Statistical Delay Bound for WirelessHART Networks

In this paper we provide a performance analysis framework for wireless industrial networks by deriving a service curve and a bound on the delay violation probability. For this purpose we use the (min,x) stochastic network calculus as well as a recently presented recursive formula for an end-to-end delay bound of wireless heterogeneous networks. The derived results are mapped to WirelessHART networks used in process automation and were validated via simulations. In addition to WirelessHART, our results can be applied to any wireless network whose physical layer conforms the IEEE 802.15.4 standard, while its MAC protocol incorporates TDMA and channel hopping, like e.g. ISA100.11a or TSCH-based networks. The provided delay analysis is especially useful during the network design phase, offering further research potential towards optimal routing and power management in QoS-constrained wireless industrial networks.Comment: Accepted at PE-WASUN 201

Design and practical implementation of a fractional order proportional integral controller (FOPI) for a poorly damped fractional order process with time delay

One of the most popular tuning procedures for the development of fractional order controllers is by imposing frequency domain constraints such as gain crossover frequency, phase margin and iso-damping properties. The present study extends the frequency domain tuning methodology to a generalized range of fractional order processes based on second order plus time delay (SOPDT) models. A fractional order PI controller is tuned for a real process that exhibits poorly damped dynamics characterized in terms of a fractional order transfer function with time delay. The obtained controller is validated on the experimental platform by analyzing staircase reference tracking, input disturbance rejection and robustness to process uncertainties. The paper focuses around the tuning methodology as well as the fractional order modeling of the process' dynamics

Coupled systems of fractional equations related to sound propagation: analysis and discussion

In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in the constitutive equations. By doing so, we embrace a vast phenomenology, including subdiffusive, superdiffusive and also memoryless processes like classical diffusions. From a mathematical point of view, we study systems of coupled fractional equations, leading to fractional diffusion equations or to equations with sequential fractional derivatives. In this framework we also propose a method to solve partial differential equations with sequential fractional derivatives by analysing the corresponding coupled system of equations

Proof Generation from Delta-Decisions

We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision procedures. At the same time, it is a new approach for automated theorem proving over real numbers. We design a first-order calculus, and transform the computational steps of constraint solving into logic proofs, which are then validated using proof-checking algorithms. As an application, we demonstrate how proofs generated from our solver can establish many nonlinear lemmas in the the formal proof of the Kepler Conjecture.Comment: Appeared in SYNASC'1