arXiv subjects

Omkar Sudhir Patil

Publications and source records attributed to Omkar Sudhir Patil.

18 recordsLinked to original sources

arXiv2026

Adaptive Control as an Information Gradient Flow: Excitation, Constraints, Energy, and Stochastic Learning

Adaptive control is usually developed through Lyapunov stability, excitation, and parameter convergence, whereas neighboring fields describe learning using convexity, information geometry, variational principles, and stochastic thermodynamics. This paper develops a constrained common language for these viewpoints. For linearly parameterized models, the excitation Gramian is simultaneously the Hessian of accumulated prediction loss and, under Gaussian observations, Fisher information up to scaling. Persistent, finite, and partial excitation become uniform, finite-horizon, and restricted temporal curvature; memory methods retain previously acquired curvature. On a closed convex parameter set, deterministic adaptation is a projected gradient/Onsager flow, with tangent and normal cones recovering projection, while composite learning supplies data-dependent symmetric dissipation. Reflected Langevin dynamics, no-flux Fokker--Planck evolution, and constrained free-energy flow provide the stochastic counterpart. The framework distinguishes information supplied by data from confinement supplied by regularization or hard constraints and connects familiar adaptive-control structures to modern variational and information-theoretic language.

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arXiv2026

Nesterov-Accelerated Concurrent Learning for Lyapunov-Based Deep Neural Networks

Concurrent learning (CL) has recently been extended to Lyapunov-based deep neural networks (DNNs) to obtain parameter convergence under finite rather than persistent excitation. However, the existing first-order law converges slowly, especially for high-dimensional systems and overparameterized networks. To address this problem, this paper develops a Nesterov-accelerated concurrent learning (NACL) adaptation law for uncertain second-order control-affine systems. The developed law drives momentum dynamics with recorded state-input data, so that all hidden layers of the DNN are updated online under a verifiable finite excitation condition. A dynamic state-derivative observer is designed to reconstruct the recorded input without acceleration measurements. The momentum variable introducesa cross term coupling the momentum lag error to the state-dependent DNN Jacobian and the tracking error, and a state-dependent normalization is introduced into the momentum filter to dominate it. A Lyapunov-based analysis establishes exponential convergence of the tracking, momentum, observer, and weight estimation errors to a bounded residual ball. Simulations on a six- degree-of-freedom unmanned underwater vehicle demonstrate a 24.5% and 62.9% reduction in the root-mean-square function approximation error relative to first-order CL and to a higher-order tuner without CL, respectively.

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arXiv2026

Decentralized Scalar Field Mapping using Gaussian Process

Decentralized Gaussian process (GP) methods provide a scalable framework for multi-agent scalar-field estimation by allowing each agent to maintain a local GP over its assigned subdomain. Because neighboring agents condition their GP models on different measurements, their GP posteriors generally disagree over overlapping regions. This paper introduces the inducing points decentralized Gaussian process (IPD-GP) framework, which exploits these discrepancies to improve posterior consistency over shared regions. Each sender constructs receiver-specific data packets by selecting inducing locations targeted at the pairwise overlap and transmitting the corresponding posterior means and variances. Each receiver then selectively assimilates informative packets as persistent fictitious measurements in its local GP. The developed architecture preserves decentralized computation and communication without requiring full dataset exchange or centralized inference. Performance is evaluated using normalized root-mean-square error, negative log predictive density, and their overlap-restricted counterparts, with comparisons against non-communicating local GPs, decentralized aggregation methods, and a centralized GP. Simulation results show that IPD-GP achieves competitive predictive accuracy while reducing inter-agent communication.

