preventing the attacker from reaching the target, which includes reaching the target and containing it in the capture disk. Depending on the initial condition, the attacker must circumnavigate the defender's capture disk, resulting in a constrained trajectory. This condition produces three phases of the game, which we analyze to solve for the game of kind. We provide the barrier surface that divides the state space into attacker-win and defender win regions, and present the corresponding strategies that guarantee win for each region. Numerical experiments demonstrate the theoretical results as well as the efficacy of the proposed strategies.

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arXiv2023

Distributed Asynchronous Discrete-Time Feedback Optimization

In this article, we present an algorithm that drives the outputs of a network of agents to jointly track the solutions of time-varying optimization problems in a way that is robust to asynchrony in the agents' operations. We consider three operations that can be asynchronous: (1) computations of control inputs, (2) measurements of network outputs, and (3) communications of agents' inputs and outputs. We first show that our algorithm converges to the solution of a time-invariant feedback optimization problem in linear time. Next, we show that our algorithm drives outputs to track the solution of time-varying feedback optimization problems within a bounded error dependent upon the movement of the minimizers and degree of asynchrony in a way that we make precise. These convergence results are extended to quantify agents' asymptotic behavior as the length of their time horizon approaches infinity. Then, to ensure satisfactory network performance, we specify the timing of agents' operations relative to changes in the objective function that ensure a desired error bound. Numerical experiments confirm these developments and show the success of our distributed feedback optimization algorithm under asynchrony.

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arXiv2023

Deep Nonlinear Adaptive Control for Unmanned Aerial Systems Operating under Dynamic Uncertainties

Recent literature in the field of machine learning (ML) control has shown promising theoretical results for a Deep Neural Network (DNN) based Nonlinear Adaptive Controller (DNAC) capable of achieving trajectory tracking for nonlinear systems. Expanding on this work, this paper applies DNAC to the Attitude Control System (ACS) of a quadrotor and shows improvement to attitude control performance under disturbed flying conditions where the model uncertainty is high. Moreover, these results are noteworthy for ML control because they were achieved with no prior training data and an arbitrary system dynamics initialization; simply put, the controller presented in this paper is practically modelless, yet yields the ability to force trajectory tracking for nonlinear systems while rejecting significant undesirable model disturbances learned through a DNN. The combination of ML techniques to learn a system's dynamics and the Lyapunov analysis required to provide stability guarantees leads to a controller with applications in safety-critical systems that may undergo uncertain model changes, as is the case for most aerial systems. Experimental findings are analyzed in the final section of this paper, and DNAC is shown to outperform the trajectory tracking capabilities of PID, MRAC, and the recently developed Deep Model Reference Adaptive Control (DMRAC) schemes.

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