Auto-Tuning and Fractional Order Controller Implementation on Hardware in the Loop System

The paper deals with the design of an auto-tuning fractional order proportional-integrative-derivative controllers and its implementation on hardware in the loop simulator for the real-time control of unknown plants. The proposed procedure can be applied to systems with delay and order greater than one, once specifications on cross-over frequency and phase margin are given. The auto-tuning procedure consists of two phases: the first one dedicated to the identification of the process at the desired cross-over frequency and the second one to determine all the parameters of the fractional order proportional-integrative-derivative controllers. The obtained controller ensures an iso-damping response of the plant. Experimental results are given to confirm the effectiveness of the proposed approach and show that the requirements are totally met for the system to be controlled.     

A new model of Hopfield network with fractional-order neurons for parameter estimation

Nonlinear Dynamics - In this paper, a neural network-based event-triggered fault detection scheme is addressed within the finite-frequency domain for a class of nonlinear Markov jump system....     

Per una teoria delle classi comunque grandi

We propose an axiomatic theory about this work based upon an original way intending the belonging idea. We think it would be necessary to distinguish among several uses of the word belonging, till now expressed by Peano's symbol. This theory is called “The theory of classes however the large ones» because we think that it comes up to the necessity don't to restrict the size of classes which are expressible by a foundational theory. It is a first order theory, showed by eight axioms; it alphabet includes a lot of infinitely simbols of belonging, one for each level, distinguished one from each other. We think that introducing a lot of symbols we can avoid the classical antinomies and we can extend the Von Neumann's process till we need. The last one restricted to distinguish between the sets and the proper classes. For us this becomes the distinction between the first and the second level. In fact this theory develops the main idea of N.B.C.'s according to which a proper class never belongs to some other class. According to our opinion a class can belong to a larger one because it is a different belonging from the belonging that exists between a set and a proper class.     

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.