On the inverse optimal control problem

The objeot of this study is to find out a corre-lation between the figures of merit of a linear control plant and the weighting matrix Q.This problem has been viewed both in the time and frequ ency domain.The main points that be studied where :-Th elimits of op timality of a linear contro 1 system.A guiding rule for the choice of the figures of merit of the closed loop system.The effect of the diagonal elements of the Q matrix on the response of the system.Some recommendations when choosing the wcighting matrix of the state.Solving the problem in the time domain we found that the use of the matrixBicatti equation, leads to a trial anderror technique.The choice of the closed loop eigen values at ran-dom gives a negative weighting matrix Q. som e boundan csexists in the choice of these vaLucs, that cannot be visuautized through the solution of the MatriX Ricatti equa-tion.Using the frequency characterisation of optimality as deduced by Kalman we found that the limits ef optima- l1tyof a linear control plant are delimited by :~