Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

Abstract

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015

Adaptive Control of a Class of Incommensurate Fractional Order Nonlinear Systems With Input Dead-Zone

“…where b r > 0 and b l > 0 are unknown bounded dead-zone breakpoints, and h r and h l are the right and left slopes. Deadzone (8) can be described as the function as follows [49]:…”

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

“…Let us consider the 3-D fractional-order Arneodo's system which is described as 62,63 When d(t) = ω(t) = 0, the chaotic behavior of the uncontrolled fractional-order Arneodo's system is shown in Figure 8. The disturbance is d(t) = sin t + cos t. The referenced signal is x d (t) ≡ 1 (here we use a constant referenced signal is for convenience purpose because the fractional-order derivative of a constant is zero, so the structure of the pseudo controllers will be simpler).…”

A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

“…Fractional-order calculations play an important role in various scientific fields. Recently the application of fractional-order is known as an important topic in engineering [1]. The problem of fractional-order equations was first raised by Leibniz in a letter in September 1695 on the fractional-order derivative, and has become an issue for research that is still under investigation [2].…”