of updated parameters is avoided and (ii) the modified tracking error asymptotically converges to a compact set of small size [10; 11; 12]. An early incorporation of the AES strategy to Lyapunov-based adaptive control is presented in [10]. The tracking error signal is substituted by the modified tracking error, which is the sum of the tracking error and a filter in terms of the input error \(\Delta u\), which is the difference between the constrained and unconstrained input signals [10; 11; 12]. In the case of high order nonlinear systems, the backstepping strategy is commonly used, and the auxiliary system is defined as a nth order filter in terms of \(\Delta u\)[11; 12; 13]. In adaptive backstepping control design, the input saturation is usually tackled by using the AES strategy [12; 14]. However, accounting for unknown varying control gain is not common in these designs. In [12], a general nonlinear time-delay system of nth order is considered, and an output feedback backstepping is designed. Moreover, the model of a two-stage chemical reactor with recirculation is considered as a second-order particular case. However, the controller design assumes the control gain as constant and perfectly known. In [15], a CSTRconsisting of a second-order SISO model is considered, in which only the output is known. The used anti-windup compensator amounts to the auxiliary system of the AES strategy. However, the controller design assumes that the control gain is perfectly known. In [14], a nth order system with unknown nonlinear control gain is considered. The unknown nonlinear nature of the control gain is tackled by using the Nussbaum gain strategy. However, the width of the convergence region of the modified tracking error depends on unknown model coefficients and terms. In summary, 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. In this study, 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. The design is based on dead zone radially unbounded forms, and a new auxiliary system is proposed. The asymptotic convergence of the modified tracking error is proved by using the [PERSON]'s lemma, accounting for the unknown varying control gain, the saturated input, and the formulated controller. It is ensured that the regular tracking error converges to a residual set of user-defined width, for the case that the input saturation eventually ceases. The main contributions of this study with respect to adaptive backstepping control designs for systems with input saturation are listed below. * The proposed auxiliary system is robust against varying and unknown control gain with unknown upper and lower bounds. This is in contrast to common adaptive backstepping control designs (see in [12; 15]) where the auxiliary system considers the control gain as constant and unknown. * The modified tracking error converges to a compact set whose width is user-defined, so that it does not depend on the bounds of either external disturbances, model terms, system states, or model parameters. This is in contrast to common adaptive backstepping control designs (see in [12; 15]) and also those that use the Nussbaum gain strategy (see in [14]) where the width of the convergence region of the modified tracking error depends on such kind of bounds. * The convergence region of the tracking error is determined for the closed loop system under the formulated controller with the proposed auxiliary system. The work is organized as follows. In Section 2, the model of the biological process, the reference model, and the statement of the control goal are presented.