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arXiv 2023年

作者： Chattopadhyay, Sudipta Sukumar, Srikant Natarajan, Vivek The Systems and Control Engineering Group Indian Institute of Technology Bombay Mumbai400076 India

We propose an adaptive algorithm for identifying the unknown parameter in a linear exponentially stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an update law driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown spatially-varying coefficient. Copyright © 2023, The Authors. All rights reserved.

关键词： Partial differential equations

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A Modified Matrix Method for Efficient Computation of Bernstein Coefficients and its GPU Parallelization

A Modified Matrix Method for Efficient Computation of Bernst...

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2022 International Conference on Electrical, Computer, Communications and Mechatronics engineering, ICECCME 2022

作者： Dhabe, Priyadarshan Nataraj, P.S.V. Vishwakarma Institute of Technology Pune Information Technology Pune India Indian Institute of Technology Bombay Systems and Control Engineering Mumbai India

ISBN: (数字)9781665470957

ISBN: (纸本)9781665470957

The Matrix Method (MM) [16] is an efficient method for computation of Bernstein coefficients (BCs) of a multivariate polynomial on a box-like domain. However, MM uses matrix transpose and reshape operations, which is time consuming for large matrices. The same operations are also costly in terms of energy for physical data movement in the computer memory [5]. In this paper, we propose the so-called Modified Matrix Method (MMM) which eliminates the matrix transpose and reshape operations in MM along with the associated data movements. We present two versions of MMM: the serial implementation and then the GPU (Graphics Processing Unit) [12], [15] parallel implementation. We then compare the performances of the proposed MMM versions versus MM on a set of multivariate polynomial test problems taken from the literature. On the test problems, we find that the proposed GPU parallel MMM implementation runs up to 27 times faster and gives up to 93% reduction in computing time over MM, on a TESLA K40. Thus, we suggest the GPU version of MMM for faster and more efficient computation of BCs of multivariate polynomials. © 2022 IEEE.

关键词： Graphics processing unit

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Adaptive Generalized Super-Twisting Sliding Mode controller for Wheeled Mobile Robot

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IFAC-PapersOnLine 2024年 57卷 345-350页

作者： Asifa Yesmin Krishanu Nath Kiran Kumari Arpita Sinha Manas Kumar Bera IDP in Systems and Control Engineering Indian Institute of Technology Bombay Mumbai India Department of Aerospace Engineering Indian Institute of Technology Bombay Mumbai India Department of Electrical Engineering Indian Institute of Science Bengaluru India Department of Electrical Engineering National Institute of Technology Rourkela Rourkela India

This paper presents the design of an adaptive generalized super-twisting sliding mode control (SMC) for reference tracking by the two-wheeled mobile robot in the presence of uncertainty. An additional linear correction term is included in the generalized super-twisting control. The designed controller can achieve the convergence of the tracking error and reduced chattering due to the generalized super-twisting structure. The detailed Lyapunov-based stability proof has been derived to ensure the stability of the two-wheeled robot. To relax the dependence on the upper bound of the unknown disturbance, the adaptive SMC has been incorporated. The appropriate adaptive gain has been designed judiciously to ensure the convergence of the sliding variable and the tracking error. Finally, the practical implementation of the proposed adaptive generalized super-twisting robust controller is carried out on a real system, specifically the Q-bot 2e, to illustrate the effectiveness of the designed controller.

关键词： Adaptive control Autonomous Mobile Robot Robust control Sliding mode control Super-twisting control

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An Integrative Approach for Analysis of Nonlinear Electrical Circuits Using-Polynomial B-Spline Expansion and B-Spline Krawczyk Operator

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International Journal of Applied and Computational Mathematics 2022年第1期8卷 1-13页

作者： Gawali, D.D. Zidna, A. Nataraj, P.S.V. Vidyavardhini’s College of Engineering and Technology Maharashtra India LGIPM University of Lorraine Metz France Systems and Control Engineering Indian Institute of Technology Bombay India