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arXiv2026

Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees

Neural ODEs learn dynamics from trajectory losses, but their adjoint gradients lack the regressor-times-parameter-error structure on which Lyapunov analyses of online adaptation rest, so training on streaming data comes without stability guarantees. We show that this structure is in fact present: the adjoint gradient decomposes exactly into a positive semi-definite trajectory operator acting on the parameter error plus a nonlinear perturbation with explicit, horizon-dependent bounds. A quadratic Lyapunov function then certifies online Neural ODE training over sliding windows under computable gain and horizon conditions, and the same certificate extends to stored data: its drift branch recovers concurrent learning, and its trajectory branch yields NODE-CL, a stored-segment Gauss-Newton method built on batched forward sensitivities that needs no state-derivative estimates. On four DeepMind Control Suite domains, NODE-CL attains the lowest median prediction error on three under velocity measurement noise, where observer-based concurrent learning degrades by up to 8x; with clean measurements it is best on the pendulum and within a factor of 1.6 of the best stored-data baseline on the cartpole and reacher.

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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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arXiv2026

Bounds on Deep Neural Network Partial Derivatives with Respect to Parameters

Deep neural networks (DNNs) have emerged as a powerful tool with a growing body of literature exploring Lyapunov-based approaches for real-time system identification and control. These methods depend on establishing bounds for the second partial derivatives of DNNs with respect to their parameters, a requirement often assumed but rarely addressed explicitly. This paper provides rigorous mathematical formulations of polynomial bounds on both the first and second partial derivatives of DNNs with respect to their parameters. We present lemmas that characterize these bounds for fully-connected DNNs, while accommodating various classes of activation function including sigmoidal and ReLU-like functions. Our analysis yields closed-form expressions that enable precise stability guarantees for Lyapunov-based deep neural networks (Lb-DNNs). Furthermore, we extend our results to bound the higher-order terms in first-order Taylor approximations of DNNs, providing important tools for convergence analysis in gradient-based learning algorithms. The developed theoretical framework develops explicit, computable expressions, for previously assumed bounds, thereby strengthening the mathematical foundation of neural network applications in safety-critical control systems.

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arXiv2026

Riemannian Lyapunov Optimizer: A Unified Framework for Optimization

We introduce Riemannian Lyapunov Optimizers (RLOs), a family of optimization algorithms that unifies classic optimizers within one geometric framework. Unlike heuristic improvements to existing optimizers, RLOs are systematically derived from a novel control-theoretic framework that reinterprets optimization as an extended state discrete-time controlled dynamical system on a Riemannian parameter manifold. Central to this framework is the identification of a Normally Attracting Invariant Manifold (NAIM), which organizes training dynamics into two distinct stages: rapid alignment of the speed state to a target graph, followed by controlled evolution within it. We formalize this by constructing a strict Lyapunov function that certifies convergence to a target manifold. This perspective yields a constructive ``optimizer generator" that not only recovers classic algorithms but enables the principled design of RLOs. We validate our theory via geometric diagnostics and demonstrate that grounding optimizer design in control theory yields state-of-the-art performance in large-scale benchmarks. Overall, RLOs bridge control theory and modern machine learning optimization, providing a unified language and a systematic toolkit for designing stable, effective optimizers.

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arXiv2025

LyLA-Therm: Lyapunov-based Langevin Adaptive Thermodynamic Neural Network Controller

Thermodynamic principles can be employed to design parameter update laws that address challenges such as the exploration vs. exploitation dilemma. In this paper, inspired by the Langevin equation, an update law is developed for a Lyapunov-based DNN control method, taking the form of a stochastic differential equation. The drift term is designed to minimize the system's generalized internal energy, while the diffusion term is governed by a user-selected generalized temperature law, allowing for more controlled fluctuations. The minimization of generalized internal energy in this design fulfills the exploitation objective, while the temperature-based stochastic noise ensures sufficient exploration. Using a Lyapunov-based stability analysis, the proposed Lyapunov-based Langevin Adaptive Thermodynamic (LyLA-Therm) neural network controller achieves probabilistic convergence of the tracking and parameter estimation errors to an ultimate bound. Simulation results demonstrate the effectiveness of the proposed approach, with the LyLA-Therm architecture achieving up to 20.66% improvement in tracking errors, up to 20.89% improvement in function approximation errors, and up to 11.31% improvement in off-trajectory function approximation errors compared to the baseline deterministic approach.

