Discrete nonlinear contraction theory based adaptive control strategy for a class of hammerstein systems with saturated hysteresis

Abstract

Smart materials actuated devices have been attracting tremendous attentions for decades, especially nowadays. Smart material actuators have been prevalently utilized in the fields such as soft robots and nano-engineering for their outstanding merits such as flexibility and ultrahigh spatial resolution. Although, usage of these smart material actuators can facilitate transmission systems design, problems show up in the control counterpart, which is still a challenging topic. As common phenomena, these actuators exhibit inherent hysteretic input-output relation which usually cause systems behave unexpectedly compared to conventional actuator such as the motors. Moreover, some actuators' behaviors can be slightly or seriously influenced by the external and internal factors, such as environmental temperature and humidity and the instinctive deterioration caused by usage. To cope with the challenging control tasks, adaptive control strategies, which are able to detect variation of actuator characteristics via estimation techniques, have been widely investigated and implemented. One of the promising generalized adaptive control schemes is developed based on the nonlinear contraction theory (NCT), which brings a more transparent and simpler process in controller design and convergence analysis. This paper proposes to design a discrete nonlinear adaptive control strategy based on the Discrete NCT (DNCT) to tackle a class of general hysteretic system considering saturation and time varying properties. The proposed control strategy combines feedback control law, adaptive law and the hysteresis compensator to guarantee desired input-output dynamic relation of the closed-loop system. Sufficient stability condition is given and verified through simulations, test result shows the system tracking error and parameters estimation error converge to zero exponentially fast.