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Estimates on the domain of validity for Lyapunov-Schmidt reduction

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Estimates on the domain of validity for Lyapunov-Schmidt red...

IEEE Conference on Decision and control

作者： Pranav Gupta Anastasia Bizyaeva Ravi Banavar Mechanical Engineering Indian Institute of Technology Bombay Mumbai Maharashtra India Sibley School of Mechanical and Aerospace Engineering Cornell University Ithaca NY USA Systems and Control Engineering Indian Institute of Technology Bombay Mumbai Maharashtra India

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

Lyapunov-Schmidt reduction is a dimensionality reduction technique in nonlinear systems analysis that is commonly utilised in the study of bifurcation problems in high-dimensional systems. The method is a systematic procedure for reducing the dimensionality of systems of algebraic equations that have singular points, preserving essential features of their solution sets. In this article, we establish estimates for the region of validity of the reduction by leveraging recently derived bounds on the Implicit Function Theorem. We then apply these bounds to an illustrative example of a two-dimensional system with a pitchfork bifurcation.

关键词： Dimensionality reduction Systematics Computational modeling Neural networks Bifurcation Aerospace electronics Mathematical models Dynamical systems Nonlinear systems

Cooperative Nonlinear Aircraft Defense Using Super Twisting Algorithm with State Constraints

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Cooperative Nonlinear Aircraft Defense Using Super Twisting ...

IEEE Conference on Decision and control

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

This paper addresses the problem of cooperative guidance design for aircraft defense systems involving a target, a defender, and an attacker, using a super-twisting algorithm and barrier Lyapunov function. The system dynamics involve unknown functions, which are treated like disturbances and estimated using an observer. Imposing practical assumptions on the lateral accelerations of the vehicles, we propose a robust guidance design also to constrain the system states by definite bounds. We derived the controller using generalized triangle guidance concepts that provide these bounds for the states. Guidance commands are derived without any kind of linearizations that enable a wider domain of applicability of the proposed approach. The convergence is analyzed using a Lyapunov function. Simulation results are presented to study the efficacy of the proposed approach.

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ReactAIvate: A Deep Learning Approach to Predicting Reaction Mechanisms and Unmasking Reactivity Hotspots

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arXiv 2024年

作者： Hoque, Ajnabiul Das, Manajit Baranwal, Mayank Sunoj, Raghavan B. Department of Chemistry Indian Institute of Technology Bombay India Department of Systems & Control Engineering Indian Institute of Technology India Tata Consultancy Services Research Mumbai India Centre for Machine Intelligence and Data Science Indian Institute of Technology Bombay India

A chemical reaction mechanism (CRM) is a sequence of molecular-level events involving bond-breaking/forming processes, generating transient intermediates along the reaction pathway as reactants transform into products. Understanding such mechanisms is crucial for designing and discovering new reactions. One of the currently available methods to probe CRMs is quantum mechanical (QM) computations. The resource-intensive nature of QM methods and the scarcity of mechanism-based datasets motivated us to develop reliable ML models for predicting mechanisms. In this study, we created a comprehensive dataset with seven distinct classes, each representing uniquely characterized elementary steps. Subsequently, we developed an interpretable attention-based GNN that achieved near-unity and 96% accuracy, respectively for reaction step classification and the prediction of reactive atoms in each such step, capturing interactions between the broader reaction context and local active regions. The near-perfect classification enables accurate prediction of both individual events and the entire CRM, mitigating potential drawbacks of Seq2Seq approaches, where a wrongly predicted character leads to incoherent CRM identification. In addition to interpretability, our model adeptly identifies key atom(s) even from out-of-distribution classes. This generalizabilty allows for the inclusion of new reaction types in a modular fashion, thus will be of value to experts for understanding the reactivity of new molecules. © 2024, CC BY.

