Design of a l1-optimal regulator: the limits of performance approach

Abstract

In this paper, the design of a l1-optimal regulator using the limits of performance [1] approach to constrain the magnitude of the control signal is proposed. We show that for the l1-optimal control case, performance indexes based on a weighted sum or weighted maximum of the process output and control output fail to achieve the objective of compromising between tight control and control effort. The limits of performance curve, which is a plot of the best achievable specifications with a given system and control configuration, on the other hand allows the designer to achieve appropriate compromise. We further show that the limits of performance curve is formed by a finite number of linear equations and its gradient is monotonically nondecreasing. A systematic method to construct the limits of performance curve is proposed.