Symmetries and Conserved Quantities of Stochastic Dynamical Control Systems

Abstract

A new definition is given for both exact and quasi symmetries of Ito and Stratonovich dynamical control systems. Determining systems of symmetries for these systems have been obtained and their relation is discussed. It is shown that conserved quantities can be found from both exact and quasi symmetries of stochastic dynamical control systems, which includes Hamiltonian control systems as a special case. Systems which can be controlled via conserved quantities have been investigated. Results have been applied to the control of an N-species stochastic Lotka—Volterra system.