In 1937, E. T. Bell said that “a major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics and to eliminate obscurity from both”. The same claim can be done for control theory. Indeed, control theory is an interdisciplinary branch of both mathematics and engineering sciences.
Further, in mathematical control theory, most of the existing methods can only be applied to systems evolving on either continuous or discrete uniform time domains. In contrast, in engineering or in several areas of industry, there are many dynamical systems that evolve on a non-uniform time domain that can be discrete with non-uniform sampling or a mixture of discrete points and closed intervals. To name a few, a cascaded system composed of a continuous-time plant, a set of discrete-time controllers and switchings among the controllers is one example. Impulsive systems (which are a relevant class of switched systems, in which the state jumps occur only at some time instances) with non-instantaneous state jumps are another examples. Other applicative areas are dynamic programming, neural network, economic modelling, cooperative control for multi-agent systems and quantum calculus to name a few.
Engineers have to face the new challenges driven by non-uniform time domain and in particular, to deal with the control, estimation and diagnostic on an arbitrary time domain. The objective of this special issue is to give some solution of the two following interesting questions:
- Is it possible to unify the theories for systems defined on continuous time domains with that for systems on discrete time domains?
- Is it possible to extend the existing theory to dynamical systems on generalized hybrid (continuous/discrete) domains?
Stephan Hilger showed, in 1988, that a broader theory, entitled “time scale theory” may give answers of the two previous questions. This theory was introduced in order to unify the theory of difference equations and differential equations. First, what is a time scale? It is a non-empty closed subset of the real number provided with an induced topology. The most classical time scales are those that represent the real time domain on which the continuous dynamical systems are studied, the time scale that represent the discrete time domain on which one studies the discrete dynamical systems. The interest of the time scale theory lies in the arbitrary choice of the time scale. Indeed, we can also choose a mixture of discrete points and closed intervals for the time scale. Further, once a result has been established for dynamic equations on an arbitrary time scale, this result holds for standard continuous differential equations and standard difference equations. Since 1988, this unified theory has grown substantially, resulting in a number of works dedicated to this new branch of mathematical analysis and control theory. This is motivated by the fact that in biology, in engineering or in several areas of industry, there are many dynamical systems that evolve on an arbitrary time domain that can be discrete with non-uniform sampling or a combination of discrete and continuous time domains. Indeed, the temporal nature of such systems cannot be represented by the real or the discrete time only. To overcome this difficulty, the time scale theory is very promising.
The objective of this special issue is to introduce innovative principles based on time scale theory to unify the control theory issues for systems defined on continuous time domains with that for systems on discrete time domains, trying to narrow the gap between continuous-time and discrete-time theories and to extend the existing results to dynamical systems on generalized hybrid domains.
This special issue takes place in the context of hybrid systems, and its main objective is to exhibit recent developments in methodologies, techniques, and applications for systems evolving on non-uniform time domain including issues such as integral inequalities on time scales, stability analysis, control and observation of nonlinear and/or switched systems on non-uniform time domains, etc. Both theoretical and application results are sought for. We invite worldwide researchers and experts to submit high-quality original research papers and critical survey articles on the following potential topics, but are not limited to:
- Non uniform sampling
- Stochastic time scales
- Stability analysis on time scales
- Reachability on time scales
- Lyapunov theory on time scales
- Stabilization on non-uniform time domains
- Observation on non-uninform time domains
- Applications of time scale theory
数学
Journal of Economic Behavior & Organization
Adam Smith, David Hume, Liberalism, and Esotericism
The central theme of the topic would be the exploration of Smith and Hume as guiding lights of the original arc of liberalism. The topic of esotericism relates, because the liberal idea is a challenging one, and is something that 18C writers may have been esoteric about.
Esoteric writing is writing that communicates a non-obvious meaning, beyond its more obvious meaning. It is associated with Leo Strauss, but now by far the best treatment of it is Arthur Melzer, Philosophy between the Lines: The Lost History of Esoteric Writing (Chicago UP, 2014), which explains esotericism clearly and enables one to separate the phenomena from other Straussian baggage.
There are a number of reasons why Adam Smith and David Hume might choose to be indirect about the consequences of liberal policy and liberal attitudes. A good case can be made that they practiced esoteric writing on several fronts. Melzer persuasively argues that esoteric writing was pervasive prior to 1800.
The special issue calls for studies focused on Smith and/or Hume, esoteric and hermeneutic analysis of text, and connections to liberalism in the original political sense of the term.
Submission: Please submit your manuscript online via JEBO’s online submission and editorial system, and select article type “Smith Hume Liberalism Esotericism”. To be considered for publication, manuscripts must be received by 21 September 2018. Please conform to the standard guidelines for submission to JEBO.
Details can be found in the Guide for Authors section at the journal’s website.
数学
Economic Modelling
Call for Papers for a Special issue on "Advances on Banking and Finance"
Economic Modelling will publish a Special Issue on the topic of "Advances on Banking and Finance", containing a selection of papers submitted to the 3rd Vietnam Symposium in Banking and Finance (VSBF), which will take place on 25-27 October 2018, in Hue city, Vietnam. For more information, please follow this link.
The Special Issue will be guest-edited by Maria-Eleni K. Agoraki (Athens University of Economics and Business, Greece), Georgios P. Kouretas (Athens University of Business and Economics, Greece & IPAG Business School, France), and Duc Khuong Nguyen (IPAG Business School, France)