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10th Indian control Conference, ICC 2024

作者： Buriuly, Somnath Vachhani, Leena The Center of Excellence in Oil Gas and Energy IIT Bombay India Systems and Control Engineering IIT Bombay India

ISBN: (纸本)9798331517212

Industrial problems, like pipeline inspection and railway track geometry inspection inside tunnels, require accurate offline estimation of the state trajectories, to determine the infrastructure parameters, say pipeline GPS coordinates, rail-track’s attitude and placement, etc. These problems are cursed with loss of observability due to the unavailability of localization data, like GPS, inside pipelines and tunnels. In addition, the states at the start and end of the recorded data are observable but not accurately or entirely known. Furthermore, a deviation is observed in the initial calibration of the Inertial Measurement Unit (IMU) sensors, and hence the recorded data are approximated sensor readings. Since the accuracy of these estimated outcomes impacts the maintenance cost of the infrastructure, it is essential to obtain the best possible estimate from the offline available sensor data. In this work, we propose an optimization-based solution to estimate the entire trajectory and self-calibrate the sensor readings, simultaneously. In particular, we formulate an offline state trajectory estimation problem with self-calibration features for the sensor readings, compute the gradients for the decisions, and propose a Lagrangian-based gradient descent algorithm. We compare the results with the state-of-the-art Extended Kalman Filter and show improvement in the mean square error values of the estimates. © 2024 IEEE.

关键词： Trajectories

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A Principal Bundle Framework for Generalised Notions of Formation and Rigidity ⁎

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IFAC-PapersOnLine 2024年第6期58卷 262-267页

作者： Rama Seshan C Ravi N Banavar Arun D Mahindrakar Control and Optimization Group IIT Madras India Systems and Control Engineering IIT Bombay India

In this work, the notions of formation and rigidity (first developed for formation control in Euclidean spaces) are recast in a general framework of principal fiber bundles and a control law is derived for second order systems for driving the system to a given formation. The Euclidean inter-agent distance measurements and congruence transformations are generalised as output maps and Lie group actions respectively, to capture more generic scenarios.

关键词： Formation Rigidity fiber Bundle Multi-Agent systems Geometric Mechanics

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A Moreau Envelope Approach for LQR Meta-Policy Estimation 63

A Moreau Envelope Approach for LQR Meta-Policy Estimation

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63rd IEEE Conference on Decision and control, CDC 2024

作者： Aravind, Ashwin Toghani, Mohammad Taha Uribe, Cesar A. Iit Bombay Centre for Systems and Control MH Mumbai India Rice University Department of Electrical and Computer Engineering HoustonTX United States

ISBN: (纸本)9798350316339

We study the problem of policy estimation for the Linear Quadratic Regulator (LQR) in discrete-time linear timeinvariant uncertain dynamical systems. We propose a Moreau Envelope-based surrogate LQR cost, built from a finite set of realizations of the uncertain system, to define a meta-policy efficiently adjustable to new realizations. Moreover, we design an algorithm to find an approximate first-order stationary point of the meta-LQR cost function. Numerical results show that the proposed approach outperforms naive averaging of controllers on new realizations of the linear system. We also provide empirical evidence that our method has better sample complexity than Model-Agnostic Meta-Learning (MAML) approaches. © 2024 IEEE.

关键词： Cost functions

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Quantitative Estimates on the Domain of Feedback Linearization

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IFAC-PapersOnLine 2023年第1期56卷 144-149页

作者： Ashutosh Jindal Ravi Banavar Debasish Chatterjee Ronit M Chitre Systems and Control Engineering IIT Bombay Powai Mumbai 400076 India

Feedback linearization (FL) is a powerful tool to enable control synthesis for nonlinear systems. Since FL is a local construction, an important notion is the domain of validity of the procedure, and in particular, quantitative estimates of these domain of applicability of the procedure. Such quantification is missing in the existing literature and this article fills in this niche using the mathematical tool of the implicit function theorem. The results provide lower bounds on the region in which a given discrete time system is feedback linearizable.

关键词： Discrete Time control systems Feedback Linearization Numerical Integration

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Measure of controllability on SO(3)

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IFAC-PapersOnLine 2023年第1期56卷 361-366页

作者： Ashutosh Jindal Ravi Banavar Debasish Chatterjee Systems and Control Engineering IIT Bombay Powai Mumbai 400076 India

The classical notion of controllability provides us with a boolean variable — whether a given system is controllable or not. However, often as engineers we seek a notion of how ‘controllable’ a given system is, so as to classify systems that are ‘easier to control’ from those which are ‘difficult to control’. In this article we derive a quantitative measure of controllability for bilinear systems defined on the Lie group of rotations SO(3). Our controllability measure is based on the worst case cost of transferring the system from a given initial condition to a given final condition arbitrarily chosen over a set of interest. Here we consider a few frequently encountered cost functions such as control energy optimization and time optimal control, and obtain a relation between the worst case cost and the system parameters.

关键词： controllability Optimal Configuration Optimal control System Design

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Robust control Design for a linearized model of a LIGO subsystem

Robust Control Design for a linearized model of a LIGO subsy...

