Nonlinear problems are more challenging and almost complex to be solved. A recently developed Homotopy Perturbation Method (HPM) is introduced. This method is used to represent the system as a less complicated (almost linear) model. To verify the effectiveness, HPM based model is compared with the nonlinear dynamic in both open and closed loop PI controlled. The error indices are approximation ...

The usual open-loop quantum and semiclassical theories of light detection are extended to include closed-loop operation in which there is feedback from the detector to the source. It is shown that the unmistakable signatures of nonclassical light associated with open-loop detection, such as sub-shot-noise spectra and sub-Poisson photo-counts, do not carry over to closed-loop systems. This behav...

The relationship between the (open-loop) optimization problem that is repeatedly solved online and the quality of the (closed-loop) schedule that is implemented, is poorly understood, even in the deterministic case. We investigate various attributes of the open-loop problem and the rescheduling algorithm that affect the quality of closed-loop schedules, viz. rescheduling frequency, scheduling h...

Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse that appear for first time five loops. Explicitly, open loops into connected trees and group them according their topological properties. Then, identify a kernel generator, so-c...