Lie group analysis of bilinear control systems
General approach to optimal control problems for physical applications based on bilinear models defined on compact Lie group manifolds is proposed. Special attention is paid for necessary conditions of optimality by R.W. Brocket and their special cases that are useful in statistical mechanics. An important analogy between dynamics of optimally controlled collisionless Liouville's ensemble and multidimensional Euler's top is stated. Some possible qualitative physical consequences of bilinear optimal control are discussed.