Feasibility in Real-Time Optimization using Lipschitz bounds: Robust optimization Vs. Adaptive filtering

This paper investigates two strategies for ensuring feasible-side convergence in Real-Time Optimization (RTO) using Lipschitz-based constraint upper bounds. Strategy 1 embeds the bounds directly into the RTO problem, while Strategy 2 uses them to adaptively tune a filter gain. We compare their performance across three types of bounds: on the plant constraints, constraint modeling error, and constraint gradient error. The results show that Strategy 1 consistently achieves superior convergence, especially under model mismatch or when initialized near active constraints. In contrast, Strategy 2 often leads to premature convergence and suboptimality. These findings support the direct enforcement of Lipschitz bounds as a more robust and effective approach for RTO design.