  This paper describes an approach for attractor selection (or multi-stability
control) in nonlinear dynamical systems with constrained actuation. Attractor
selection is obtained using two different deep reinforcement learning methods:
1) the cross-entropy method (CEM) and 2) the deep deterministic policy gradient
(DDPG) method. The framework and algorithms for applying these control methods
are presented. Experiments were performed on a Duffing oscillator, as it is a
classic nonlinear dynamical system with multiple attractors. Both methods
achieve attractor selection under various control constraints. While these
methods have nearly identical success rates, the DDPG method has the advantages
of a high learning rate, low performance variance, and a smooth control
approach. This study demonstrates the ability of two reinforcement learning
approaches to achieve constrained attractor selection.
