A Randomized Algorithm for Optimal PID Controllers

Abstract

A randomized algorithm is suggested for the syntheses of optimal PID controllers for MIMO coupled systems, where the optimality is with respect to the H ∞ -norm, the H 2 -norm and the LQR functional, with possible system-performance specifications defined by regional pole-placement. Other notions of optimality (e.g., mixed H 2 / H ∞ design, controller norm or controller sparsity) can be handled similarly with the suggested algorithm. The suggested method is direct and thus can be applied to continuous-time systems as well as to discrete-time systems with the obvious minor changes. The presented algorithm is a randomized algorithm, which has a proof of convergence (in probability) to a global optimum.