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arXiv2025

Online ResNet-Based Adaptive Control for Nonlinear Target Tracking

A generalized ResNet architecture for adaptive control of nonlinear systems with black box uncertainties is developed. The approach overcomes limitations in existing methods by incorporating pre-activation shortcut connections and a zeroth layer block that accommodates different input-output dimensions. The developed Lyapunov-based adaptation law establishes exponential convergence to a neighborhood of the target state despite unknown dynamics and disturbances. Furthermore, the theoretical results are validated through a comparative experiment.

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arXiv2025

Distributed RISE-based Control for Exponential Heterogeneous Multi-Agent Target Tracking of Second-Order Nonlinear Systems

A distributed implementation of a Robust Integral of the Sign of the Error (RISE) controller is developed for multi-agent target tracking problems with exponential convergence guarantees. Previous RISE-based approaches for multi-agent systems required 2-hop communication, limiting practical applicability. New insights from a Lyapunov-based design-analysis approach are used to eliminate the need for multi-hop communication required in previous literature, while yielding exponential target tracking. The new insights include the development of a new P-function that works in tandem with the graph interaction matrix in the Lyapunov function. Nonsmooth Lyapunov-based stability analysis methods are used to yield semi-global exponential convergence to the target agent state despite the presence of bounded disturbances with bounded derivatives. The resulting outcome is a controller that achieves exponential target tracking with only local information exchange between neighboring agents.

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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

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

Lyapunov-Based Deep Residual Neural Network (ResNet) Adaptive Control

Deep Neural Network (DNN)-based controllers have emerged as a tool to compensate for unstructured uncertainties in nonlinear dynamical systems. A recent breakthrough in the adaptive control literature provides a Lyapunov-based approach to derive weight adaptation laws for each layer of a fully-connected feedforward DNN-based adaptive controller. However, deriving weight adaptation laws from a Lyapunov-based analysis remains an open problem for deep residual neural networks (ResNets). This paper provides the first result on Lyapunov-derived weight adaptation for a ResNet-based adaptive controller. A nonsmooth Lyapunov-based analysis is provided to guarantee asymptotic tracking error convergence. Comparative Monte Carlo simulations are provided to demonstrate the performance of the developed ResNet-based adaptive controller. The ResNet-based adaptive controller shows a 64% improvement in the tracking and function approximation performance, in comparison to a fully-connected DNN-based adaptive controller.

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arXiv2025

Adaptive Deep Neural Network-Based Control Barrier Functions

Safety constraints of nonlinear control systems are commonly enforced through the use of control barrier functions (CBFs). Uncertainties in the dynamic model can disrupt forward invariance guarantees or cause the state to be restricted to an overly conservative subset of the safe set. In this paper, adaptive deep neural networks (DNNs) are combined with CBFs to produce a family of controllers that ensure safety while learning the system's dynamics in real-time without the requirement for pre-training. By basing the least squares adaptation law on a state derivative estimator-based identification error, the DNN parameter estimation error is shown to be uniformly ultimately bounded. The convergent bound on the parameter estimation error is then used to formulate CBF-constraints in an optimization-based controller to guarantee safety despite model uncertainty. Furthermore, the developed method is extended for use under intermittent loss of state-feedback. A switched systems analysis for CBFs is provided with a maximum dwell-time condition during which the feedback can be unavailable. Comparative simulation results demonstrate the ability of the developed method to ensure safety in an adaptive cruise control problem and when feedback is lost, unlike baseline methods. Results show improved performance compared to baseline methods and demonstrate the ability of the developed method to ensure safety in feedback-denied environments.

