Control of Discrete Time Chaotic Systems via Combination of Linear and Nonlinear Dynamic Programming

Abstract

In this article by introducing and subsequently applying the Min–Max method, chaos has been suppressed in discrete time systems. By using this nonlinear technique, the chaotic behavior of Behrens–Feichtinger model is stabilized on its first and second-order unstable fixed points (UFP) in presence and absence of noise signal. In this step, a comparison has also been carried out among the proposed Min–Max controller and the Pyragas delayed feedback control method. Next, to reduce the computation required for controller design, the clustering method has been introduced as a quantization method in the Min–Max control approach. To improve the performance of the acquired controller through clustering method obtained with the Min–Max method, a linear optimal controller is also introduced and combined with the previously discussed nonlinear control law. The resultant combined controller has been applied on the Henon map and through comparison with both Pyragas controller, and the linear optimal controller alone, its advantages are discussed.

Exponential Stability for the Schlögl System by Pyragas Feedback

“…if 156 ≤ t ≤ 160 (23) with some positive κ. For a sufficiently large weight κ, κ = 100 in our computations, we obtain a very fine numerical adjustment, cf.…”

“…Our first motivation for this example was to mimic the solution of the linear delay equation (23), that has delayŝ = 1 and weightω = −π/2, with a the solution of the nonlinear ode (22). By an optimization method, we found the "strange" pair s = 1.240683838477202 if 156 ≤ t ≤ 160,…”

“…The existence of periodic solutions of nonlinear parabolic equations is studied in [27]. Stabilization towards desired periodic orbits is also considered in [1] for a pendulum system and in [23,24] for discrete time chaotic systems. Optimal control problem for systems governed by the stochastic FitzHugh-Nagumo equation with a Gaussian noise are studied in [2].…”

An Adaptive Centralized Approach to Control Chaotic and Hyperchaotic Dynamics of Smart Valves Network

“…Some other efforts related to the chaos control can be found in Refs. [17][18][19][20][21][22][23][24][25][26][27][28].…”