Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation

Chapter 1Introduction

Over the past decades, fractional calculus has attracted increasing interest from researchers, and has been widely applied in fields in engineering and physics, such as system control [1], electromechanics [2], and signal processing [3]. Since the mathematical model of a real plant can be accurately described via the fractional-order differential method [4, 5], many systems can be expressed as fractional differential equations, for example, fractional-order economic systems [6], fractional-order biological population models [7], fractional-order financial systems [8], and fractional-order chaotic and hyperchaotic systems [9–15]. With the development of fractional calculus, problems of control and synchronization control for fractional-order systems have been extensively investigated. So far, some important control schemes have been reported for fractional-order systems as follows.

Sliding-model control

It is well known that sliding-mode control is an effective robust control scheme and has the features of fast global convergence and high robustness to external disturbances [16]. In recent years, sliding-mode control has been investigated for integer-order linear and nonlinear systems [17–25] and many important results have been reported for the control of fractional-order systems using the sliding-mode technique. Dadras and Momeni [6] studied the control for a fractional-order economical system using the sliding-mode method. Chaos control was investigated ...