arXiv subjects

Wanjiku A. Makumi

Publications and source records attributed to Wanjiku A. Makumi.

6 recordsLinked to original sources

arXiv2026

Simultaneous Online System Identification and Control using Composite Adaptive Lyapunov-Based Deep Neural Networks

Although deep neural network (DNN)-based controllers are popularly used to control uncertain nonlinear dynamic systems, most results use DNNs that are pretrained offline and the corresponding controller is implemented post-training. Recent advancements in adaptive control have developed controllers with Lyapunov-based update laws (i.e., control and update laws derived from a Lyapunov-based stability analysis) for updating the DNN weights online to ensure the system states track a desired trajectory. However, the update laws are based on the tracking error, and offer guarantees on only the tracking error convergence, without providing any guarantees on system identification. This paper provides the first result on simultaneous online system identification and trajectory tracking control of nonlinear systems using adaptive updates for all layers of the DNN. A combined Lyapunov-based stability analysis is provided, which guarantees that the tracking error, state-derivative estimation error, and DNN weight estimation errors are uniformly ultimately bounded. Under the persistence of excitation (PE) condition, the tracking and weight estimation errors are shown to exponentially converge to a neighborhood of the origin, where the rate of convergence and the size of this neighborhood depends on the gains and a factor quantifying PE, thus achieving system identification and enhanced trajectory tracking performance. As an outcome of the system identification, the DNN model can be propagated forward to predict and compensate for the uncertainty in dynamics under intermittent loss of state feedback. Comparative simulation results are provided on a two-link manipulator system and an unmanned underwater vehicle system with intermittent loss of state feedback, where the developed method yields significant performance improvement compared to baseline methods.

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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

Lyapunov-Based Physics-Informed Deep Neural Networks with Skew Symmetry Considerations

Deep neural networks (DNNs) are powerful black-box function approximators which have been shown to yield improved performance compared to traditional neural network (NN) architectures. However, black-box algorithms do not incorporate known physics of the system and can yield results which are physically implausible. Physics-informed neural networks (PINNs) have grown in popularity due to their ability to leverage known physical principles in the learning process which has been empirically shown to improve performance compared to traditional black-box methods. This paper introduces the first physics-informed DNN controller for an Euler-Lagrange dynamic system where the adaptation laws are designed using a Lyapunov-based stability analysis to account for the skew-symmetry property of the inertia matrix and centripetal-Coriolis matrix. A Lyapunov-based stability analysis is provided to guarantee asymptotic convergence of the tracking error and the skew-symmetric prediction error. Simulations indicate that the developed update law demonstrates improvement in individual and overall function approximation capabilities when compared to a physics-informed adaptation law which does not incorporate knowledge of system symmetries.

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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

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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