关键词： Reaction intermediates

Algorithmic construction of Lyapunov functions for continuous vector fields via convex semi-infinite programs

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arXiv 2023年

作者： Gupta, Raavi Chattopadhyay, Sameep Paruchuri, Pradyumna Chatterjee, Debasish Department of Electrical Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India Systems & Control Engineering Indian Institute of Technology 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 [DACC22] 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 *** Codes 93D05, 93D20, 65K05, 65P40 © 2023, CC BY-NC-ND.

关键词： Lyapunov functions

Informativeness and Trust in Bayesian Persuasion

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SSRN

SSRN 2024年

作者： Deori, Reema Kulkarni, Ankur A. Center for Systems and Control Indian Institute of Technology Bombay Powai Maharashtra Mumbai400076 India

A persuasion policy successfully persuades an agent to pick a particular action only if the information is designed in a manner that convinces the agent that it is in their best interest to pick that action. Thus, it is natural to ask, what makes the agent trust the persuader's suggestion?We study a Bayesian persuasion interaction between a sender and a receiver where the sender has access to private information about a source and the receiver attempts to recover this information from messages sent by the sender. The sender crafts these messages in an attempt to maximize its utility which depends on the source symbol and the symbol recovered by the receiver. Our goal is to characterize the min-max equilibrium utility of the sender, called the \textit{Stackelberg game value}, and the amount of true information revealed by the sender during *** find that the Stackelberg game value is given by the optimal value of a \textit{linear program} on probability distributions constrained by certain \textit{trust constraints}. These constraints encode that any signal in a persuasion strategy must contain more truth than untruth and thus impose a fundamental bound on the extent of obfuscation a sender can perform in any attempt to persuade the *** define \textit{informativeness} of the sender as the minimum value of the expected number of symbols truthfully revealed by the sender in any accumulation point of a sequence of $\varepsilon$-equilibrium persuasion strategies, and show that it is given by the optimal value of another linear program. Informativeness gives a fundamental bound on the amount of information the sender must reveal to persuade a receiver. Closed form expressions for the Stackelberg game value and the informativeness are presented for structured utility functions. This work generalizes our previous work~\cite{deori2022information} where the sender and the receiver were constrained to play only deterministic strategies and a similar notion of

关键词： Linear programming

Informativeness and Trust in Bayesian Persuasion

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arXiv 2024年

作者： Deori, Reema Kulkarni, Ankur A. Center for Systems and Control Indian Institute of Technology Bombay Powai Maharashtra Mumbai400076 India

A persuasion policy successfully persuades an agent to pick a particular action only if the information is designed in a manner that convinces the agent that it is in their best interest to pick that action. Thus, it is natural to ask, what makes the agent trust the persuader’s suggestion? We study a Bayesian persuasion interaction between a sender and a receiver where the sender has access to private information about a source and the receiver attempts to recover this information from messages sent by the sender. The sender crafts these messages in an attempt to maximize its utility which depends on the source symbol and the symbol recovered by the receiver. Our goal is to characterize the min-max equilibrium utility of the sender, called the Stackelberg game value, and the amount of true information revealed by the sender during persuasion. We find that the Stackelberg game value is given by the optimal value of a linear program on probability distributions constrained by certain trust constraints. These constraints encode that any signal in a persuasion strategy must contain more truth than untruth and thus impose a fundamental bound on the extent of obfuscation a sender can perform in any attempt to persuade the receiver. We define informativeness of the sender as the minimum value of the expected number of symbols truthfully revealed by the sender in any accumulation point of a sequence of Ε-equilibrium persuasion strategies, and show that it is given by the optimal value of another linear program. Informativeness gives a fundamental bound on the amount of information the sender must reveal to persuade a receiver. Closed form expressions for the Stackelberg game value and the informativeness are presented for structured utility functions. This work generalizes our previous work [1] where the sender and the receiver were constrained to play only deterministic strategies and a similar notion of informativeness was characterized. Comparisons between the previous a

关键词： Linear programming

Nonlinear control of a Laboratory Gas Turbine Engine with Uncertain System Dynamics

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Nonlinear Control of a Laboratory Gas Turbine Engine with Un...

