arXiv subjects

Patrick McNamee

Publications and source records attributed to Patrick McNamee.

10 recordsLinked to original sources

arXiv2026

Lyapunov Constructions for System Interconnections Arising from Adaptation in Some Optimization Methods

Interconnected systems have been widely studied, with a focus on interconnected systems whose subsystems are solely input-to-state stable (ISS) or passive systems. The focus of this work is on the interconnected systems that appear in adaptive gradient methods. In adaptive gradient methods, one subsystem seeks to move parameters of a cost function towards a minimizer while the other subsystem works to estimate some derivative information about the cost function to help determine the direction of the parameter update. This work studies instances of such interconnected systems and gives various Lyapunov function constructions for them using different techniques. In doing so, adaptive gradient optimizers are proven to be globally asymptotically stable (GAS), and the methods for constructing the Lyapunov functions that certify this are presented.

math.OC↗

arXiv2026

Logarithmic Barrier Functions for Practically Safe Extremum Seeking Control

This paper presents a methodology for Practically Safe Extremum Seeking (PSfES), designed to optimize unknown objective functions while strictly enforcing safety constraints via a Logarithmic Barrier Function (LBF). Unlike traditional safety-filtered approaches that may induce chattering, the proposed method augments the cost function with an LBF, creating a repulsive potential that penalizes proximity to the safety boundary. We employ averaging theory to analyze the closed-loop dynamics. A key contribution of this work is the rigorous proof of practical safety for the original system. We establish that the system trajectories remain confined within a safety margin, ensuring forward invariance of the safe set for a sufficiently fast dither signal. Furthermore, our stability analysis shows that the model-free ESC achieves local practical convergence to the modified minimizer strictly within the safe set, through the sequential tuning of small parameters. The theoretical results are validated through numerical simulations.

eess.SY↗

arXiv2025

Servos for Local Map Exploration Onboard Nonholonomic Vehicles for Extremum Seeking

Extremum seeking control (ESC) often employs perturbation-based estimates of derivatives for some sensor field or cost function. These estimates are generally obtained by simply multiplying the output of a single-unit sensor by some time-varying function. Previous work has focused on sinusoidal perturbations to generate derivative estimates with results for arbitrary order derivatives of scalar maps or higher up to third-order derivatives of multivariable maps. This work extends the perturbations from sinusoidal to bounded periodic or almost periodic functions and considers multivariable maps. A necessary and sufficient condition is given for determining if time-varying functions exist for estimating arbitrary order derivatives of multivariable maps for any given bounded periodic or almost periodic dither signal. These results are then used in a source seeking controller for a nonholonomic vehicle with a sensor actuated by servo. The conducted simulation and real-world experiments demonstrate that by distributing the local map exploration to a servo, the nonholonomic vehicle was able to achieve a faster convergence to the source.

eess.SY↗

arXiv2025

Stabilization of Age-Structured Competing Populations

Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography. While coupled age-structured IPDEs modeling two or more interacting species occur naturally in epidemiology and ecology, they remain relatively underexplored. Prior work has primarily addressed stable and marginally stable dynamics. In constrast, this work considers an exponentially unstable model of two competing predator populations, formally referred to in the literature as ``competition'' dynamics. If one were to apply an input that simultaneously harvests both predator species, one would have control over only the product of the densities of the species, not over their ratio. Therefore, it is necessary to design a control input that directly harvests only one of the two predator species, while indirectly influencing the other via a backstepping approach. The model is transformed into a system of two coupled ordinary differential equations (ODEs), of which only one is actuated, and two autonomous, exponentially stable integral delay equations (IDEs) which enter the ODEs as nonlinear disturbances. The ODEs are globally stabilized with backstepping and an estimate of the region of attraction of the asymptotically stabilized equilibrium of the full IPDE system is provided, under a positivity restriction on control. Additionally, the full IPDE system is also shown to be local exponential stable. Such generalizations of competition dynamics open exciting possibilities for future research directions for systems with more than two species.

eess.SY↗

arXiv2025

Extremum Seeking (ES) is Practically Stable Whenever Model-Based ES is Stable

Extremum seeking control (ESC) are optimization algorithms in continuous time, with model-based ESCs using true derivative information of the cost function and model-free ESCs utilizing perturbation-based estimates instead. Stability analysis of model-free ESCs often employs the associated average system, whose stability is dependent on the selection of the dither signal. We demonstrate first the challenge of this analysis approach by showing selections of relative dither amplitudes and rates at different ESC inputs which result in the average system always having an unstable equilibrium. Then we go on to show that, if the model-based ESC is globally asymptotically stable (GAS), then the average system is semiglobally practically asymptotically stable (sGPAS), and the model-free ESC is semiglobally practically uniformly asymptotically stable (sGPUAS). Thus, we free the system analyst from analyzing the stability of the average system with various dither signals, as it is sufficient to analyze the stability of the model-based ESC. The result for the original model-free ESC also provides a guideline for the user for how to select the dither amplitudes to ensure sGPUAS.

math.OC↗

arXiv2024

Adaptive Extremum Seeking Control via the RMSprop Optimizer

Extremum Seeking Control (ESC) is a well-known set of continuous time algorithms for model-free optimization of a cost function. One issue for ESCs is the convergence rates of parameters to extrema of unknown cost functions. The local convergence rate depends on the second, or sometimes higher, order derivatives of the unknown cost function. To mitigate this dependency, we propose the use of the RMSprop optimizer for ESCs as RMSprop is an adaptive gradient-based optimizer which attempts to have a normalized convergence rate in all parameters. Practical stability results are given for this RMSprop ESC (RMSpESC). In particular notability, the proof of practical stability uses Lyapunov function based on observed contracting, attractive sets. Versions of this Lyapunov function could be applied to other areas of applications, in particular for interconnected systems.

