Constraint Selection in Optimization-Based Controllers
Haejoon Lee, Panagiotis Rousseas, Dimitra Panagou
TL;DR
This paper addresses real-time constraint management in optimization-based controllers by solving a maxFS problem to maximize the number of satisfied constraints at each time step. It proposes a Lagrange-multiplier–informed heuristic that tests feasibility via a small dual LP, avoids slack-variable expansions, and uses past multipliers to iteratively discard soft constraints while allowing reintroduction. The approach yields significantly faster feasibility checks and scales well with the number of constraints, achieving performance comparable to state-of-the-art methods. The results demonstrate practical applicability to safe, efficient human-in-the-loop control in dynamic environments, with improved computational efficiency for real-time deployment.
Abstract
Human-machine collaboration often involves constrained optimization problems for decision-making processes. However, when the machine is a dynamical system with a continuously evolving state, infeasibility due to multiple conflicting constraints can lead to dangerous outcomes. In this work, we propose a heuristic-based method that resolves infeasibility at every time step by selectively disregarding a subset of soft constraints based on the past values of the Lagrange multipliers. Compared to existing approaches, our method requires the solution of a smaller optimization problem to determine feasibility, resulting in significantly faster computation. Through a series of simulations, we demonstrate that our algorithm achieves performance comparable to state-of-the-art methods while offering improved computational efficiency.