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European control Conference (ECC)

作者： Ashmita Roy Nishant Mittal Ravi N. Banavar Systems and Control Engineering IIT Bombay India Department of Electrical Engineering IIT Bombay India

Laser Interferometer Gravitational wave Observatory (LIGO) is a gravitational wave antenna used to detect the infinitesimal contraction and expansion of space by a passing gravitational wave. LIGO comprises several subsystems which isolate the optics from seismic noise. Of these, we focus on the quadruple pendulum suspension system and attempt to design a stabilizing controller for a simpler version of the system, the two wire simple pendulum. A nonlinear model of the two wire simple pendulum based on the Euler-Lagrange theory is derived. This is linearised about an equilibrium and a stabilising controller using a robust control paradigm called $H_{\infty} $ synthesis, is explored as a candidate design paradigm for the two wire simple pendulum. In particular, in this broad framework of $H_{\infty} $ synthesis we adopt a technique called coprime factorisation. Different types of uncertainties like parametric and nonlinear uncertainties have also been considered and an upper bound on the nonlinear uncertainties in the system is determined

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Self-Calibrating Offline Trajectory Estimation Technique for Sporadically Observable systems

Self-Calibrating Offline Trajectory Estimation Technique for...

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Indian control Conference (ICC)

作者： Somnath Buriuly Leena Vachhani Center of Excellence in Oil Gas and Energy IIT Bombay IITB-Monash Research Academy India Systems and Control Engineering IIT Bombay India

ISBN: (数字)9798331517212

ISBN: (纸本)9798331517229

Industrial problems, like pipeline inspection and railway track geometry inspection inside tunnels, require accurate offline estimation of the state trajectories, to determine the infrastructure parameters, say pipeline GPS coordinates, rail-track's attitude and placement, etc. These problems are cursed with loss of observability due to the unavailability of localization data, like GPS, inside pipelines and tunnels. In addition, the states at the start and end of the recorded data are observable but not accurately or entirely known. Furthermore, a deviation is observed in the initial calibration of the Inertial Measurement Unit (IMU) sensors, and hence the recorded data are approximated sensor readings. Since the accuracy of these estimated outcomes impacts the maintenance cost of the infrastructure, it is essential to obtain the best possible estimate from the offline available sensor data. In this work, we propose an optimization-based solution to estimate the entire trajectory and self-calibrate the sensor readings, simultaneously. In particular, we formulate an offline state trajectory estimation problem with self-calibration features for the sensor readings, compute the gradients for the decisions, and propose a Lagrangian-based gradient descent algorithm. We compare the results with the state-of-the-art Extended Kalman Filter and show improvement in the mean square error values of the estimates.

关键词： Accuracy Pipelines Estimation Inertial navigation Inspection Trajectory Kalman filters Observability Optimization Global Positioning System

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Novel min-max reformulations of linear inverse problems

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2022年第1期23卷 1271-1316页

作者： Mohammed Rayyan Sheriff Debasish Chatterjee Systems and Control Engineering IIT Bombay Mumbai India

In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refer to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a variety of settings with applications ranging from medical image processing, recommender systems, etc. We propose a slightly generalized version of the error constrained linear inverse problem and obtain a novel and equivalent convex-concave min-max reformulation by providing an exposition to its convex geometry. Saddle points of the min-max problem are completely characterized in terms of a solution to the LIP, and vice versa. Applying simple saddle point seeking ascend-descent type algorithms to solve the min-max problems provides novel and simple algorithms to find a solution to the LIP. Moreover, the reformulation of an LIP as the min-max problem provided in this article is crucial in developing methods to solve the dictionary learning problem with almost sure recovery constraints.

关键词： linear inverse problems min-max problems dictionary learning

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A DISCRETE-TIME PONTRYAGIN MAXIMUM PRINCIPLE UNDER RATE CONSTRAINTS

arXiv

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arXiv 2023年

作者： Ganguly, Siddhartha Das, Souvik Chatterjee, Debasish Banavar, Ravi Systems & Control Engineering IIT Bombay Powai Mumbai400076 India

Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the global behavior of their paths. While the problem of actuator saturation has been studied extensively, little attention has been devoted to the problem of actuators having limited bandwidth. While attempts have been made in the direction of incorporating frequency constraints on state-action trajectories before, rate constraints on the control at the design stage have not been studied extensively in the discrete-time regime. This article contributes toward filling this lacuna. In particular, we establish a new discrete-time Pontryagin maximum principle with rate constraints being imposed on the control trajectories, and derive first-order necessary conditions for optimality. A brief discussion on the existence of optimal control is included, and numerical examples are provided to illustrate the results. Copyright © 2023, The Authors. All rights reserved.

关键词： Maximum principle

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A numerical algorithm for attaining the Chebyshev bound in optimal learning

arXiv

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arXiv 2023年

作者： Paruchuri, Pradyumna Chatterjee, Debasish Systems & Control Engineering IIT Bombay Powai Mumbai400076 India

Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center problem in the context of optimal learning from a finite set of data points. For a hypothesis space realized as a compact but not necessarily convex subset of a finite-dimensional subspace of some underlying Banach space, this algorithm computes the Chebyshev radius and the Chebyshev center of the hypothesis space, thereby solving the problem of optimal recovery of functions from data. The algorithm itself is based on, and significantly extends, recent results for near-optimal solutions of convex semi-infinite problems by means of targeted sampling, and it is of independent interest. Several examples of numerical computations of Chebyshev centers are included in order to illustrate the effectiveness of the algorithm. Copyright © 2023, The Authors. All rights reserved.

关键词： Banach spaces

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