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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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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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Constrained trajectory synthesis via quasi-interpolation

Constrained trajectory synthesis via quasi-interpolation

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IEEE Conference on Decision and control

作者： Siddhartha Ganguly Nakul Randad Debasish Chatterjee Ravi Banavar Systems & Control Engineering IIT Bombay Mumbai India Department of Aerospace Engineering IIT Bombay Mumbai India

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

In this article we introduce QuITO — Quasi-Interpolation based Trajectory Optimization, a direct multiple shooting algorithm to solve a class of constrained nonlinear minimum energy optimal control problems. This technique is based on the theory of approximate approximations – a quasi-interpolation scheme. We parameterize the control trajectory using the quasi-interpolation formula, and we discretize the optimal control problem using the collocation points on a uniform cardinal grid, thereby transcribing the optimal control problem (OCP) into a nonlinear program (NLP). Several examples are provided to show the numerical fidelity of the algorithm.

关键词： Optimal control Approximation algorithms Trajectory optimization

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A Moreau Envelope Approach for LQR Meta-Policy Estimation

A Moreau Envelope Approach for LQR Meta-Policy Estimation

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IEEE Conference on Decision and control

作者： Ashwin Aravind Mohammad Taha Toghani César A. Uribe Centre for Systems and Control IIT Bombay Mumbai MH India Department of Electrical and Computer Engineering Rice University Houston TX USA

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

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.

关键词： Linear systems Uncertain systems Costs Uncertainty System realization Estimation Cost function Numerical models Trajectory Convergence

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Route planning for capacity restricted agents over railway network, without disrupting train schedules

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IFAC-PapersOnLine 2022年第1期55卷 38-45页

作者： Somnath Buriuly Leena Vachhani Arpita Sinha Sivapragasam Ravitharan Sunita Chauhan Somnath Buriuly is with the Systems and Control Engineering IIT Bombay India and Department of Mechanical and Aerospace Monash University Australia Dr Leena Vachhani is Professor at Systems and Control Engineering IIT Bombay India Dr Arpita Sinha is Professor at Systems and Control Engineering IIT Bombay India Mr Sivapragasam Ravitharan is Director at Monash Institute of Railway Technology Monash University Australia Prof Sunita Chauhan is Professor at Department of Mechanical and Aerospace Monash University Australia

Deploying mobile instrumentation for railway track inspection is a routing and scheduling problem, that can be benefited from plans which don’t disrupt regular train schedules. In this work, we avoid disrupting train schedules by modeling unavailability of railway tracks, thereby improving reliability without sacrificing on costs. The approach involves a novel mathematical formulation for C apacitated A rc R outing P roblem with T emporal restrictions due to arc U navailabilities (CARP-TU). In addition, we discuss the challenges in CARP-TU w.r.t sibling problems, and propose a suitable column generation algorithm for improving upper and lower bounds. The proposed algorithm is validated over few benchmark datasets, and then two variants of the proposed algorithm are compared to analyse the bound improvements w.r.t problem size.

关键词： Capacitated Arc Routing Problem Temporal Arc Unavailability Railway Robotics Column generation Dynamic Programming

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Dynamic consensus and adaptive bias compensation for multi-agent linear systems over directed networks

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IFAC-PapersOnLine 2023年第2期56卷 2626-2631页

作者： Maitreyee Dutta Elena Panteley Srikant Sukumar Antonio Loría Systems and Control Engineering Department IIT Bombay India Laboratoire des signaux et systèmes CNRS 3 Rue Joliot Curie 91192 Gif-sur-Yvette France

Biased measurements in an inter-networked systems can have severe repercussions in closed-loop stability of the individual systems and decelerate dynamical consensus among the interacting agents. Bias in the measurement, even constant, cannot be dealt with ad hoc techniques of robust control, in the presence of additive perturbations, because the control gain amplifies the disturbance. One way to account for the effect of measurement bias is then to rely on adaptive control. This has been done in the literature in the context of individual systems, but to the best of our knowledge not for multi-agent systems, while ensuring consensus control. In this paper we provide a model-reference-adaptive-control scheme to ensure dynamic consensus of generic (stabilizable) linear systems interconnected over directed graphs and under the influence of constant bias measurements. Our controller ensures global asymptotic stability of the synchronization manifold and convergence of the bias estimates.

关键词： Measurement bias directed graphs multi-agent systems linear systems Lyapunov stability

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