H(infinity)-Optimal Control and Related ...

1. Front Matter

   Pages i-xii

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2. A General Introduction to Minimax (H∞-Optimal) Designs

   • Tamer Başar, Pierre Bernhard

   Pages 1-12

3. Basic Elements of Static and Dynamic Games

   • Tamer Başar, Pierre Bernhard

   Pages 13-27

4. The Discrete-Time Minimax Design Problem With Perfect State Measurements

   • Tamer Başar, Pierre Bernhard

   Pages 28-71

5. Continuous-Time Systems With Perfect State Measurements

   • Tamer Başar, Pierre Bernhard

   Pages 72-113

6. The Continuous-Time Problem With Imperfect State Measurements

   • Tamer Başar, Pierre Bernhard

   Pages 114-150

7. The Discrete-Time Problem With Imperfect State Measurements

   • Tamer Başar, Pierre Bernhard

   Pages 151-179

8. Performance Levels For Minimax Estimators

   • Tamer Başar, Pierre Bernhard

   Pages 180-193

9. Appendix A: Conjugate Points

   • Tamer Başar, Pierre Bernhard

   Pages 194-207

10. Appendix B: Danskin’s Theorem

    • Tamer Başar, Pierre Bernhard

    Pages 208-212

11. References

    • Tamer Başar, Pierre Bernhard

    Pages 213-220

12. Back Matter

    Pages 221-225

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One of the major concentrated activities of the past decade in control theory has been the development of the so-called "HOO-optimal control theory," which addresses the issue of worst-case controller design for linear plants subject to unknown additive disturbances, including problems of disturbance attenuation, model matching, and tracking. The mathematical OO symbol "H " stands for the Hardy space of all complex-valued functions of a complex variable, which are analytic and bounded in the open right­ half complex plane. For a linear (continuous-time, time-invariant) plant, oo the H norm of the transfer matrix is the maximum of its largest singular value over all frequencies. OO Controller design problems where the H norm plays an important role were initially formulated by George Zames in the early 1980's, in the context of sensitivity reduction in linear plants, with the design problem posed as a mathematical optimization problem using an (HOO) operator norm. Thus formulated originally in the frequency domain, the main tools used during the early phases of research on this class of problems have been operator and approximation theory, spectral factorization, and (Youla) parametrization, leading initially to rather complicated (high-dimensional) OO optimal or near-optimal (under the H norm) controllers.

• control
• control theory
• Mathematica
• measurement
• optimal control
• optimization
• Tracking

• Coordinated Science Laboratory, University of Illinois, Urbana, USA

  Tamer Başar

• Inria, Unité de Recherche Sophia-Antipolis, Valbone Cedex, France

  Pierre Bernhard

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