Iterative Identification and Control

In this chapter, we first review the changing role of the model in control system design over the last fifty years. We then focus on the development over the last ten years of the intense research activity and on the important progress that has taken place in the interplay between modelling, identification and robust control design. The major players of this interplay are presented; some key technical difficulties are highlighted, as well as the solutions that have been obtained to conquer them. We end the chapter by presenting the main insights that have been gained by a decade of research on this challenging topic. 1.1 A not-so-brief Historical Perspective There are many ways of describing the evolution of a field of science and engineering over a period of half a century, and each such description is necessarily biased, oversimplified and sketchy. But I have always learned some new insight from such sketchy descriptions, whoever the author. Thus, let me attempt to start with my own modest perspective on the evolution of modelling, identification and control from the post-war period until the present day. Until about 1960, most of control design was based on model-free methods. This was the golden era of Bode and Nyquist plots, of Ziegler-Nichols charts and lead/lag compensators, of root-locus techniques and other graphical design methods. From model-free to model-based control design The introduction of the parametric state-space models by Kalman in 1960, together with the solution of optimal control and optimal filtering problems in a Linear Quadratic Gaussian (LQG) framework [90,91] gave birth to a tremendous development of model-based control design methods. Successful applications abounded, particularly in aerospace, where accurate models were readily available. From modelling to identification The year 1965 can be seen as the founding year for parametric identification with the publication of two milestone papers. The paper [80] set the stage for state-space realisation theory which, twenty-five years later, became the major stepping stone towards what is now called subspace identification. The paper [12] proposed a Maximum Likelihood (ML) framework for the identification of input-output (i. e., ARMAX) models that gave rise to the celebrated