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Relatively optimal control

Motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task, the concept of relative optimality, roughly optimality for a specific (nominal) plant initial condition, has been recently introduced. A relatively optimal control is a stabilizing controller such that, if initialized at its zero state, produces the optimal (constrained) behavior for the nominal initial condition of the plant (without feedforwarding and tracking the optimal trajectory). In this presentation we show that one of such controllers is linear, dead--beat, and its order is equal to the length of the horizon minus the plant order, thus of complexity which is known a--priori. The fact that the closed--loop plant has zero eigenvalues is associated with the fact that a zero--state terminal constraint is considered for the optimal trajectory. Then we discuss how to remove this assumption and we consider an optimal problem without zero terminal state. The stability of the closed--loop system can be achieved by assigning an arbitrary closed--loop characteristic stable polynomial to the plant. An explicit solution is provided. We discuss several applications of the technique such as the optimal arrival to an invariant target set and the constrained (relatively optimal) linear quadratic problem. We also show how to choose the characteristic polynomial in such a way that the constraints (which are enforced on a finite horizon) can be globally or ultimately satisfied. Although the technique is basically suitable for state feedback, we show how to extend it for the measurement feedback case, provided that a suitable observer initialization is possible.
Type of Seminar:
Public Seminar
Prof. Franco Blanchini
University of Udine, Italy
Jun 02, 2004   17:15

ETH Zentrum, Gloriastrasse 35, Building ETZ, Room E6
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Franco Blanchini was born on 29 December 1959, in Legnano (Italy). He received the Laurea degree in Electrical Engineering from the University of Trieste, Italy, in 1984. In 1985 he was Lecturer of Numerical Analysis at the Faculty of Science at the University of Udine, Italy. He was Research Associate of System Theory from 1986 to 1991. From November 1992 to October 2000, he was Associate Professor of Automatic Control at the Engineering Faculty of the University of Udine. Since November 2000 he is Professor of Automatic Control at the Engineering Faculty of the University of Udine. He is affiliated with the Department of Mathematics and Computer Science in Udine and he is Director of the Laboratory of System Dynamics of the Department. He was member of the program committees of the 1997 Conference on Decision and Control, S. Diego, California, of the 1999 Conference on Decision and Control, Phoenix, Arizona, of the 2001 Conference on Decision and Control, Orlando, Florida and of the 2003 Conference on Decision and Control, Maui Hawaii. He was co-author of the plenary lecture "Minicourse on Saturation in Control", at the 19th Benelux Meeting on Systems and Control, 2000. He was Chairman of the workshop on Uncertain Dynamical Systems of the IFAC Technical Committee on Robust Control, Cascais, Portugal, July 18-20, 2002. He has been nominated Program Vice-Chairman for the conference Joint CDC-ECC, Seville, Spain, December 2005. He is the recipient of 2001 ASME Oil & Gas Application Committee Best Paper Award as a co-author of the article ``Experimental evaluation of a High--Gain Control for Compressor Surge Instability". He is the recipient of the 2002 IFAC prize survey paper award as author or the article "Set Invariance in Control--a survey", Automatica, November, 1999. He was nominated Senior Member IEEE in 2003. He is Associate Editor of Automatica since 1996.