math.OC↗

arXiv2024

Extremum Seeking is Stable for Scalar Maps that are Strictly but Not Strongly Convex

For a map that is strictly but not strongly convex, model-based gradient extremum seeking has an eigenvalue of zero at the extremum, i.e., it fails at exponential convergence. Interestingly, perturbation-based model-free extremum seeking has a negative Jacobian, in the average, meaning that its (practical) convergence is exponential, even though the map's Hessian is zero at the extremum. While these observations for the gradient algorithm are not trivial, we focus in this paper on an even more nontrivial study of the same phenomenon for Newton-based extremum seeking control (NESC). NESC is a second-order method which corrects for the unknown Hessian of the unknown map, not only in order to speed up parameter convergence, but also (1) to make the convergence rate user-assignable in spite of the unknown Hessian, and (2) to equalize the convergence rates in different directions for multivariable maps. Previous NESC work established stability only for maps whose Hessians are strictly positive definite everywhere, so the Hessian is invertible everywhere. For a scalar map, we establish the rather unexpected property that, even when the map behind is strictly convex but not strongly convex, i.e., when the Hessian may be zero, NESC guarantees practical asymptotic stability, semiglobally. While a model-based Newton-based algorithm would run into non-invertibility of the Hessian, the perturbation-based NESC, surprisingly, avoids this challenge by leveraging the fact that the average of the perturbation-based Hessian estimate is always positive, even though the actual Hessian may be zero.

math.OC↗

arXiv2023

Feature Aggregation in Joint Sound Classification and Localization Neural Networks

This study addresses the application of deep learning techniques in joint sound signal classification and localization networks. Current state-of-the-art sound source localization deep learning networks lack feature aggregation within their architecture. Feature aggregation enhances model performance by enabling the consolidation of information from different feature scales, thereby improving feature robustness and invariance. This is particularly important in SSL networks, which must differentiate direct and indirect acoustic signals. To address this gap, we adapt feature aggregation techniques from computer vision neural networks to signal detection neural networks. Additionally, we propose the Scale Encoding Network (SEN) for feature aggregation to encode features from various scales, compressing the network for more computationally efficient aggregation. To evaluate the efficacy of feature aggregation in SSL networks, we integrated the following computer vision feature aggregation sub-architectures into a SSL control architecture: Path Aggregation Network (PANet), Weighted Bi-directional Feature Pyramid Network (BiFPN), and SEN. These sub-architectures were evaluated using two metrics for signal classification and two metrics for direction-of-arrival regression. PANet and BiFPN are established aggregators in computer vision models, while the proposed SEN is a more compact aggregator. The results suggest that models incorporating feature aggregations outperformed the control model, the Sound Event Localization and Detection network (SELDnet), in both sound signal classification and localization. The feature aggregation techniques enhance the performance of sound detection neural networks, particularly in direction-of-arrival regression.

cs.SD↗

arXiv2023

Autonomous search of real-life environments combining dynamical system-based path planning and unsupervised learning

In recent years, advancements have been made towards the goal of using chaotic coverage path planners for autonomous search and traversal of spaces with limited environmental cues. However, the state of this field is still in its infancy as there has been little experimental work done. The existing experimental works have not developed robust methods to satisfactorily address the immediate set of problems a chaotic coverage path planner needs to overcome in order to scan realistic environments within reasonable coverage times. These immediate problems are as follows: (1) an obstacle avoidance technique that reduces halts or disruptions in continuous chaotic trajectories, (2) a means to spread chaotic trajectories across the environment (especially crucial for large and/or complex-shaped environments) that need to be covered, and (3) a real-time coverage calculation technique that is accurate and independent of cell size. This study addresses these problems by developing a novel applied framework for real-world applications of chaotic coverage path planners while providing techniques for effective obstacle avoidance, chaotic trajectory dispersal, and accurate real-time coverage calculation. These algorithms were created within the ROS framework and make up a newly developed chaotic path planning application. The performance of this application was comparable to that of a conventional optimal path planner. The performance tests were carried out in environments of various sizes, shapes, and obstacle densities, both in real-life and Gazebo simulations.

cs.RO↗

arXiv2021

Online search of unknown terrains using a dynamical system-based path planning approach

Surveillance and exploration of large environments is a tedious task. In spaces with limited environmental cues, random-like search is an effective approach as it allows the robot to perform online coverage of environments using simple algorithm designs. One way to generate random-like scanning search is to use nonlinear dynamical systems to impart chaos into the searching robot's controller. This will result in the generation of unpredictable yet deterministic trajectories, allowing designers to control the system and achieve a high scanning coverage of an area. However, the unpredictability comes at the cost of increased coverage time and a lack of scalability, both of which have been ignored by the state-of-the-art chaotic path planners. This work introduces a new, scalable technique that helps a robot to steer away from the obstacles and cover the entire search space in a short period of time. The technique involves coupling and manipulating two chaotic systems to reduce the coverage time and enable scanning of unknown environments with different online properties. Using this new technique resulted in an average 49% boost in the robot's performance compared to the state-of-the-art planners. the overall search performance of the chaotic planner remained comparable to optimal systems while still ensuring unpredictable paths.

cs.RO↗