We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-tostate stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for ...

The dilatation generator measures the scaling dimensions of local operators in a conformal field theory. In this thesis we consider the example of maximally supersymmetric gauge theory in four dimensions and develop and extend techniques to derive, investigate and apply the dilatation operator. These tools are perfectly suited for precision tests of the dynamical AdS/CFT conjecture. In particul...

this paper focuses on the effects of closed- control on the calculation of the dynamic load carrying capacity (dlcc) for mobile-base flexible-link manipulators. in previously proposed methods in the literature of dlcc calculation in flexible robots, an open-loop control scheme is assumed, whereas in reality, robot control is achieved via closed loop approaches which could render the calculated ...

2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory Abstract It is shown that the vacuum value of the 2d gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus-n > 1 Riemann surface are mapped. Because of the above singularity, one can not construct modular invariant mult...

Given an exact Lagrangian embedding Q ⊂ M , we construct an A∞ restriction functor from the wrapped Fukaya category of M to the category of modules on the differential graded algebra of chains over the based loop space of Q. If M is the cotangent bundle of Q, this functor induces an A∞ equivalence between the wrapped Floer cohomology of a cotangent fibre and the chains over the based loop space...

Let Sn be a simple random walk (SRW) defined on Z . We construct a stochastic process from Sn by erasing loops of length at most N , where α ∈ (0,∞) and N is the scaling parameter that will be taken to infinity in determining the limiting distribution. We call this process the N loop erased walk (N LEW). Under some assumptions we will prove that for 0 < α < 1 1+2ζ , the limiting distribution is...

This paper develops a hierarchical control architecture for so called sequential behaviours, i.e. for plant dynamics and specifications that are represented as formal languages of infinite-length words. Our main result is the elaboration of structural properties that (a) allow for abstraction based controller design and that (b) are preserved under closed-loop composition. Thus, we propose to a...

Carbonation of magnesiumand calcium-silicate minerals to form their respective carbonates is one method to sequester carbon dioxide. Process development studies have identified reactor design as a key component affecting both the capital and operating costs of ex-situ mineral sequestration. Results from mineral carbonation studies conducted in a batch autoclave were utilized to design and const...

Considering a linear system, we construct hybrid loops consisting in a (possibly non stabilizing) given linear dynamic continuous-time controller with a jump rule when some conditions of the state occur. This allows us to study the performance improvement problem. More precisely, we firstly show the interest of an hybrid loop to maximize the decay rate when the gain of the controller is limited...

We show a necessary and sufficient condition for a finite-dimensional highest weight representation of the sl2 loop algebra to be irreducible. We present an algorithm by which we can construct all possible finite-dimensional highest weight representations that have the same given highest weight. For two simple cases, we derive dimensions of all such reducible representations, explicitly. The re...