Control of Differential Equations: ODE, Transport Equation, and Wave Equation

Jena, Vaibhav Kumar (2017) Control of Differential Equations: ODE, Transport Equation, and Wave Equation. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Vaibhav Kumar Jena (12MS065)) MS_dissertation_Vaibhav_Kumar_Jena.pdf - Submitted Version Restricted to Repository staff only Download (629kB)

Abstract

The work in this thesis consists of results in control theory of differential equations, namely that of ordinary differential equation, transport equation, wave equation, and wave equation with nonlocal spatial integral term. For control of ODE, an equivalent criteria known as Kalman’s condition is provided, which involves calculating the rank of a special matrix derived from the ODE itself. For transport equation, controllability is shown by two methods- by explicit solution method and by using duality of controllability and observability. For the case of wave equation, we use Fourier series and multiplier method to prove controllability. Finally, for the non-local term wave equation we again use duality method. Here observability inequality is proved by contradiction and a so called compactness uniqueness argument. We also present the results related to the existence and uniqueness of solution for linear ODE and linear PDEs of hyperbolic type namely, transport equation, wave equation, and non local term wave equation.

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