An Information Theoretic Approach to Nonlinear Systems

In this book, the nonlinear dynamical systems have been considered in the view of Fokker--Planck--Kolmogorov formalism which describes the evolution of the state densities of the dynamical systems. The state densities are direct measures of uncertainty about the states of the nonlinear dynamical systems. Their relation to the system theory and the second law of thermodynamics is investigated. The mathematical origin of the second law of the thermodynamics and information theoretical limits of the control theory have been summarised and new approach for the optimal control of the dynamics by means of the entropy reduction through the Fokker-Planck--Kolmogorov formalism has been discussed.