Chaotifying Fuzzy Hyperbolic Model Using Adaptive Inverse Optimal Control Approach

It is well known that most conventional control methods and many special techniques can be used for chaos control [Chen & Dong, 1998] whether the purpose is to reduce “bad” chaos or to introduce “good” chaos. Numerous control methodologies have been proposed, developed, tested and applied. Due to its great potential in nontraditional applications such as those found within the context of physical, chemical, mechanical, electrical, optical and particularly, biological and medical systems [Schiff et al., 1994; Yang et al., 1995], making a nonchaotic system chaos or strengthening the existing chaos, known as “chaotification” (also known as “anticontrol”), has attracted increasing attention in recent years. The process of chaos control is now understood as a transition from chaos to order and sometimes from order to chaos, depending on the purpose of the application in different circumstances. Recent studies have shown that any discrete map can be chaotified in the sense of Devaney or Li–Yorke by a state-feedback controller with a uniformly bounded control-gain sequence designed to make all Lyapunov exponents of the controlled system strictly positive or arbitrarily assigned [Chen & Lai, 1997; Chen & Lai, 1998; Wang & Chen, 1999, 2000a, 2000b, 2000c]. Even if there are some research works showing that a class of continuous stable systems can be chaotified