Feasible-Set Reshaping for Constraint Qualification in Optimization-Based Control

TL;DR

This paper introduces a feasible-set reshaping method for optimization-based control that guarantees constraint qualification by projecting constraints onto a positive span, ensuring LICQ and improving controller design.

Contribution

The paper proposes a novel feasible-set reshaping technique that guarantees LICQ in real-time control problems where the feasible set depends on the plant state.

Findings

Reshaped feasible set is nonempty if the original set is nonempty.

The method ensures LICQ in the reshaped feasible set.

Constructed Lipschitz continuous QP-based controllers demonstrate effectiveness.

Abstract

This paper presents a novel feasible-set reshaping technique to optimization-based control with ensured constraint qualification. In our problem setting, the feasible set of admissible control inputs depends on the real-time state of the plant, and the linear independence constraint qualification (LICQ) may not be satisfied in some regions of interest. By feasible-set reshaping, we project the constraints of the original feasible set onto an appropriately chosen constant matrix with its rows forming a positive span of the space of the optimization variable. It is proved that the reshaped feasible set is nonempty and satisfies LICQ, as long as the original feasible set is nonempty. The effectiveness of the proposed method is verified by constructing Lipschitz continuous quadratic-program-based (QP-based) controllers based on the reshaped feasible sets.