arXiv subjects

Nikhil Chopra

Publications and source records attributed to Nikhil Chopra.

At least 19 recordsLinked to original sources

arXiv2026

Commutator-Driven Stability Bounds for Periodic Switching

Averaged models are widely used to analyze periodically switched linear systems, yet the stability of the averaged flow does not automatically guarantee the stability of the true switched dynamics. The discrepancy arises from noncommutativity among the subsystem generators, so stability certificates benefit from bounds that expose this dependence in a form compatible with Lyapunov contraction metrics. We derive an explicit operator-norm bound for the one-period mismatch between the switched and averaged propagators, in which the leading-order error depends explicitly on the pairwise commutator norms of the scaled mode generators, with a closed-form prefactor depending only on the generator norms. This bound yields a computable threshold for the switching period below which the switched system inherits exponential stability from its averaged model, uniformly certified over admissible duty fractions. The analysis extends to an arbitrary number of switching modes via telescoping induction, and a semidefinite program provides sampled duty-dependent Lyapunov metrics for implementing the certificate.

math.OC↗

arXiv2026

DREAM: Domain-aware Reasoning for Efficient Autonomous Underwater Monitoring

The ocean is warming and acidifying, increasing the risk of mass mortality events for temperature-sensitive shellfish such as oysters. This motivates the development of long-term monitoring systems. However, human labor is costly and long-duration underwater work is highly hazardous, thus favoring robotic solutions as a safer and more efficient option. To enable underwater robots to make real-time, environment-aware decisions without human intervention, we must equip them with an intelligent "brain." This highlights the need for persistent,wide-area, and low-cost benthic monitoring. To this end, we present DREAM, a Vision Language Model (VLM)-guided autonomy framework for long-term underwater exploration and habitat monitoring. The results show that our framework is highly efficient in finding and exploring target objects (e.g., oysters, shipwrecks) without prior location information. In the oyster-monitoring task, our framework takes 31.5% less time than the previous baseline with the same amount of oysters. Compared to the vanilla VLM, it uses 23% fewer steps while covering 8.88% more oysters. In shipwreck scenes, our framework successfully explores and maps the wreck without collisions, requiring 27.5% fewer steps than the vanilla model and achieving 100% coverage, while the vanilla model achieves 60.23% average coverage in our shipwreck environments.

cs.RO↗

arXiv2025

Trapped-ion quantum simulation of the Fermi-Hubbard model as a lattice gauge theory using hardware-aware native gates

The Fermi-Hubbard model (FHM) is a simple yet rich model of strongly interacting electrons with complex dynamics and a variety of emerging quantum phases. These properties make it a compelling target for digital quantum simulation. Trotterization-based quantum simulations have shown promise, but implementations on current hardware are limited by noise, necessitating error mitigation techniques like circuit optimization and post-selection. A mapping of the FHM to a Z2 LGT was recently proposed that restricts the dynamics to a subspace protected by additional symmetries, and its ability for post-selection error mitigation was verified through noisy classical simulations. In this work, we propose and demonstrate a suite of algorithm-hardware co-design strategies on a trapped-ion quantum computer, targeting two key aspects of NISQ-era quantum simulation: circuit compilation and error mitigation. In particular, a novel combination of iteratively preconditioned gradient descent (IPG) and subsystem von Neumann Entropy compression reduces the 2-qubit gate count of FHM quantum simulation by 35%, consequently doubling the number of simulatable Trotter steps when used in tandem with error mitigation based on conserved symmetries, debiasing and sharpening techniques. Our work demonstrates the value of algorithm-hardware co-design to operate digital quantum simulators at the threshold of maximum circuit depths allowed by current hardware, and is broadly generalizable to strongly correlated systems in quantum chemistry and materials science.

quant-ph↗

arXiv2025

Cascade IPG Observer for Underwater Robot State Estimation

This paper presents a novel cascade nonlinear observer framework for inertial state estimation. It tackles the problem of intermediate state estimation when external localization is unavailable or in the event of a sensor outage. The proposed observer comprises two nonlinear observers based on a recently developed iteratively preconditioned gradient descent (IPG) algorithm. It takes the inputs via an IMU preintegration model where the first observer is a quaternion-based IPG. The output for the first observer is the input for the second observer, estimating the velocity and, consequently, the position. The proposed observer is validated on a public underwater dataset and a real-world experiment using our robot platform. The estimation is compared with an extended Kalman filter (EKF) and an invariant extended Kalman filter (InEKF). Results demonstrate that our method outperforms these methods regarding better positional accuracy and lower variance.

