Jackson and Grosu [1995a] have recently proved that a new OPCL control method, involving both closed and open loop components, always has a basin of entrainment to any smooth goal dynamics, g(t) ⊂ Rn, for any dynamic system (Lipschitz flow), dx/dt = F (x, t), x ⊂ Rn. Moreover, they showed that the basins of entrainment can be made the entire phase space ("global") for many standard dynamic systems, and in particular for the Chua system [Chua et al., 1986]. In contrast to entrainment, it has been pointed out [Jackson, 1990] that migration controls, which act only for limited time and produce transfers between attractors of a multiple-attractor system, can be of great importance. The Chua system can possess five attractors, and the present study shows how it is possible to reliably produce migrations between any of these attractors using only five experimentally-obtained data points in the phase space. This migration control does not require any knowledge about the basins of attraction, nor the state of the system when the control is initiated. Moreover, the OPCL method can be used to obtain refined models of the physical system, by applying the general resonance method proposed previously [Chang et al., 1991].
Practical Stability of Dynamic Systems with Time Delays in Terms of Two Measurements
