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

Alejandro Rincón,Fredy E Hoyos,John E Candelo-Becerra

doi:10.3390/app11010251

Alejandro Rincón, Fredy E Hoyos + Show 1 more

Open Access

https://doi.org/10.3390/app11010251

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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.

Highlights

Automatic control of biological processes based on non-adaptive schemes is commonly affected by model uncertainty: (i) uncertain time varying coefficients of the reaction rates, (ii) uncertain time varying reaction yields, (iii) uncertain concentrations, and (iv) varying and uncertain or noisily measured inflow substrate concentration [1,2,3]
An adaptive backstepping controller was developed for a second order plant model subject to unknown model parameters, unknown reaction rate, unknown varying control gain, and input saturation
The controller provides important contributions to adaptive control design for second-order models with input saturation:. It tackles the combined effect of constrained control input and unknown varying control gain with unknown bounds

Summary

Introduction

Automatic control of biological processes based on non-adaptive schemes is commonly affected by model uncertainty: (i) uncertain time varying coefficients of the reaction rates, (ii) uncertain time varying reaction yields, (iii) uncertain concentrations, and (iv) varying and uncertain or noisily measured inflow substrate concentration [1,2,3]. In the aforementioned AES-based robust adaptive backstepping control designs, the modified tracking error converges to a compact set whose width depends on the bounds of either external disturbances, model terms or model parameters [11,12,14]. This implies that such bounds must be known to achieve a user-defined magnitude of the steady value of the modified tracking error. A modified/new robust adaptive backstepping controller is developed for a second-order SISO nonlinear system, tackling the effect of input saturation and unknown varying control gain with unknown upper and lower bounds.

Reference Model

Control Goal

Controller Design

Boundedness and Convergence Analysis

Simulation Example

Conclusions