Open Problems in Mathematical Systems and Control Theory

✍ Scribed by Dirk Aeyels, Joan Peuteman (auth.), Vincent Blondel, Eduardo D. Sontag, Mathukumalli Vidyasagar, Jan C. Willems (eds.)

• Publisher: Springer-Verlag London
• Year: 1999
• Tongue: English
• Leaves: 276
• Series: Communications and Control Engineering
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Uniform asymptotic stability of linear time-varying systems....Pages 1-5
Positive system realizations....Pages 7-10
System approximation in the 2-norm....Pages 11-14
Is it possible to recognize local controllability in a finite number of differentiations?....Pages 15-18
Open problems in sequential parametric estimation....Pages 19-22
Conditions for the existence and uniqueness of optimal matrix scalings....Pages 23-25
Matrix inequality conditions for canonical factorization of rational transfer function matrices....Pages 27-29
Open problems in ℓ 1 optimal control....Pages 31-33
Efficient neural network learning....Pages 35-38
Mechanical feedback control systems....Pages 39-44
Three problems on the decidability and complexity of stability....Pages 45-51
Simultaneous stabilization of linear systems and interpolation with rational functions....Pages 53-59
Forbidden state control synthesis for timed Petri net models....Pages 61-66
On matrix mortality in low dimensions....Pages 67-69
Entropy and random feedback....Pages 71-74
A stabilization problem....Pages 75-78
Spectral factorization of a spectral density with arbitrary delays....Pages 79-82
Lyapunov exponents and robust stabilization....Pages 83-88
Regular spectral factorizations....Pages 89-93
Convergence of an algorithm for the Riemannian SVD....Pages 95-98
Some open questions related to flat nonlinear systems....Pages 99-103
Approximation of complex µ ....Pages 105-107
Spectral value sets of infinite-dimensional systems....Pages 109-113
Selection of the number of inputs and states....Pages 115-119
Input-output gains of switched linear systems....Pages 121-124
Robust stability of linear stochastic systems....Pages 125-129
Monotonicity of performance with respect to its specification in H ∞ control....Pages 131-136
Stable estimates in equation error identification: An open problem....Pages 137-140
Elimination of latent variables in real differential algebraic systems....Pages 141-147
How conservative is the circle criterion?....Pages 149-151
On chaotic observer design....Pages 153-156
The minimal realization problem in the max-plus algebra....Pages 157-162
Input design for worst-case identification....Pages 163-166
Max-plus-times linear systems....Pages 167-170
Closed-loop identification and self-tuning....Pages 171-176
To estimate the L 2 -gain of two dynamic systems....Pages 177-179
Open problems in the area of pole placement....Pages 181-191
An optimal control theory for systems defined over finite rings....Pages 193-201
Re-initialization in discontinuous systems....Pages 203-209
Control-Lyapunov functions....Pages 211-216
Spectral Nevanlinna-Pick Interpolation....Pages 217-220
Phase-sensitive structured singular value....Pages 221-224
When does the algebraic Riccati equation have a negative semi-definite solution?....Pages 225-228
Representing a nonlinear input-output differential equation as an input-state-output system....Pages 229-237
Shift policies in QR-like algorithms and feedback control of self-similar flows....Pages 239-243
Equivalences of discrete-event systems and of hybrid systems....Pages 245-249
Covering numbers for input-output maps realizable by neural networks....Pages 251-257
A powerful generalization of the Carleson measure theorem?....Pages 259-265
Lyapunov theory for high order differential systems....Pages 267-272
Performance lower bound for a sampled-data signal reconstruction....Pages 273-276
Coprimeness of factorizations over a ring of distributions....Pages 277-279
Where are the zeros located?....Pages 281-284
Back Matter....Pages 285-288
....Pages 289-289

✦ Subjects

Control, Robotics, Mechatronics