2021 International Symposium of Asian control Association on Intelligent Robotics and Industrial Automation, IRIA 2021

作者： Singh, Richa Nandy, Subhashis Maity, Arnab Nataraj, P.S.V. Indian Institute of Technology Bombay Department of Aerospace Engineering Powai400076 India Indian Institute of Technology Bombay IDP in Systems and Control Engineering Powai400076 India

ISBN: (纸本)9781665433235

A sliding mode control (SMC) design approach is presented in this paper to ensure the robust tracking of a laboratory-based gas turbine engine (GTE) subjected to noise and uncertainties in parameters and disturbances. The design of SMC is defined as the main objective to compute the requirement of fuel flow for the engine such that the shaft speed of the GTE tracks its commanded signal with minimum control effort while adhering to physical constraints. Further, an approximation task of the discontinuous signum function is performed by a saturation function to attenuate the chattering phenomena. The proposed control design is then verified on a validated mathematical model of GTE subjected to uncertainties and noise. The closed-loop GTE responses truly accomplish the superiority of the proposed design approach of SMC control in achieving satisfactory tracking performance of the gas turbine engine. © 2021 IEEE.

关键词： Sliding mode control

Robustification of Unscented Kalman Filtering to Identify Faults in Gas Turbine Engine

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IFAC-PapersOnLine 2022年第1期55卷 826-831页

作者： Subhashis Nandy Richa Singh Arnab Maity P.S.V. Nataraj Department of Aerospace Engineering Indian Institute of Technology Bombay Mumbai - 400076 India IDP in Systems and Control Engineering Indian Institute of Technology Bombay Mumbai - 400076 India

A methodology is proposed to improve the robustification of the Unscented Kalman Filtering by adjusting the measurement noise covariance matrix by introducing two adaptive factors. The combined effect of the two adaptive factors helps to identify and filter the outliers more prominently. Improvement in the proposed robust UKF algorithm is established by analyzing the percentage reduction of accumulation error for different conditions with the larger measurement noise covariance. In addition, a method of fault identification of gas turbine engines is developed by the proposed robust UKF approach in the presence of system and measurement noises. The proposed fault identification method deals with the analysis of the residual signature of different states along with the cost function of the derived algorithm. Different component and sensor anomalies are introduced in the nonlinear dynamic model of the gas turbine engine to produce the faulty situations. The deviations in performances are compared with the nominal behavior to obtain the residual signature. A comparative study is performed to identify the faulty scenarios.

关键词： Unscented Kalman filtering Robustification Component faults Sensor faults Residual Cost function Fault identification

Vision-based indoor localization of nano drones in controlled environment with its applications

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arXiv 2024年

作者： Singh, Simranjeet Kumar, Amit Chemban, Fayyaz Pocker Fernandes, Vikrant Penubaku, Lohit Arya, Kavi Electrical Engineering Department Indian Institute of Technology Bombay Mumbai India Embedded Real-Time Systems e-Yantra Lab Indian Institute of Technology Bombay Mumbai India Computer Science and Engineering Department Indian Institute of Technology Bombay Mumbai India

Navigating unmanned aerial vehicles in environments where GPS signals are unavailable poses a compelling and intricate challenge. This challenge is further heightened when dealing with Nano Aerial Vehicles (NAVs) due to their compact size, payload restrictions, and computational capabilities. This paper proposes an approach for localization using off-board computing, an off-board monocular camera, and modified open-source algorithms. The proposed method uses three parallel proportional-integral-derivative controllers on the off-board computer to provide velocity corrections via wireless communication, stabilizing the NAV in a custom-controlled environment. Featuring a 3.1cm localization error and a modest setup cost of 50 USD, this approach proves optimal for environments where cost considerations are paramount. It is especially well-suited for applications like teaching drone control in academic institutions, where the specified error margin is deemed acceptable. Various applications are designed to validate the proposed technique, such as landing the NAV on a moving ground vehicle, path planning in a 3D space, and localizing multi-NAVs. The created package is openly available at https://***/simmubhangu/eyantra drone to foster research in this field. © 2024, CC BY.

关键词： Drones