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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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On the Algorithmic Construction of Lyapunov Functions for Continuous Vector Fields

SSRN

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SSRN 2023年

作者： Gupta, Raavi Chattopadhyay, Sameep Paruchuri, Pradyumna Chatterjee, Debasish Department of Electrical Engineering IIT Bombay Powai Mumbai400076 India Systems & Control Engineering IIT Bombay Powai Mumbai400076 India

This article presents a novel numerically tractable technique for synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an isolated equilibrium point of a given vector field, a selection is made of a compact neighborhood of the equilibrium and a dictionary of functions in which a Lyapunov function is expected to lie. Then an algorithmic procedure based on the recent work [DAC22] is deployed on the preceding neighborhood-dictionary pair and charged with the task of finding a function satisfying a compact family of inequalities that defines the behavior of a Lyapunov function on the selected neighborhood. The technique applies to continuous nonlinear vector fields without special algebraic structures and does not even require their analytical expressions to proceed. Several numerical examples are presented to illustrate our results. © 2023, The Authors. All rights reserved.

关键词： Lyapunov functions

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QuITO: Numerical software for constrained nonlinear optimal control problems

arXiv

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arXiv 2023年

作者： Ganguly, Siddhartha Randad, Nakul D'Silva, Rihan Aaron Raj, Mukesh S. Chatterjee, Debasish Systems & Control Engineering IIT Bombay Powai Mumbai400076 India Aerospace Engineering IIT Bombay Powai Mumbai400076 India Mechanical Engineering IIT Bombay Powai Mumbai400076 India

We introduce the MATLAB-based software QuITO (Quasi-Interpolation based Trajectory Optimization) to numerically solve a wide class of constrained nonlinear optimal control problems (OCP). The solver is based on the QuITO (the same abbreviation) algorithm, which is a direct multiple shooting (DMS) technique that leverages a particular type of quasi-interpolation scheme for control trajectory parameterization. The software is equipped with several options for numerical integration, and optimization solvers along with a Graphical User Interface (GUI) to make the process of designing and solving the OCPs smooth and seamless for users with minimum coding experience. We demonstrate with two benchmark numerical examples the procedure to generate constrained state and control trajectories using QuITO. Copyright © 2023, The Authors. All rights reserved.

关键词： Graphical user interfaces

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Consensus of Nonholonomic systems Using a Geometric PD controller

Consensus of Nonholonomic Systems Using a Geometric PD Contr...

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European control Conference (ECC)

作者： Harsh Oza Rama Seshan Ravi Banavar Systems & Control Engineering IIT Bombay Powai Mumbai India Dept of Electrical Engineering IIT Madras Chennai India

Formation control, incorporating the nonholonomic constraints upfront, is a challenging task. At the individual agent level, Brockett’s theorem states that nonholonomic systems cannot be stabilized to a point using smooth, and time-invariant feedback control law. We present a solution to the formation problem in a geometric framework by incorporating the constraint distribution at an individual agent level that obeys each agent’s nonholonomic constraints. The objective of the consensus is then tackled by introducing a suitable Morse function. Critical points of the chosen Morse function form a consensus manifold. We take inspiration from the consensus law on Euclidean space and draw a comparison. The negative gradient of the Morse function forms the proportional control leading the trajectory to the set of critical points which is same as the consensus manifold. In addition, we propose a corollary that enables a priori specified orientation regulation in a set of wheeled mobile robots. These findings are verified using several numerical experiments with random initial conditions

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Fraud Detection and Deterrence in Electronic Voting Machines: A Game-Theoretic Approach

Fraud Detection and Deterrence in Electronic Voting Machines...