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arXiv2025

Collaborative Spacecraft Servicing under Partial Feedback using Lyapunov-based Deep Neural Networks

Multi-agent systems are increasingly applied in space missions, including distributed space systems, resilient constellations, and autonomous rendezvous and docking operations. A critical emerging application is collaborative spacecraft servicing, which encompasses on-orbit maintenance, space debris removal, and swarm-based satellite repositioning. These missions involve servicing spacecraft interacting with malfunctioning or defunct spacecraft under challenging conditions, such as limited state information, measurement inaccuracies, and erratic target behaviors. Existing approaches often rely on assumptions of full state knowledge or single-integrator dynamics, which are impractical for real-world applications involving second-order spacecraft dynamics. This work addresses these challenges by developing a distributed state estimation and tracking framework that requires only relative position measurements and operates under partial state information. A novel $ρ$-filter is introduced to reconstruct unknown states using locally available information, and a Lyapunov-based deep neural network adaptive controller is developed that adaptively compensates for uncertainties stemming from unknown spacecraft dynamics. To ensure the collaborative spacecraft regulation problem is well-posed, a trackability condition is defined. A Lyapunov-based stability analysis is provided to ensure exponential convergence of errors in state estimation and spacecraft regulation to a neighborhood of the origin under the trackability condition. The developed method eliminates the need for expensive velocity sensors or extensive pre-training, offering a practical and robust solution for spacecraft servicing in complex, dynamic environments.

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arXiv2024

Lyapunov-Based Deep Neural Networks for Adaptive Control of Stochastic Nonlinear Systems

Controlling nonlinear stochastic dynamical systems involves substantial challenges when the dynamics contain unknown and unstructured nonlinear state-dependent terms. For such complex systems, deep neural networks can serve as powerful black box approximators for the unknown drift and diffusion processes. Recent developments construct Lyapunov-based deep neural network (Lb-DNN) controllers to compensate for deterministic uncertainties using adaptive weight update laws derived from a Lyapunov-based analysis based on insights from the compositional structure of the DNN architecture. However, these Lb-DNN controllers do not account for non-deterministic uncertainties. This paper develops Lb-DNNs to adaptively compensate for both the drift and diffusion uncertainties of nonlinear stochastic dynamic systems. Through a Lyapunov-based stability analysis, a DNN-based approximation and corresponding DNN weight adaptation laws are constructed to eliminate the unknown state-dependent terms resulting from the nonlinear diffusion and drift processes. The tracking error is shown to be uniformly ultimately bounded in probability. Simulations are performed on a nonlinear stochastic dynamical system to show efficacy of the proposed method.

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arXiv2023

Lyapunov-Based Dropout Deep Neural Network (Lb-DDNN) Controller

Deep neural network (DNN)-based adaptive controllers can be used to compensate for unstructured uncertainties in nonlinear dynamic systems. However, DNNs are also very susceptible to overfitting and co-adaptation. Dropout regularization is an approach where nodes are randomly dropped during training to alleviate issues such as overfitting and co-adaptation. In this paper, a dropout DNN-based adaptive controller is developed. The developed dropout technique allows the deactivation of weights that are stochastically selected for each individual layer within the DNN. Simultaneously, a Lyapunov-based real-time weight adaptation law is introduced to update the weights of all layers of the DNN for online unsupervised learning. A non-smooth Lyapunov-based stability analysis is performed to ensure asymptotic convergence of the tracking error. Simulation results of the developed dropout DNN-based adaptive controller indicate a 38.32% improvement in the tracking error, a 53.67% improvement in the function approximation error, and 50.44% lower control effort when compared to a baseline adaptive DNN-based controller without dropout regularization.

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arXiv2020

Adaptive Control of Time-Varying Parameter Systems with Asymptotic Tracking

A continuous adaptive control design is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. The key feature of this design is a robust integral of the sign of the error (RISE)-like term in the adaptation law which compensates for potentially destabilizing terms in the closed-loop error system arising from the time-varying nature of uncertain parameters. A Lyapunov-based stability analysis ensures asymptotic tracking, and boundedness of the closed-loop signals.

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