Convergence to the Globally Optimal Controller

Abstract

Starting in Chap. 5, the particularities of the H ₂ cost functions that are minimized in data-driven control design are explored. Convergence to the globally optimal controller is sought in a data-driven control design, so the properties of the cost function are analyzed with respect to this goal. A number of properties of these particular cost functions and of some basic optimization algorithms when applied to them are presented in this chapter. From these properties, guidelines for the optimization are provided, involving the choice of the optimization algorithm and the automatic selection of step sizes. Step size policies that speed up the convergence to the global minimum are presented, and a general choice of optimization algorithm is advocated: start with the steepest descent then switch to the Newton-Raphson method when sufficiently close to the global optimum. A case study is presented to illustrate the convergence properties of the various algorithmic choices. The theoretical results also set the stage for the synthetic procedures to be presented in Chap. 6.