a feedback model for the evolution of civilizations

The paper proposes a simple feedback model capable of explaining the evolution of various civilizations as determined by historians and scientists. The forward path of this feedback model consists of a first-order system, accounting for an accumulation process, in series with a pure time delay, and its feedback path consists of a constant possibly preceded by a filter. To account for an eventual decline, a smoothed derivative term can also be added. It is shown how the evolution pattern depends on few model parameters susceptible to interesting interpretations, thus providing a powerful "tool for thought". The relation of the suggested model with the Phillips model of a closed economy is also pointed out

state response decomposition for model reduction

The decomposition of the overall forced response into a steady-state and a transient component can be exploited to find reduced-order models that retain both long-term and short-term characteristics of the original system behaviour. To this purpose, the state-space expressions of the aforementioned components in response to inputs with rational transform are derived. The reduced-order model is then obtained by considering separately the asymptotic and transient terms. The suggested approach is tested on benchmark examples of very high dimension

Feedback Models of Two Classical Philosophical Positions and a Semantic Problem

The notion of feedback has been exploited with considerable success in scientific and technological fields as well as in the sciences of man and society. Its use in philosophical, cultural and educational contexts, however, is still rather meagre, even if some notable attempts can be found in the literature. This paper shows that the feedback concept can help learn and understand some classical philosophical theories. In particular, attention focuses on Fichte\u2019s doctrine of science, usually presented in obscure terms following its inventor\u2019s style, and on the vulgate version of Hegel\u2019s dialectic. Also a classic problem of linguistics concerning the meaning of sentences in partially unknown languages is interpreted with the aid of feedback diagrams. Even if the analysis is only qualitative, it is believed that it may serve as a useful tool for thought for both students and researchers

On the rational approximation of fractional order systems

This paper is concerned with the finite-dimensional approximation of a fractional-order system represented in state-space form. To this purpose, resort is made to the Oustaloup method for approximating a fractional-order integrator by a rational filter. By applying this method to the RHS of the state equation of the fractional-order system, a matrix differential equation is obtained. This equation is then realized in a state-space form whose state matrix exhibits a (sparse) block-companion structure. To reduce the dimension of this integer-order model, an efficient method for L2 approximation can profitably be applied. Numerical simulations show that the suggested approach compares favourably with alternative techniques recently presented in the literature to the same purpose

A mathematical approach to the analysis of scientific presentations

The paper provides a mathematical approach to the problem of presenting a scientific work in the most effective way. To this purpose, a performance index that measures the quality of the presentation is first introduced. The speaker\u2019s task is that of maximising this index by properly choosing a suitable decision variable (control law). Since the index depends on the ability of the audience to assimilate new information, the solution requires to know the level of knowledge of the spectators. It is assumed that this knowledge is distributed among them according to a density function with a unique maximum similar to the classic bell-shaped Gaussian curve. The adopted decision variable, whose time course should be found, accounts for the current information content of the talk, defined as the amount of knowledge required to understand what is being presented. The optimal solution shows that the information conveyed to the audience should be kept close to the maximum of the aforementioned knowledge distribution

Routh-type L2L_2 model reduction revisited

summary:A computationally simple method for generating reduced-order models that minimise the $L_2$ norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the $L_2$-optimal approximation. Two examples taken from the relevant literature show that the suggested techniques may lead to approximations that are not worse than those afforded by popular more cumbersome techniques