Adaptive Control for a Biological Process under Input Saturation and Unknown Control Gain via Dead Zone Lyapunov Functions

Abstract

In this work, substrate control of a biological process with unknown varying control gain, input saturation, and uncertain reaction rate is addressed. A novel adaptive controller is proposed, which tackles the combined effect of input saturation and unknown varying control gain with unknown upper and lower bounds. The design is based on dead zone radially unbounded Lyapunov-like functions, with the state backstepping as control framework. The convergence of the modified tracking error and the boundedness of the updated parameters are ensured by means of the Barbalat’s lemma. As the first distinctive feature, a new second-order auxiliary system is proposed that tackles the effect of saturated input and the unknown varying control gain with unknown upper and lower bounds. As the second distinctive feature, the modified tracking error converges to a compact set whose width is user-defined, so that it does not depend on bounds of either external disturbances, model terms, or model coefficients. The convergence region of the current tracking error is determined for the closed loop system subject to the formulated controller and the proposed auxiliary system. Finally, numerical simulation illustrates the performance of the proposed controller.

Keywords

• input saturation
• uncertain nonlinear system
• adaptive control
• unknown control gain
• backstepping control
• dead zone Lyapunov function