Abstract
The design of adaptive chattering‐free sliding mode controller (SMC) for chaotic systems with unknown input nonlinearities is studied in this paper. A smooth hyperbolic tangent function is utilized to replace the discontinuous sign function; therefore, the proposed adaptive SMC ensures that not only the chaos phenomenon can be suppressed effectively but also the chattering often appearing in the traditional discontinuous SMC with sign function is eliminated, even when the unknown input nonlinearity is present. A sufficient condition for stability of closed‐loop system is acquired by Lyapunov theory. The numerical simulation results are illustrated to verify the proposed adaptive sliding mode control method.
Highlights
In recent decades, sliding mode control is one of the popular control theories due to its robustness and insensitivity to parameter uncertainty and external disturbance [1, 2]. e trajectories of sliding mode controller (SMC) systems can be driven onto a specified sliding surface and slide toward desired stable condition, which is called sliding motion. ere are many methodologies used to select sliding surfaces, while the different control law is obtained, and it is guaranteed that the controlled system is stable [2]
In [3, 4], the new SMC-based fuzzy controller and robust hybrid controller are applied to the 7-degree-of-freedom upper-limb exoskeleton robot such that the undesired external disturbance can be suppressed
Erefore, the SMC can be used to overcome undesired external disturbance successfully; in [5], a class of linear switched system is discussed for the cooperative stabilization problem and a novel class of switching signals is proposed
Summary
In recent decades, sliding mode control is one of the popular control theories due to its robustness and insensitivity to parameter uncertainty and external disturbance [1, 2]. e trajectories of SMC systems can be driven onto a specified sliding surface and slide toward desired stable condition, which is called sliding motion. ere are many methodologies used to select sliding surfaces, while the different control law is obtained, and it is guaranteed that the controlled system is stable [2]. Erefore, many different methods have been proposed to solve the problems of chaos control and suppression for chaotic systems, such as adaptive feedback control [13,14,15,16], Mathematical Problems in Engineering sliding mode control [11, 17, 18], PID control [19,20,21], optimal control [22,23,24,25,26], and robust control [27,28,29] among many others [30, 31]. The adaptive continuous SMC design for chaotic systems with unknown input nonlinearity is studied. We present numerical simulation results to illustrate the effectiveness of the proposed adaptive continuous SMC scheme
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