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IEEE Conference on Decision and control

作者： Anuj S. Vora Ankur A. Kulkarni Delft Center for Systems and Control TU Delft Delft NL Systems and Control Engineering IIT Bombay Mumbai India

We study a setting where a detector wishes to detect and deter adversarial manipulation in an electronic voting machine. An adversary tries to win the election by tampering the votes while obfuscating its manipulation. We pose this problem as a game between the detector and the adversary and characterize the equilibrium payoffs for the players and the asymptotic nature of these payoffs. We find that if the detector is too cautious, then in equilibrium the adversary wins with a probability higher than its prior probability of winning. We derive an expression for the deterrence threshold, i.e., the minimum level of false-alarm that the detector should endure so that the adversary is not any better off by the manipulation. With this, asymptotically, the detector can ensure that the probability of missed-detection becomes zero by appropriately adjusting the rate of decay of probability of false-alarm. But if this rate of decay is too ‘fast’, then the adversary can get an arbitrarily high probability of winning in spite of having a vanishing prior probability of winning. We then extend the results to a setting where the detector has incomplete information about the adversary.

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Polyhedral study of a temporal rural postman problem: application in inspection of railway track without disturbing train schedules

arXiv

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arXiv 2024年

作者： Buriuly, Somnath Vachhani, Leena Ravitharan, Sivapragasam Sinha, Arpita Chauhan, Sunita CoE-OGE IIT Bombay India Systems and Control Engineering IIT Bombay India Department of Mechanical and Aerospace Engineering Monash University Australia Center for Equitable & Personalized Health Plaksha University India

The Rural Postman Problem with Temporal Unavailability (RPP-TU) is a variant of the Rural Postman Problem (RPP) specified for multi-agent planning over directed graphs with temporal constraints. These temporal constraints represent the unavailable time intervals for each arc during which agents cannot traverse the arc. Such arc unavailability scenarios occur in non-disruptive routing and scheduling of the instrumented wagons for inspecting railway tracks, without disturbing the train schedules, i.e. the scheduled trains prohibit access to the tracks in the signal blocks (sections of railway track separated by signals) for some finite interval of time. A three-index formulation for the RPP-TU is adopted from the literature. The three-index formulation has binary variables for describing the route information of the agents, and continuous non-negative variables to describe the schedules at pre-defined locations. A relaxation of the three-index formulation for RPPTRU, referred to as Cascaded Graph Formulation (CGF), is investigated in this work. The CGF has attributes that simplify the polyhedral study of time-dependent arc routing problems like RPP-TRU. A novel branch-and-cut algorithm is proposed to solve the RPP-TU, where branching is performed over the service arcs. A family of facet-defining inequalities, derived from the polyhedral study, is used as cutting planes in the proposed branch-and-cut algorithm to reduce the computation time by up to 48%. Finally, an application of this work is showcased using a simulation case study of a railway inspection scheduling problem based on Kurla-Vashi-Thane suburban network in Mumbai, India. An improvement of 93% is observed when compared to a Benders' decomposition based MILP solver from the literature. © 2024, CC BY.

关键词： Directed graphs

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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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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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Geometric Modelling and control of Flexible Serial Robot Links

Geometric Modelling and Control of Flexible Serial Robot Lin...

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European control Conference (ECC)

作者： Nishant Mittal Shreya Shrivastava Viyom Vivek José Ángel Acosta Ravi Banavar Electrical Engg. Dept. IIT Bombay Engg. Phy. Dept. IIT Bombay Systems & Control group IIT Bombay Dept. de Ingeniería de Sistemas y Automática Universidad de Sevilla Spain Systems & Control Engineering group IIT Bombay

The article presents the initial attempts to provide a geometric framework for modelling and control of flexible link robotic manipulators whose end-effector interacts with a compliant surface. The case study presented here restricts itself to planar flexible link manipulators. Ideas from Lie groups and Lie algebras have been employed to derive the forward and inverse kinematic maps, and their associated Jacobian. Finally we employ the geodesic equation to write down the comprehensive dynamical equations of the system. A geometrical interpretation of the Jacobian is presented and a velocity-level control law proposed earlier in literature is recast in the geometric language. Lastly we incorporate Christoffel symbols in the dynamic model of the flexible manipulator highlighting the underlying geometry. Using this framework, an existing velocity based control law is synthesized and simulated. Results demonstrate that the geometric framework yields a smoother and faster error convergence.

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