Seminář Decoupling - Open Problem and Original Solution

Lektor: 

prof. Ing. Vladimír Kučera, DrSc., dr. h. c. Czech Institute of Informatics, Robotics, and Cybernetics, Czech Technical University, Prague

Datum akce: 
Pátek, 3. Listopad 2017 - 9:00 - 12:00

This seminar is intended for the enthusiasts in linear systems and control.

A solution will be presented to the long-standing open problem of linear systems theory – diagonal decoupling by static-state feedback. The earliest known investigation of system decoupling dates back to 1934, a state space formulation of the problem appeared in 1964, and a solution for square and invertible systems followed in 1967. All past solutions were obtained under restrictive assumptions on system and feedback such as same number of inputs and outputs or specific internal couplings. It was Vladimír Kučera who resolved the unrestricted problem in 2017.

Decoupling is a problem of compensating a complex multi-input multi-output system in such a way that each system output is independently controlled by one system input and not influenced by the other inputs. The system is assumed to be linear, time-invariant, and giving rise to a proper rational transfer function matrix. Decoupling can always be achieved using dynamic compensation, which increases the order of the system. The static-state feedback, however, does not increase the order and therefore may involve only the internal dynamics.

The mechanisms for the comprehension of the solvability of this very complex problem are presented for the very first time. The formulation avoids restrictive hypotheses concerning system and decoupling feedback. The existence of a solution is shown to depend on the existence of three lists of nonnegative integers conditioned by and only by system invariants with respect to the transformations permitted while decoupling. The solvability conditions are necessary and sufficient. The necessity proof is based on existence results whereas the sufficiency proof is based on constructive arguments and provides an algorithm to determine a decoupling control law.

When a system is decoupled, it is broken down into single-input single-output noninteracting subsystems. That is why decoupling is also called noninteractive control. Such a structure is desirable in a number of applications, since considerable computational as well as conceptual simplicity can be accrued for subsequent system design. Indeed, the interactive loops are the source of major complications, whereas the decoupled structure is amenable to simple single-loop control system design techniques.

The seminar is divided in two parts. Part I includes an historical perspective, the problem formulation, and mathematical preliminaries. Part II includes a solvability condition, a synthesis of decoupling feedback, and illustrative examples. Part I is a prerequisite for Part II.


 

Vladimír Kučera  was born in Prague, Czech Republic in 1943. He graduated from the Czech Technical University in Prague and obtained his research degrees from the Czechoslovak Academy of Sciences.

Since 1967 he has been Researcher at the Institute of Information Theory and Automation, one of the research institutes of the Academy of Sciences of the Czech Republic. Since 1998 he has been a Professor of Control Engineering at the Czech Technical University in Prague. Currently he serves the university as Distinguished Researcher and Vice Director of the newly established Czech Institute of Informatics, Robotics, and Cybernetics. He held many visiting positions at prestigious European, American, Asian, and Australian universities. His research interests include linear systems and control theory. He contributed to the theory of Riccati equations and pioneered the use of polynomial equations in the synthesis of linear control systems. His best-known result is the parameterization of all controllers that stabilize a given plant, known as the Youla-Kučera parameterization, which has become a new paradigm in robust and optimal control.

Prof. Kučera is a Life Fellow of IEEE and an Advisor, Fellow, and a former President of IFAC. His awards include the National Prize of the Czech Republic in 1989 and the Automatica Prize Paper Award in 1990. He is an Honorary Professor of the Northeastern University, Shenyang, China, and received honorary doctorates from Université Paul Sabatier, Toulouse, France and Université Henri Poincaré, Nancy, France. In 2006, he was appointed Chevalier dans l’ordre des Palmes académiques by the French Government.

Místo konání: 

Ústav automatizace a měřicí techniky
FEKT VUT v Brně
Technická 12
612 00 Brno
(zasedací místnost ÚAMT SD3.102)

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Kontakt: 

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