This project will consider the problem of applying linear quadratic Gaussian (LQG) optimal control to a simple oscillator system with a double well potential function. The idea is to design a potential function that behaves as a standard quadratic potential along way from the equilibrium points but actually has two closely spaced equilibrium points corresponding to the double well potential. This will mean that far from the equilibrium points, the system can be approximated as a linear oscillator and the standard LQG control theory can be applied. However, close to the equibrium points, the system will exhibit a nonlinear behaviour and it is hoped that the controller can be designed so that the invariant state probability distribution shows an equal probabity of being in either equilibrium point. The problem is motivated by a corresponding problem in quantum control in which feedback control is applied to generate a Schodinger cat state. This project will be only concerned with classical dynamics and control but will motivate future research on the quantum problem. Students undertaking this project should have successfully completed ENGN3223.