Robust Fixed Point Transformations-Based Control of Chaotic Systems

keywords: Robust fixed point transformations, Duffing system, nonlinear control, adaptive control, chaos synchronization
Nowadays, nonlinear control is a very important task because machines are playing an ever increasing role in life. Lyapunov's 2 rm nd method is a popular tool by the use of which various controllers can be designed like adaptive neural networks, fuzzy controllers, and neuro-fuzzy solutions, or the sliding mode controllers and the well-known PID feedback controllers. Robust Fixed Point Transformation is a procedure which can be built for almost any type of controller in case an approximate model is used to estimate the controlled system's behavior. In this paper, a new approach to Robust Fixed Point Transformations (RFPT) is introduced by integrating a second controller in the system. Authors show that this additional, ``recalculated'' controller not just improves the original controller's results, but halves the tracking errors achieved by the previous RFPT methods.
mathematics subject classification 2000: 34-H05, 34-H10, 49-J15, 49-K15, 58-E25, 62-F35, 70-Q05, 93-B52, 93-C10, 93C15, 93-C40
reference: Vol. 32, 2013, No. 3, pp. 487–507