Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown quantized input and control directions subject to actuator failures

Abstract

This article addresses an adaptive backstepping control design for uncertain fractional-order nonlinear systems in the strict-feedback form subject to unknown input quantization, unknown state-dependent control directions, and unknown actuator failure. The system order can be commensurate or noncommensurate. The total number of failures is allowed to be infinite. The Nussbaum function is used to deal with the problem of unknown control directions. Compared with the existing results, the control gains can be functions of states and the knowledge of quantization parameters and characteristics of the actuator failure are unknown. By applying the backstepping control approach based on the frequency-distributed model, it is proved that all the closed-loop signals remain bounded and the output tracking error converges to the origin asymptotically. Finally, the effectiveness of the proposed controller is demonstrated by two simulation examples.

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

“…Each of these two methods has distinct benefits and may be utilized depending on the type of constraints imposed on the system. The indirect technique is widely used for the stability analysis of incommensurate order systems and the asymptotic stability analysis [9][10][11]. This technique is based on the frequency distributed models and uses the integer-order derivative of Lyapunov functions in the stability analysis [12].…”

“…Some studies examined a general framework for integer-order and FO systems that includes the four types of input nonlinearities mentioned above. These studies developed adaptive backstepping controllers for handling input nonlinearities without having any information about their characteristics [7,9,50]. In this study, a controller has been design, which copes with these four kinds of the input nonlinearity without knowing their characteristics.…”

“…In that work, the unmeasured states are estimated by using a linear observer. In [9], the indirect Lyapunov method and adaptive backstepping control have been applied to ensure the asymptotic stability of strict‐feedback systems with hysteresis input quantization, unknown control direction, and an infinite number of actuator failures. In [19], an observer‐based NN‐based DSC controller for a switched FO strict‐feedback system with hysteresis input quantization and an event‐triggered mechanism has been designed by using a linear FO filter to reduce computational burden.…”

Neural network control of fractional-order chaotic systems with unknown control direction

“…In [24] , the quantized control strategy was employed to study the control topic of FOCSs, and the unknown control direction was also considered. In [25] , by using a Nussbaum function, the unknown control gain parameter was approximated by fuzzy logic systems. It should be noted that in above literatures, the Nussbaum function is used as the same in the integer-order systems, i.e., the characteristics of fractional order systems are not well utilized.…”

Adaptive vibration control for constrained moving vehicle-mounted nonlinear 3D rigid-flexible manipulator system subject to actuator failures

“…In Boulouma et al (2017), the authors developed an adaptive fault-tolerant compensation controller to address actuator failure and system uncertainty problems in wing rock motion control. Sabeti et al (2021) proposed an adaptive backstepping method to deal with actuator failures of uncertain nonlinear fractional-order systems and achieve output tracking. The authors in Rugthum and Tao (2021) focused on a cooperative robotic manipulator system with actuator failures and proposed an adaptive fault-tolerant control scheme.…”