Time-delay systems with constant or variable delays can take the form of delay differential equations (DDEs) from a mathematical point of view. DDEs combine the continuous aspect of differential equations and sample features of difference equations. Such “mixed difference equations” go back to the astronomer’s three-body problem of Condorcet in 1767. R.E. Bellman & K.L. Cooke published a seminal study on DDEs in the 1960’s. Russian mathematician Komanovskii, Myshlis & Nosov (1999) developed the study of their stability and applications to the industrial problems. Mathematical software packages like Mathematica® and MATLAB® introduced solvers recently for DDEs with constant delays. DDEs are essential for modeling, forecasting, and simulation of complex real-life systems for which delays cannot be neglected. Time-delay systems are applied extensively in various domains of science and industry such as mechanical systems, electrical systems, industrial processes, and biological systems. Some delays are due to inherent properties of a system where the propagation of effects takes time. The necessity of feedback controls to stabilize a system also introduce some inevitable delays. This study introduces this modeling process and analysis using some real-life deterministic applications from mechanical engineering dynamics and control such as with the metal rolling system.
Brief Biography of the Speaker:
André A. Keller (Prof.) is at present an Associated Researcher at the Center for Research in Computer Science, Signal, and Automatic Control of Lille, by the University de Lille in France. He received a Doctorat d’Etat’ (PhD.) in Economics/ Operations Research from the University of Paris 1 Panthéon-Sorbonne, and a post-doctorate from the University Paris X Nanterre. He is a Reviewer for the international journals major publishers such as Elsevier, Hindawi, Springer, World Academic Publishing, World Scientific, WSEAS Press. He taught applied mathematics (optimization techniques) and econometric modeling, microeconomics, the theory of games and dynamic macroeconomic analysis. His experience centers are in building and analyzing large-scale macroeconomic systems, as well as forecasting. His research interests include high-frequency time-series modeling with application to the foreign exchange market, discrete mathematics (graph theory, combinatorial optimization), stochastic differential games and tournaments, circuit analysis, optimal control under uncertainties. (fuzzy control). His publications consist of writing articles, book chapters, and books. The book chapters are on semi-reduced forms (Martinus Nijhoff, 1984), econometrics of technical change (Springer and IISA, 1989), advanced time-series analysis (Woodhead Faulkner, 1989), stochastic differential games (Nova Science, 2009), optimal fuzzy control (InTech, 2009). One book is “Time-delay systems with Applications to Economic Dynamics & Control” (LAP, 2010). One another book is “Mathematical Optimization Terminology: A Comprehensive Glossary of Terms”(Elsevier/Academic Press, USA, 2017). Other recent books are on “Multi-Objective Optimization in Theory and Practice I: Classical Methods (2017) and II: Evolutionary Algorithm” (submitted).