糖心TV Complexity Science Events
Complexity Centre and MathSys CDT events carry priority over room D1.07.
To book D1.07 please email Sheetal dot Sharma at warwick dot ac dot uk
Please note that your event booking is for D1.07 only. The adjacent common room is a private area for the MathSys Centre that cannot used as part of your booking.
Complexity Forum - Ivan Tyukin
Speaker: Ivan Tyukin (Leicester)
Title: Non-uniform small-gain theorems and their applications to computational neuroscience
Abstract: We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamical systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This, however, is neither a necessary requirement, nor is it always useful. Systems may, for instance, be inherently unstable (e.g. intermittent, itinerant, meta-stable) or the problem statement may include requirements that cannot be satisfied with stable solutions. This is often the case in general optimization problems and in nonlinear parameter identification or adaptation. Conventional techniques for these cases rely either on detailed knowledge of the system's vector-fields or require boundeness of its states. The presently proposed method relies only on estimates of the input-output maps and steady-state characteristics. The method requires the possibility of representing the system as an interconnection of a stable, contracting, and an unstable, exploratory part. We illustrate with examples how the method can be applied to
1) analyzing the asymptotic behavior of locally unstable systems
2) problems of parameter identification and adaptation in the presence of nonlinear parametrizations; in particular to the problem of fitting model neurons to data
3) proving existence of a recurrent neural-net capable of classifying unknown signals of a given class
4) designing simple decision-making systems.
The relation of our results to conventional small-gain theorems will aslo be discussed.