Control of exits from a safe region: a stochastic Melnikov approach

For a wide class of stochastically excited multistable systems the Melnikov necessary condition for chaos contains information on the effectiveness of the various frequency components of the excitation in inducing exits from a potential well. This information can be used to develop an open-loop control procedure aimed at reducing the system's exit rate. The Melnikov approach is based on a first-order approximation and is in principle applicable only for small perturbations. Nevertheless, results of simulations show that it is valid qualitatively even if the excitations are relatively large. We test the effectiveness of the proposed control procedure, and briefly review the use of the phase space flux factor to assess or design the control systems.