cs.RO↗

arXiv2025

3D Water Quality Mapping using Invariant Extended Kalman Filtering for Underwater Robot Localization

Water quality mapping for critical parameters such as temperature, salinity, and turbidity is crucial for assessing an aquaculture farm's health and yield capacity. Traditional approaches involve using boats or human divers, which are time-constrained and lack depth variability. This work presents an innovative approach to 3D water quality mapping in shallow water environments using a BlueROV2 equipped with GPS and a water quality sensor. This system allows for accurate location correction by resurfacing when errors occur. This study is being conducted at an oyster farm in the Chesapeake Bay, USA, providing a more comprehensive and precise water quality analysis in aquaculture settings.

cs.RO↗

arXiv2024

On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier.

math.OC↗

arXiv2024

Reinforcement Learning Driven Cooperative Ball Balance in Rigidly Coupled Drones

Multi-drone cooperative transport (CT) problem has been widely studied in the literature. However, limited work exists on control of such systems in the presence of time-varying uncertainties, such as the time-varying center of gravity (CG). This paper presents a leader-follower approach for the control of a multi-drone CT system with time-varying CG. The leader uses a traditional Proportional-Integral-Derivative (PID) controller, and in contrast, the follower uses a deep reinforcement learning (RL) controller using only local information and minimal leader information. Extensive simulation results are presented, showing the effectiveness of the proposed method over a previously developed adaptive controller and for variations in the mass of the objects being transported and CG speeds. Preliminary experimental work also demonstrates ball balance (depicting moving CG) on a stick/rod lifted by two Crazyflie drones cooperatively.

cs.RO↗

arXiv2024

UIVNAV: Underwater Information-driven Vision-based Navigation via Imitation Learning

Autonomous navigation in the underwater environment is challenging due to limited visibility, dynamic changes, and the lack of a cost-efficient accurate localization system. We introduce UIVNav, a novel end-to-end underwater navigation solution designed to drive robots over Objects of Interest (OOI) while avoiding obstacles, without relying on localization. UIVNav uses imitation learning and is inspired by the navigation strategies used by human divers who do not rely on localization. UIVNav consists of the following phases: (1) generating an intermediate representation (IR), and (2) training the navigation policy based on human-labeled IR. By training the navigation policy on IR instead of raw data, the second phase is domain-invariant -- the navigation policy does not need to be retrained if the domain or the OOI changes. We show this by deploying the same navigation policy for surveying two different OOIs, oyster and rock reefs, in two different domains, simulation, and a real pool. We compared our method with complete coverage and random walk methods which showed that our method is more efficient in gathering information for OOIs while also avoiding obstacles. The results show that UIVNav chooses to visit the areas with larger area sizes of oysters or rocks with no prior information about the environment or localization. Moreover, a robot using UIVNav compared to complete coverage method surveys on average 36% more oysters when traveling the same distances. We also demonstrate the feasibility of real-time deployment of UIVNavin pool experiments with BlueROV underwater robot for surveying a bed of oyster shells.

cs.RO↗

arXiv2023

Quantum Circuit Optimization through Iteratively Pre-Conditioned Gradient Descent

For typical quantum subroutines in the gate-based model of quantum computing, explicit decompositions of circuits in terms of single-qubit and two-qubit entangling gates may exist. However, they often lead to large-depth circuits that are challenging for noisy intermediate-scale quantum (NISQ) hardware. Additionally, exact decompositions might only exist for some modular quantum circuits. Therefore, it is essential to find gate combinations that approximate these circuits to high fidelity with potentially low depth, for example, using gradient-based optimization. Traditional optimizers often run into problems of slow convergence requiring many iterations, and perform poorly in the presence of noise. Here we present iteratively preconditioned gradient descent (IPG) for optimizing quantum circuits and demonstrate performance speedups for state preparation and implementation of quantum algorithmic subroutines. IPG is a noise-resilient, higher-order algorithm that has shown promising gains in convergence speed for classical optimizations, converging locally at a linear rate for convex problems and superlinearly when the solution is unique. Specifically, we show an improvement in fidelity by a factor of $10^4$ for preparing a 4-qubit W state and a maximally entangled 5-qubit GHZ state compared to other commonly used classical optimizers tuning the same ansatz. We also show gains for optimizing a unitary for a quantum Fourier transform using IPG, and report results of running such optimized circuits on IonQ's quantum processing unit (QPU). Such faster convergence with promise for noise-resilience could provide advantages for quantum algorithms on NISQ hardware, especially since the cost of running each iteration on a quantum computer is substantially higher than the classical optimizer step.

quant-ph↗

arXiv2023

A Control Theoretic Framework for Adaptive Gradient Optimizers in Machine Learning