This paper addresses the problem of finding a set of all direct current (DC) operating points of a nonlinear circuit, which is a crucial step in its development and requires the solution of a nonlinear system of polynomial equations. We propose a novel algorithm for finding the set of all solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n dimensional box. The proposed algorithm is based on the following techniques: (i) B-Spline expansion to obtain a polynomial B-Spline form of the original polynomial in power form;(ii) B-Spline Krawczyk contractor for domain pruning. To avoid the repeated evaluation of function value the algorithm suggested uses B-Spline coefficients to find the value of Krawczyk operator and the computation of derivative of polynomial function. We solved three circuit analysis problems using the proposed algorithm and compared the performance of proposed algorithm with INTLAB-based solver and found that the former is more efficient in terms of computation time and number of iterations. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： DC operating points Interval method Krawczyk contractor Nonlinear circuits Polynomial B-Spline form Polynomial systems

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Motion Planning of Nonholonomic Cooperative Mobile Manipulators

arXiv

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arXiv 2025年

作者： Patra, Keshab Sinha, Arpita Guha, Anirban Department of Mechanical Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India Systems & Control Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India

We propose a real-time implementable motion planning technique for cooperative object transportation by nonholonomic mobile manipulator robots (MMRs) in an environment with static and dynamic obstacles. The proposed motion planning technique works in two steps. A novel visibility vertices-based path planning algorithm computes a global piece-wise linear path between the start and the goal location in the presence of static obstacles offline. It defines the static obstacle free space around the path with a set of convex polygons for the online motion planner. We employ a Nonliner Model Predictive control (NMPC) based online motion planning technique for nonholonomic MMRs that jointly plans for the mobile base and the manipulator’s arm. It efficiently utilizes the locomotion capability of the mobile base and the manipulation capability of the arm. The motion planner plans feasible motion for the MMRs and generates trajectory for object transportation considering the kinodynamic constraints and the static and dynamic obstacles. The efficiency of our approach is validated by numerical simulation and hardware experiments in varied environments. Copyright © 2025, The Authors. All rights reserved.

关键词： Constrained optimization

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Flatness-based motion planning for a non-uniform moving cantilever Euler-Bernoulli beam with a tip-mass

arXiv

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arXiv 2024年

作者： Chatterjee, Soham Batra, Aman Natarajan, Vivek The Centre for Systems and Control Engineering Indian Institute of Technology Bombay Mumbai400076 India

Consider a non-uniform Euler-Bernoulli beam with a tip-mass at one end and a cantilever joint at the other end. The cantilever joint is not fixed and can itself be moved along an axis perpendicular to the beam. The position of the cantilever joint is the control input to the beam. The dynamics of the beam is governed by a coupled PDE-ODE model with boundary input. On a natural state-space, there exists a unique state trajectory for this beam model for every initial state and each smooth control input which is compatible with the initial state. In this paper, we study the motion planning problem of transferring the beam from an initial state to a final state over a prescribed time-interval. We address this problem by extending the generating functions approach to flatness-based control, originally proposed in the literature for motion planning of parabolic PDEs, to the beam model. We prove that such a transfer is possible if the initial and final states belong to a certain set, which also contains steady-states of the beam. We illustrate our theoretical results using simulations and experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： Flexible structures

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Explicit feedback synthesis for nonlinear robust model predictive control driven by quasi-interpolation

arXiv

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arXiv 2023年

作者： Ganguly, Siddhartha Chatterjee, Debasish Systems and Control Engineering Indian Institute of Technology Bombay India

We present QuIFS (Quasi-Interpolation driven Feedback Synthesis): an offline feedback synthesis algorithm for explicit nonlinear robust minmax model predictive control (MPC) problems with guaranteed quality of approximation. The underlying technique is driven by a particular type of grid-based quasi-interpolation scheme. The QuIFS algorithm departs drastically from conventional approximation algorithms that are employed in the MPC industry (in particular, it is neither based on multi-parametric programming tools nor does it involve kernel methods), and the essence of its point of departure is encoded in the following challenge-answer approach: Given an error margin Ε > 0, compute in a single stroke a feasible feedback policy that is uniformly Ε-close to the optimal MPC feedback policy for a given nonlinear system subjected to constraints and bounded uncertainties. Closed-loop stability and recursive feasibility under the approximate feedback policy are also established. We provide a library of numerical examples to illustrate our results. Copyright © 2023, The Authors. All rights reserved.

关键词： Model predictive control

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Frequency Selective control of an Ensemble Using RF Pulses Designed via the TOPS Algorithm in NMR Spectroscopy

Frequency Selective Control of an Ensemble Using RF Pulses D...

