Balanced Safety-Critical High-Gain Control for Uncertain Nonlinear Systems With Input Saturation

In this paper, we propose the dynamic high-gain scaling technique and solutions to input saturation for uncertain strict-feedback nonlinear systems. Although high gain affords fast response and high accuracy for the improvement of tracking performance, there are two inescapable potential risks: (i) excessive high gain would amplify the negative effects from non-vanishing mismatched uncertainties; (ii) high gain may conflict with the limited regulation capacity. Herein, two strategies based on invariance property are applied to high-gain control, aiming to address these two risks separately. On the one hand, by defining the function of performance robustness evaluation (PRE), the scaling gain grows to speed up the convergence rate and then maintains at an acceptable high level while guaranteeing the robustness to uncertainties in an invariant set. On the other hand, for handling the input saturation, the control barrier function (CBF)-based quadratic program (QP) describes the function of performance safety evaluation (PSE) that helps assess the system safety and decide whether the compensation for saturation is necessary, as such, the balance between performance and saturation gets achieved. Numerical simulations and a semi-physical experiment are performed to investigate the performance of our proposed methodology.