Adaptive gradient methods have become popular in optimizing deep neural networks; recent examples include AdaGrad and Adam. Although Adam usually converges faster, variations of Adam, for instance, the AdaBelief algorithm, have been proposed to enhance Adam's poor generalization ability compared to the classical stochastic gradient method. This paper develops a generic framework for adaptive gradient methods that solve non-convex optimization problems. We first model the adaptive gradient methods in a state-space framework, which allows us to present simpler convergence proofs of adaptive optimizers such as AdaGrad, Adam, and AdaBelief. We then utilize the transfer function paradigm from classical control theory to propose a new variant of Adam, coined AdamSSM. We add an appropriate pole-zero pair in the transfer function from squared gradients to the second moment estimate. We prove the convergence of the proposed AdamSSM algorithm. Applications on benchmark machine learning tasks of image classification using CNN architectures and language modeling using LSTM architecture demonstrate that the AdamSSM algorithm improves the gap between generalization accuracy and faster convergence than the recent adaptive gradient methods.

cs.LG↗

arXiv2023

Iteratively Preconditioned Gradient-Descent Approach for Moving Horizon Estimation Problems

Moving horizon estimation (MHE) is a widely studied state estimation approach in several practical applications. In the MHE problem, the state estimates are obtained via the solution of an approximated nonlinear optimization problem. However, this optimization step is known to be computationally complex. Given this limitation, this paper investigates the idea of iteratively preconditioned gradient-descent (IPG) to solve MHE problem with the aim of an improved performance than the existing solution techniques. To our knowledge, the preconditioning technique is used for the first time in this paper to reduce the computational cost and accelerate the crucial optimization step for MHE. The convergence guarantee of the proposed iterative approach for a class of MHE problems is presented. Additionally, sufficient conditions for the MHE problem to be convex are also derived. Finally, the proposed method is implemented on a unicycle localization example. The simulation results demonstrate that the proposed approach can achieve better accuracy with reduced computational costs.

math.OC↗

arXiv2022

Cartographer_glass: 2D Graph SLAM Framework using LiDAR for Glass Environments

We study algorithms for detecting and including glass objects in an optimization-based Simultaneous Localization and Mapping (SLAM) algorithm in this work. When LiDAR data is the primary exteroceptive sensory input, glass objects are not correctly registered. This occurs as the incident light primarily passes through the glass objects or reflects away from the source, resulting in inaccurate range measurements for glass surfaces. Consequently, the localization and mapping performance is impacted, thereby rendering navigation in such environments unreliable. Optimization-based SLAM solutions, which are also referred to as Graph SLAM, are widely regarded as state of the art. In this paper, we utilize a simple and computationally inexpensive glass detection scheme for detecting glass objects and present the methodology to incorporate the identified objects into the occupancy grid maintained by such an algorithm (Google Cartographer). We develop both local (submap level) and global algorithms for achieving the objective mentioned above and compare the maps produced by our method with those produced by an existing algorithm that utilizes particle filter based SLAM.

cs.RO↗

arXiv2022

Co-Design of Lipschitz Nonlinear Systems

Empirical experiences have shown that simultaneous (rather than conventional sequential) plant and controller design procedure leads to an improvement in performance and saving of plant resources. Such a simultaneous synthesis procedure is called as "co-design". In this letter we study the co-design problem for a class of Lipschitz nonlinear dynamical systems having a quadratic control objective and state-feedback controller. We propose a novel time independent reformulation of the co-design optimization problem whose constraints ensure stability of the system. We also present a gradient-based co-design solution procedure which involves system coordinate transformation and whose output is provably stable solution for the original system. We show the efficacy of the solution procedure through co-design of a single-link robot.

eess.SY↗

arXiv2021

Generalized AdaGrad (G-AdaGrad) and Adam: A State-Space Perspective

Accelerated gradient-based methods are being extensively used for solving non-convex machine learning problems, especially when the data points are abundant or the available data is distributed across several agents. Two of the prominent accelerated gradient algorithms are AdaGrad and Adam. AdaGrad is the simplest accelerated gradient method, which is particularly effective for sparse data. Adam has been shown to perform favorably in deep learning problems compared to other methods. In this paper, we propose a new fast optimizer, Generalized AdaGrad (G-AdaGrad), for accelerating the solution of potentially non-convex machine learning problems. Specifically, we adopt a state-space perspective for analyzing the convergence of gradient acceleration algorithms, namely G-AdaGrad and Adam, in machine learning. Our proposed state-space models are governed by ordinary differential equations. We present simple convergence proofs of these two algorithms in the deterministic settings with minimal assumptions. Our analysis also provides intuition behind improving upon AdaGrad's convergence rate. We provide empirical results on MNIST dataset to reinforce our claims on the convergence and performance of G-AdaGrad and Adam.

