Efficient strategy for the occasionally proportional feedback method in controlling chaos

Abstract

In this work, the generic mechanism of the occasionally proportional feedback (OPF) technique in controlling chaos has been explored extensively. Except for stabilizing the unstable states that are embedded in the chaotic attractors, the OPF method is also found to generate a great number of new states during the control processes. The forms and characteristics of these new states have been addressed. Moreover, we clarify the roles of the parameters in the OPF method and this clarification leads to a practical and systematic approach in adjusting the parameters for control. To demonstrate the validity, an analogous electronic circuit of the resistively shunted Josephson junction oscillator is employed in addition to a numerical illustration of the logistic mapping.

Adaptive Sliding Mode Vibration Control of a Nonlinear Smart Beam: A Comparison with Self-Tuning Ziegler-Nichols PID Controller

“…Consider an n i -input, single-output fuzzy system with n r fuzzy IF-THEN rules as Rule r: If x 1 is à r 1 and … and x n i is à r n i then yb r where x = [x 1 … x n i ] and are the input and output of the fuzzy system, respectively, b r is the fuzzy singleton for the output of the th rule, and à r 1 … à r n i are fuzzy sets characterized by Gaussian membership functions as (14) In which c j r and σ j r are the center and width of the Gaussian membership function. Using singleton fuzzifier, product inference, and center average defuzzifier, the output of the fuzzy system is obtained as (15) Define the firing strength of the rth rule as (16) Then the output of the fuzzy system can be rewritten as (17) where B = [b 1 … b nr ] T and W = [w 1 … w nr ] T . It has been proven that fuzzy system (17) is a universal approximator [32].…”

“…They first introduced a new method for controlling a nonlinear dynamical structural system. Numerous control methods have been proposed for controlling chaos [13][14][15][16] after that. Several nonlinear control techniques, such as feedback linearization [17], sliding-mode control [8][9][10], backstepping [21,22], and adaptive control algorithms [23,24] have been also applied for controlling of chaotic structural systems.…”

Chaos Synchronization in Josephson Junctions

“…Their method is a modification of the OGY method where a nonexistent high period orbits can be stabilized as well as low-period orbits. Moreover, the technique can be completely analog which makes it very fast so it can be employed in a wide range of applications [8][9][10][11][12]. In our previous paper [13], we have shown that a nonlinear backstepping controller can be designed to control the bifurcation as well as incipient chaos that have been experienced in the RCLSJ (shunted nonlinear resistivecapacitive-inductance) Josephson Junction effectively.…”