Using Probabilistic Reliability analysis for Quantifying reliability of a system is already a common practice in Reliability Engineering community. This method plays an important role in analyzing reliability of nuclear plants and its various components. In Nuclear Power Plants Reactor Core Cooling System is a component of prime importance as its breakdown can disrupt Cooling System of power plant. In this paper, we present a framework for early quantification of Reliability and illustrated with a Safety Critical and Control System as case study which runs in a Nuclear Power Plant.
The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.