NCMW - Control Theory for Differential Equations (2022)

Venue: IISER, Kolkata

Dates: 28 Nov 2022 to 10 Dec 2022

Convener(s)

This NCMW aims to introduce the participants to the control theory for systems governed by ordinary differential equations (ODE) . The motivation comes from the need to understand and control the differential equations modeling various physical phenomena. The controllability problem, generally speaking, is to move a dynamical system by means of suitable control (input), from one state to the desired state in finite time, whereas stabilizability refers to the system being brought to rest or an equilibrium state as time tends to infinity.In the first week we plan to discuss some topics from existence and stability for linear and nonlinear ODE, that are required for the subsequent lectures. In the second week, we introduce the notion of controllability and stabilizability for the finite dimensional linear systems and establish several criteria and techniques to check controllability or stabilizability of a system. At the end of second week, we will focus on controllability and stabilizability of some nonlinear differential equations using various new methods, like Iterated Lie brackets technique and phantom tracking method (as explained in the book and recent papers of Jean Michel Coron). These methods have wide ranging applicationsin current research on control of Partial Differential Equations, to be covered in a later workshop.