VARIATIONAL APPROACH FOR BRACHISTOCHRONE AND OPTIMAL CONTROL PROBLEMS

Abstract

In this project work a review of the salient features of classical control system design are elegantly discussed along with the limitations which necessitated the evolution of modern optimal control system. Design of classical control system generally requires meeting the desired specifications in time and frequency domain approach e.g. rise time, peak overshoot, settling time, steady state error etc in time domain and gain margin, phase margin, bandwidth, resonant frequency, resonant peak magnitude etc in frequency domain respectively. Minimization of performance measure which is building block of optimal control problem has been explained in a juxtaposed manner by variational and dynamic programming method. Brachistochrone problem which is said to be the mother of variational approach for optimal control problem has been heuristically delved into. Analogical evolution of variational calculus from differential calculus has been meticulously expatiated in a coherent and well organized ...