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. Note to Practitioners—The motivation of this article is that stringent time response constraints are necessary for security or to increase productivity in practical applications, while control constraints exist widely in control systems. The lack of constraint satisfaction may inevitably result in safety defects, performance degradation. Based on these observations, a balanced safety-critical high-gain control scheme is proposed for input-constrained nonlinear uncertain strict-feedback systems. The contribution focuses on finding a balanced relationship between rapid response ability, robustness to mismatched uncertainties, and finite regulation capability in the high-gain control framework, since excessive control gain would potentially amplify the effect of non-vanishing mismatched uncertainty or lead to unexpected control saturation. Moreover, the theoretical derivation demonstrates that: only the system has the tolerance of matched uncertainties when the high gain grows to infinity, otherwise there must exit a maximum value for high gain to maintain the robustness and stability; the PSE function assesses the system safety under saturation conditions and decides whether to continue improving control performance or compensate for saturation for the maintenance of stability.