Chaos in a class of reacting systems induced by robust asymptotic feedback

Chaotic behavior in a controlled reacting system is discussed. The open-loop dynamics of the reactor (i.e., without control actions) does not display chaos. The feedback control has a unique adjust parameter, L. For all L>L*≥0, the reactor under control actions converges to a prescribed point. L is a parameter, then the above condition implies that if L is larger than any constant L* the reactor is stabilized at the prescribed point. However, homoclinic chaos can be induced by the continuous robust asymptotic feedback if 0<L≤L*. Indeed, the closed-loop system (i.e., the reactor under feedback ations) displays four regions. In the first one, a limit cycle with large amplitude is found. In the second one, chaotic behavior is displayed. Small amplitude limit cycle is found in the third region. Finally, in the fourth region, the feedback yields asymptotic convergence of the trajectories to the prescribed point.