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control Conference (ICC), 2019 Sixth indian

作者： Justin Jacob Navin Khaneja Department of Systems and Control Engineering Indian Institute of Technology Bombay Mumbai India Faculty of Systems and Control Engineering Department Indian Institute of Technology Bombay Mumbai India

NMR spectroscopy is all about manipulating the nuclear spin of an atom, and we use radio frequency (RF) pulses for this. This paper introduces the TOPS algorithm, which focuses on phase manipulation in RF pulse design. It addresses the requirement for selective excitation/inversion in MRI and protein resonance experiments and demonstrates the application of the TOPS-2 algorithm in designing phase-modulated frequency selective pulses. The paper presents the algorithm for designing pulses using the TOPS approach to achieve specific objectives such as selective inversion and excitation. Experimental validation of the selective pulse sequence is performed using a sample consisting of 0.5 % H 2 O in 99.5% D 2 O.

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Adaptive Continuous Terminal Sliding Mode control for Unmanned Aerial Vehicle

Adaptive Continuous Terminal Sliding Mode Control for Unmann...

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indian control Conference (ICC)

作者： Sunil Kumar Asifa Yesmin Arpita Sinha Anirban Guha TIH Foundation for IoT and IoE Indian Institute of Technology Bombay Mumbai India IDP in Systems and Control Engineering Indian Institute of Technology Bombay Mumbai India Department of Mechanical Engineering Indian Institute of Technology Bombay Mumbai India

ISBN: (数字)9798331517212

ISBN: (纸本)9798331517229

This paper introduces an improved control strategy for tracking the altitude and attitude of the quadcopter unmanned aerial vehicle (UAV) in the presence of external disturbance, known as adaptive super-twisting terminal sliding mode control (AST-TSMC). This approach ensures finite-time convergence of the sliding variable and error trajectories using a real second-order sliding mode. An adaptive super-twisting approach is incorporated to reduce the reliance on the upper bound of the unknown disturbance and achieve continuous control. A nonlinear sliding surface is designed to ensure the finite time convergence of the sliding variable and the tracking error. The Lyapunov-based stability analysis is presented to confirm the finite-time convergence. Comparative simulation results of AST-TSMC, ST-TSMC, and TSMC are presented to demonstrate the strategy's performance. The effectiveness of the proposed approach is validated through MATLAB simulation results.

关键词： Upper bound Attitude control Simulation Switches Autonomous aerial vehicles Stability analysis Trajectory Sliding mode control Convergence Quadrotors

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State-Constrained Adaptive Guidance for Three-Body Pursuit-Evasion Using Super Twisting Algorithm

State-Constrained Adaptive Guidance for Three-Body Pursuit-E...

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American control Conference (ACC)

作者： Bhagyashri Gurjar Shashi Ranjan Kumar Dwaipayan Mukherjee Department of Aerospace Engineering Intelligent Systems & Control Lab Indian Institute of Technology Bombay Mumbai India Department of Electrical Engineering Indian Institute of Technology Bombay Mumbai India

ISBN: (数字)9798350382655

ISBN: (纸本)9798350382662

In this paper, we address the problem of robust guidance for a three-body pursuit-evasion problem involving a target, a defender, and an attacker, where the goal is to safeguard the target (an aircraft) from the attacker, using the defender. Thus, the target and the defender may act as a team of vehicles whose common goal is to safeguard the target from the attacker. Additionally, it is desired to maintain necessary constraints on certain states. An adaptive guidance law is proposed for the target-defender team to ensure optimal performance within this set-up. The target-defender dynamics are considered for designing the guidance law with only approximate knowledge of the unknown parameters of the attacker. A robust guidance command is designed using a super-twisting algorithm with adaptive gains. The unknown disturbance bounds required for control implementation are obtained using a novel norm observer. We consider the complete nonlinear model of the system for control design, thereby enabling a wider domain of applicability of the proposed approach. The convergence is established using Lyapunov analysis, which also ensures satisfaction of the required state constraints. Relevant simulation results are presented to study the efficacy of the proposed approach.

关键词： Navigation control design Simulation Heuristic algorithms Line-of-sight propagation Observers Stability analysis

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