Open Problems in Mathematical Systems and Control Theory

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.

Contenu

1 Uniform asymptotic stability of linear time-varying systems.- 2 Positive system realizations.- 3 System approximation in the 2-norm.- 4 Is it possible to recognize local controllability in a finite number of differentiations?.- 5 Open problems in sequential parametric estimation.- 6 Conditions for the existence and uniqueness of optimal matrix scalings.- 7 Matrix inequality conditions for canonical factorization of rational transfer function matrices.- 8 Open problems in ?1 optimal control.- 9 Efficient neural network learning.- 10 Mechanical feedback control systems.- 11 Three problems on the decidability and complexity of stability.- 12 Simultaneous stabilization of linear systems and interpolation with rational functions.- 13 Forbidden state control synthesis for timed Petri net models.- 14 On matrix mortality in low dimensions.- 15 Entropy and random feedback.- 16 A stabilization problem.- 17 Spectral factorization of a spectral density with arbitrary delays.- 18 Lyapunov exponents and robust stabilization.- 19 Regular spectral factorizations.- 20 Convergence of an algorithm for the Riemannian SVD.- 21 Some open questions related to flat nonlinear systems.- 22 Approximation of complex ?.- 23 Spectral value sets of infinite-dimensional systems.- 24 Selection of the number of inputs and states.- 25 Input-output gains of switched linear systems.- 26 Robust stability of linear stochastic systems.- 27 Monotonicity of performance with respect to its specification in H? control.- 28 Stable estimates in equation error identification: An open problem.- 29 Elimination of latent variables in real differential algebraic systems.- 30 How conservative is the circle criterion?.- 31 On chaotic observer design.- 32 The minimal realization problem in the max-plus algebra.- 33 Input design for worst-case identification.- 34 Max-plus-times linear systems.- 35 Closed-loop identification and self-tuning.- 36 To estimate the L2-gain of two dynamic systems.- 37 Open problems in the area of pole placement.- 38 An optimal control theory for systems defined over finite rings.- 39 Re-initialization in discontinuous systems.- 40 Control-Lyapunov functions.- 41 Spectral Nevanlinna-Pick Interpolation.- 42 Phase-sensitive structured singular value.- 43 Conservatism of the standard upper bound test: Is sup$$ \left( {\bar \mu /\mu } \right) $$ finite? Is it bounded by 2?.- 44 When does the algebraic Riccati equation have a negative semi-definite solution?.- 45 Representing a nonlinear input-output differential equation as an input-state-output system.- 46 Shift policies in QR-like algorithms and feedback control of self-similar flows.- 47 Equivalences of discrete-event systems and of hybrid systems.- 48 Covering numbers for input-output maps realizable by neural networks.- 49 A powerful generalization of the Carleson measure theorem?.- 50 Lyapunov theory for high order differential systems.- 51 Performance lower bound for a sampled-data signal reconstruction.- 52 Coprimeness of factorizations over a ring of distributions.- 53 Where are the zeros located?.