Finite Dimensional Control Theory

Chhatria, Balakrishna (2019) Finite Dimensional Control Theory. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Balakrishna Chhatria (14MS055)) 14MS055.pdf - Submitted Version Restricted to Repository staff only Download (366kB)

Abstract

Control theory is the study of the dynamics of a control system where one can use suitable controls to get the desired result. Controllability problems and the stabilization problems of control system are one of the most common ones. Here we will study about finite-dimensional linear control system. In chapter 2 we will study about the finite dimensional linear time invariant control system. We will see some conditions regarding the controllability of the control system. We will encounter the "Kalman rank condition", which can be used easily to check wheather a linear finite dimensional time invariant control system is controllable or not. In chapter 3 we will get idea about linear finite dimensional time-varying control system. Necessary and suficient condition for controllability and Kalman type condition for controllabilty , we will study. In chapter 4 we get to know about some scenario where we can get the local controllability of the non-linear finite dimensional control system. Using the linearized system we will obtain the local controllability. The methods that we studied in the chapter 4 will not suffice in many nonlinear control system to get the local controllability. So we study two different methods "Return method" and "Power series expansion method" in chapter 5 and chapter 6 respectively which will help us to recover local controllabilty in some cases where the method in chapter 4 falter. At last we study a method by JEAN-MICHEL CORON AND IVONNE RIVAS where we get to construct explicit time varying feedback law which will stabilize some class of control system.

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