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Online Course

Nonlinear System Analysis

Indian Institute of Technology Madras and NPTEL via Swayam

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Overview

All systems are inherently nonlinear in nature. This course deals with the analysis of nonlinear systems. The need for special tools to analyze nonlinear systems arises from the fact that the principle of superposition on which linear analysis is based, fails in the nonlinear case. The course exposes the students to various tools to analyze the behaviour of nonlinear systems, culminating in the stability analysis, which is of paramount importance in control systems.     INTENDED AUDIENCE :PhD, MS/M. Tech/ ME, Senior Undergraduate students from EE, ME, AE, PH PRE- REQUISITES : Undergrad control engineering, basic knowledge of differential equations and linear algebra is highly desirable. SUPPORT INDUSTRY : Any robotics, space and defence related industries

Syllabus

COURSE LAYOUT Week 1 : Why nonlinear systems? - Non-linear Models of Physical Systems Week 2 : Mathematical Preliminaries: Finite dimensional normed spaces, Euclidean space and its topology Week 3 : Infinite dimensional Banach spaces - Contraction mapping theorem Week 4 : Existence and Uniqueness results for solutions to non linear ODEs Week 5 : ODEs as vector fields - One dimensional systems - Phase portrait of second order linear systems - Equilibrium points, linearization and their classification Week 6 : Examples: Simple pendulum, Bead on a hoop, Lotka-Volterra models for predation and competition, biological transcriptional system, van der Pol oscillator and conservative systems, non linear circuits - Limit cycles Week 7 : Bifurcations of two dimensional flows: Saddle-node, pitchfork, transcritical and Hopf - their normal forms Week 8 : Notions of stability - Lyapunov and LaSalle’s theorems Week 9 : Finding Lyapunov functions: Linear systems, variable gradient method - Center Manifold Theorem Week 10 : Physical Non-linearities - Interconnections and feedback - Aizermann’s conjecture - Passivity Week 11 : PR systems - Dissipation equality - Passive filters Week 12 : KYP Lemma - Popov and circle criterion

Taught by

Prof. Ramkrishna Pasumarthy, Prof. Arunkumar D Mahindrakar

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