Seminar Title
Linear Control System: A Superspace View
Seminar Type
Progress Seminar
Department
Mathematics
Speaker Name
Aroonima Sahoo ( Rollno : 519ma2007)
Speaker Type
Student
Venue
Department Seminar Room
Date & Time
16 Aug 2022 17:00
Contact
Prof. Kishor Chandra Pati
Abstract

A control system deals with a system that commands, or regulates the behavior of inputs to achieve a desired result. So, control problems are omnipresent. Moreover, the dynamics of almost all phenomena can be expressed using differential equations. In modern control theory, a control system is represented using coupled first order ordinary differential equations. A general state-space representation of a linear control system on a vector space is given by 𝑋̇ = 𝐴(𝑡)𝑋(𝑡) + 𝐵(𝑡)𝑢(𝑡), where 𝐴 is the state matrix, 𝐵 is the input matrix, 𝑋 is the state vector and 𝑢 is the control input vector. In general, the state-space of a linear control system is a vector space on ℝ or ℂ. But here, we assume the state-space to be a superspace, which is analogous to vector space over an anti-commuting algebra, called Grassmann algebra. Controllability and Observability are two of the major problems of a control system, which can be determined using the infamous Kalman&rsquos rank criterion. So, we have extended the rank criterion for linear control system on superspace.