Learning-Enabled Iterative Convex Optimization for Safety-Critical Model Predictive Control

Safety remains a central challenge in control of dynamical systems, particularly when the boundaries of unsafe sets are complex (e.g., nonconvex, nonsmooth) or unknown. This paper proposes a learning-enabled framework for safety-critical Model Predictive Control (MPC) that integrates Discrete-Time High-Order Control Barrier Functions (DHOCBFs) with iterative convex optimization. Unlike existing methods that primarily address CBFs of relative degree one with fully known unsafe set boundaries, our approach generalizes to arbitrary relative degrees and addresses scenarios where the unsafe set boundaries must be inferred. We extract pixel-based data specifically from unsafe set boundaries and train a neural network to approximate local linearizations of these boundaries. The learned models are incorporated into the linearized DHOCBF constraints at each time step, enabling real-time constraint satisfaction within the MPC framework. An iterative convex optimization procedure is developed to accelerate computation while maintaining formal safety guarantees. The benefits of computational performance and safe avoidance of obstacles with diverse shapes are examined and confirmed through numerical results. By bridging model-based control with learning-based environment modeling, this framework advances safe autonomy for discrete-time systems operating in complex and partially known settings.