Robust Control and H-Infinity-Optimization - Tutorial Paper
Robust control systems may successfully be designed by ~'=-optimization, in particular, by reformulating the design problem as a mixed sensitivity problem. Key Words--~=-optimal control; robust control.
Abstract--The paper presents a tutorial exposition of
~=-optimal regulation theory, emphasizing the relevance of the mixed sensitivity problem for robust control system design. 1. INTRODUCTION
THE INVESTIGATION OF ~®-optimization of control systems began in 1979 with a conference paper by
Zames (1979), who considered the minimization of the oo-norm of the sensitivity function of a single-input-single-output linear feedback system.
The work dealt with some of the basic questions of
"classical" control theory, and immediately caught a great deal of attention. It was soon extended to more general problems, in particular when it was recognized that the approach allows dealing with robustness far more directly than other optimization methods.
The name "~K~-optimization" is somewhat unfortunate.
~® is one member of the family of spaces introduced by the mathematician Hardy. It is the space of functions on the complex plane that are analytic and bounded in the right-half plane. The space plays an important role in the deeper mathematics needed to solve K-optimal control problems. This paper presents a tutorial exposition of the subject. The emphasis is on explaining the relevance of K-optimization for control engineering. The paper presents few new results, and does not at all do justice to the extensive theoretical and mathematical literature on the subject. The presentation is limited to single-input-single-output (SISO) control systems.
Many of the arguments carry over to the multi-input-
* Received 6 February 1992; revised 6 July 1992; received in final form 23 August 1992. The original version of this paper was presented at the IFAC Symposium on Design
Methods of Control Systems which was held in Ziirich,
Switzerland during
Abstract--The paper presents a tutorial exposition of
~=-optimal regulation theory, emphasizing the relevance of the mixed sensitivity problem for robust control system design. 1. INTRODUCTION
THE INVESTIGATION OF ~®-optimization of control systems began in 1979 with a conference paper by
Zames (1979), who considered the minimization of the oo-norm of the sensitivity function of a single-input-single-output linear feedback system.
The work dealt with some of the basic questions of
"classical" control theory, and immediately caught a great deal of attention. It was soon extended to more general problems, in particular when it was recognized that the approach allows dealing with robustness far more directly than other optimization methods.
The name "~K~-optimization" is somewhat unfortunate.
~® is one member of the family of spaces introduced by the mathematician Hardy. It is the space of functions on the complex plane that are analytic and bounded in the right-half plane. The space plays an important role in the deeper mathematics needed to solve K-optimal control problems. This paper presents a tutorial exposition of the subject. The emphasis is on explaining the relevance of K-optimization for control engineering. The paper presents few new results, and does not at all do justice to the extensive theoretical and mathematical literature on the subject. The presentation is limited to single-input-single-output (SISO) control systems.
Many of the arguments carry over to the multi-input-
* Received 6 February 1992; revised 6 July 1992; received in final form 23 August 1992. The original version of this paper was presented at the IFAC Symposium on Design
Methods of Control Systems which was held in Ziirich,
Switzerland during