Polynomial Control: Past, Present and Future

Polynomial Control: Past, Present and Future

Vladimir Kucera

President, International Federation of Automatic Control (IFAC)
Dean, Faculty of Electrical Engineering, Czech Technical Univ., Prague

Tuesday 7 June, 11am

UTA Campus room NH 111, Nedderman Hall

Polynomial techniques have made important contributions to systems and control theory. Engineers in industry often find polynomial and frequency domain methods easier to utilize than state equation based techniques. Control theorists show that results obtained in isolation using either approach are in fact closely related.

Polynomial system description provides input-output models for linear systems with rational transfer functions. These models display two important system properties, namely poles and zeros, in a transparent manner. A performance specification in terms of polynomials is natural in many situations, see pole allocation techniques.

A specific control system design technique, called polynomial equation approach, was developed in the 1960s and 1970s. The distinguishing feature of this technique is a reduction of controller synthesis to a solution of linear polynomial equations of specific (Diophantine or Bezout) type.

In most cases, control systems are designed to be stable and to meet additional specifications, such as optimality and robustness. It is therefore natural to design the systems step by step: stabilization first, then the additional specifications each at a time. For this it is obviously necessary to have any and all solutions of the current step available before proceeding any further.

This motivates the need for a parametrization of all controllers that stabilize a given plant. In fact this result has become a key tool for the sequential design paradigm. The additional specifications are met by selecting an appropriate parameter. This is simple, systematic, and transparent. However, the strategy suffers from an excessive grow of the controller order.

The lecture is a guided tour through the polynomial control system design. The origins of the parametrization of stabilizing controllers, called Youla or Youla-Kucera parametrization, are explained. Historical and personal notes are added. Standard results on pole placement and H2 control are summarized. New and exciting applications of the parametrization result are then discussed: stabilization subject to input constraints, output overshoot reduction, fixed order controller design, and robust stabilization.

Vladimír Kučera was born in Prague, Czech Republic, in 1943. He graduated in Electrical Engineering from the CzechTechnicalUniversity in Prague in 1966, and received the CSc. and DrSc. Degrees in Control Engineering from the Czechoslovak Academy of Sciences in 1970 and 1979, respectively.

The research interests of V. Kučera include linear systems, optimal and robust control. He has contributed to the theory of the Riccati equation, pioneered the use of polynomial equations in control system design, and paved the way to the parametrization of all stabilizing controllers.

From 1970 to 1990 he was a Research Scientist, and from 1990 to 1998 the Director of the Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic. Since 1995 he has been Professor of Control Engineering, and since 2000 the Dean of the Faculty of Electrical Engineering, CzechTechnicalUniversity in Prague.

He held visiting positions at the National Research Council, Ottawa, Canada (1970-1971), University of Florida, Gainesville, U.S.A. (1977), Ecole Nationale Supérieure de Mécanique, Nantes, France (1981-1982), Australian National University, Canberra, Australia (1984), Uppsala Universitet, Sweden (1989), Eidgenössische Technische Hochschule, Zürich, Switzerland (1992), Politecnico di Milano, Italy (1995), and was Nippon Steel Professor at the Chair of Intelligent Control, Tokyo Institute of Technology, Japan, in 1994.

V. Kučera is the author of four books, including Discrete Linear Control: The Polynomial Equation Approach (Wiley, 1979) and Analysis and Design of Discrete Linear Control Systems (Prentice-Hall, 1991), and published 250 research papers. He is President of IFAC, Fellow of IEEE, Fellow of IEE, and Vice-President of the CzechAcademy of Engineering. He received many awards, including the National Prize of the CzechRepublic in 1989 and Automatica Best Paper Award in 1990. He is an Honorary Professor at the NortheasternUniversity, Shenyang, China (1996) and received a Doctor honoris causa degree from Université Paul Sabatier, Toulouse (2003).