cs.LG↗

arXiv2021

On Accelerating Distributed Convex Optimizations

This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a server, and there is no inter-agent communication. The agents' goal is to learn a parameter vector that optimizes the aggregate of their local costs without revealing their local data points. In principle, the agents can solve this problem by collaborating with the server using the traditional distributed gradient-descent method. However, when the aggregate cost is ill-conditioned, the gradient-descent method (i) requires a large number of iterations to converge, and (ii) is highly unstable against process noise. We propose an iterative pre-conditioning technique to mitigate the deleterious effects of the cost function's conditioning on the convergence rate of distributed gradient-descent. Unlike the conventional pre-conditioning techniques, the pre-conditioner matrix in our proposed technique updates iteratively to facilitate implementation on the distributed network. In the distributed setting, we provably show that the proposed algorithm converges linearly with an improved rate of convergence than the traditional and adaptive gradient-descent methods. Additionally, for the special case when the minimizer of the aggregate cost is unique, our algorithm converges superlinearly. We demonstrate our algorithm's superior performance compared to prominent distributed algorithms for solving real logistic regression problems and emulating neural network training via a noisy quadratic model, thereby signifying the proposed algorithm's efficiency for distributively solving non-convex optimization. Moreover, we empirically show that the proposed algorithm results in faster training without compromising the generalization performance.

math.OC↗

arXiv2021

Iterative Pre-Conditioning for Expediting the Gradient-Descent Method: The Distributed Linear Least-Squares Problem

This paper considers the multi-agent linear least-squares problem in a server-agent network. In this problem, the system comprises multiple agents, each having a set of local data points, that are connected to a server. The goal for the agents is to compute a linear mathematical model that optimally fits the collective data points held by all the agents, without sharing their individual local data points. This goal can be achieved, in principle, using the server-agent variant of the traditional iterative gradient-descent method. The gradient-descent method converges linearly to a solution, and its rate of convergence is lower bounded by the conditioning of the agents' collective data points. If the data points are ill-conditioned, the gradient-descent method may require a large number of iterations to converge. We propose an iterative pre-conditioning technique that mitigates the deleterious effect of the conditioning of data points on the rate of convergence of the gradient-descent method. We rigorously show that the resulting pre-conditioned gradient-descent method, with the proposed iterative pre-conditioning, achieves superlinear convergence when the least-squares problem has a unique solution. In general, the convergence is linear with improved rate of convergence in comparison to the traditional gradient-descent method and the state-of-the-art accelerated gradient-descent methods. We further illustrate the improved rate of convergence of our proposed algorithm through experiments on different real-world least-squares problems in both noise-free and noisy computation environment.

math.OC↗

arXiv2021

Robustness of Iteratively Pre-Conditioned Gradient-Descent Method: The Case of Distributed Linear Regression Problem

This paper considers the problem of multi-agent distributed linear regression in the presence of system noises. In this problem, the system comprises multiple agents wherein each agent locally observes a set of data points, and the agents' goal is to compute a linear model that best fits the collective data points observed by all the agents. We consider a server-based distributed architecture where the agents interact with a common server to solve the problem; however, the server cannot access the agents' data points. We consider a practical scenario wherein the system either has observation noise, i.e., the data points observed by the agents are corrupted, or has process noise, i.e., the computations performed by the server and the agents are corrupted. In noise-free systems, the recently proposed distributed linear regression algorithm, named the Iteratively Pre-conditioned Gradient-descent (IPG) method, has been claimed to converge faster than related methods. In this paper, we study the robustness of the IPG method, against both the observation noise and the process noise. We empirically show that the robustness of the IPG method compares favorably to the state-of-the-art algorithms.

math.OC↗

arXiv2020

Preserving Statistical Privacy in Distributed Optimization

We present a distributed optimization protocol that preserves statistical privacy of agents' local cost functions against a passive adversary that corrupts some agents in the network. The protocol is a composition of a distributed ``{\em zero-sum}" obfuscation protocol that obfuscates the agents' local cost functions, and a standard non-private distributed optimization method. We show that our protocol protects the statistical privacy of the agents' local cost functions against a passive adversary that corrupts up to $t$ arbitrary agents as long as the communication network has $(t+1)$-vertex connectivity. The ``{\em zero-sum}" obfuscation protocol preserves the sum of the agents' local cost functions and therefore ensures accuracy of the computed solution.

cs.CR↗