Open Problems in Mathematical Systems and Control Theory

1. Front Matter

   Pages i-xii

   PDF

2. Uniform asymptotic stability of linear time-varying systems

   • Dirk Aeyels, Joan Peuteman

   Pages 1-5

3. Positive system realizations

   • Brian D. O. Anderson

   Pages 7-10

4. System approximation in the 2-norm

   • A. C. Antoulas

   Pages 11-14

5. Is it possible to recognize local controllability in a finite number of differentiations?

   • Andrei A. Agrachev

   Pages 15-18

6. Open problems in sequential parametric estimation

   • Er-Wei Bai, Roberto Tempo, Yinyu Ye

   Pages 19-22

7. Conditions for the existence and uniqueness of optimal matrix scalings

   • Venkataramanan Balakrishnan

   Pages 23-25

8. Matrix inequality conditions for canonical factorization of rational transfer function matrices

   • Venkataramanan Balakrishnan

   Pages 27-29

9. Open problems in ℓ ₁ optimal control

   • Bassam Bamieh, Munther A. Dahleh

   Pages 31-33

10. Efficient neural network learning

    • Peter L. Bartlett

    Pages 35-38

11. Mechanical feedback control systems

    • Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden

    Pages 39-44

12. Three problems on the decidability and complexity of stability

    • Vincent D. Blondel, John N. Tsitsiklis

    Pages 45-51

13. Simultaneous stabilization of linear systems and interpolation with rational functions

    • Vincent D. Blondel

    Pages 53-59

14. Forbidden state control synthesis for timed Petri net models

    • R. K. Boel, G. Stremersch

    Pages 61-66

15. On matrix mortality in low dimensions

    • Olivier Bournez, Michael Branicky

    Pages 67-69

16. Entropy and random feedback

    • Stephen P. Boyd

    Pages 71-74

17. A stabilization problem

    • Roger Brockett

    Pages 75-78

18. Spectral factorization of a spectral density with arbitrary delays

    • Frank M. Callier, Joseph J. Winkin

    Pages 79-82

19. Lyapunov exponents and robust stabilization

    • F. Colonius, D. Hinrichsen, F. Wirth

    Pages 83-88

20. Regular spectral factorizations

    • Ruth F. Curtain, Olof J. Staffans

    Pages 89-93

System and Control theory is one of the most exciting areas of contemporary engineering mathematics. From the analysis of Watt's steam engine governor - which enabled the Industrial Revolution - to the design of controllers for consumer items, chemical plants and modern aircraft, the area has always drawn from a broad range of tools. It has provided many challenges and possibilities for interaction between engineering and established areas of 'pure' and 'applied' mathematics. This impressive volume collects a discussion of more than fifty open problems which touch upon a variety of subfields, including: chaotic observers, nonlinear local controlability, discrete event and hybrid systems, neural network learning, matrix inequalities, Lyapunov exponents, and many other issues. Proposed and explained by leading researchers, they are offered with the intention of generating further work, as well as inspiration for many other similar problems which may naturally arise from them. With extensive references, this book will be a useful reference source - as well as an excellent addendum to the textbooks in the area.

• Petri net
• chemical plants
• control
• control system
• control theory
• design
• feedback
• hybrid systems
• neural networks
• nonlinear system
• optimal control
• research
• scaling
• stability
• stabilization

• Institute of Mathematics, University of Leige, Liege, Belgium

  Vincent Blondel

• Department of Mathematics, Rutgers University, New Brunswick, USA

  Eduardo D. Sontag

• Centre for Arificial Intelligence and Robotics, Bangalore, India

  Mathukumalli Vidyasagar

• Institute of Mathematics, Rijksuniversiteit te Groningen, Av Groningen, The Netherlands

  Jan C. Willems

Policies and ethics