MELNIKOV-BASED OPEN-LOOP CONTROL OF ESCAPE FOR A CLASS OF NONLINEAR-SYSTEMS

The performance of certain nonlinear stochastic systems is deemed acce ptable if during a specified time interval, the systems have sufficien tly low probabilities of escape from a preferred region of phase space . We propose an open-loop control method for reducing these probabilit ies. The method is applicable to stochastic systems whose dissipation- and excitation-free counterparts have homoclinic or heteroclinic orbit s. The Melnikov relative scale factors are system properties containin g information. on the frequencies of the random forcing spectral compo nents that are most effective in inducing escapes. Numerical simulatio ns show that substantial (advantages can be achieved in some cases by designing control systems that rake into account the information conta ined in the Melnikov scale factors.