Regions of attraction and applications to control theory by ?tefan Balint, Liliana Br?escu, Eva Kaslik

Regions of attraction are important not only for mathematics but also for the control of dynamics in mechanics, thermodynamics, electronics, chemistry and biology. Real systems in general are built so that for a given external input (control) they exhibit one (or several) equilibrium states. The transfer from a steady state to another steady state is made by changing the values of the control parameters (inputs). It is known in engineering applications that large transfers may not be possible by a single change but if the change is made in small steps the transfer can be successful. The mathematical explanation is that by small successive changes the system is conducted through the regions of attraction of asymptotically stable steady states to the desired steady state.

This volume aims to present effective methods of estimation of the regions of attraction of asymptotically stable steady states in the case of autonomous analytical differential equations and also of discrete semi-dynamical systems. It also shows how these regions can be used, e.g. in the control of the shape of a single crystal during growth; in the control of the flight of a space shuttle and in the control of a Hopfield type neural network.

Cambridge University Press