Suboptimal Safety-Critical Control for Continuous Systems Using Prediction–Correction Online Optimization

This article presents an innovative efficient safety-critical control scheme for nonlinear systems by combining techniques of control barrier function (CBF) and online time-varying optimization. The idea lies in that when directly calling the complete optimization solvers used in the CBF method, such as CBF-based quadratic programming (CBF-QP), is computationally inefficient for complex tasks, the suboptimal solutions obtained from online learning techniques can be an alternatively reliable choice for ensuring both efficiency and control performance. By using the barrier-based interior point method, the original optimization problem with CBF constraints is reduced to an unconstrained one with approximate optimality. Then, Newton- and gradient-based continuous dynamics are introduced to generate alternative cheap solutions while ensuring safety. By further considering the lag effect of online tracking, a prediction term is added to the dynamics. In this way, the online cheap solutions are proven to exponentially converge to the time-varying suboptimal solutions of the interior point method. Furthermore, the safety criteria are established, and the robustness of the designed algorithms is analyzed theoretically. Finally, the effectiveness is illustrated by conducting two experiments on obstacle avoidance and anti-swing tasks.