MPC for Linear Systems With Concave Inequality Constraints and Convexification Loss Analysis

In this article, we propose a model predictive control (MPC) algorithm using sequential convex programming (SCP) to address concave inequality constraints. Based on traditional SCP, we introduce two methods to improve the solution quality and reduce the cost when SCP is stopped early at each time step. First, we analyze multiple explicit representations of a single constraint and propose a method to reduce convexification loss without solving additional nested dual problems. Second, we map the expansion points to the constraint boundary and propose the second method, which minimizes the loss to the greatest extent, referred to as weak loss convexification. Both methods are incorporated into a suboptimal MPC framework, guaranteeing recursive feasibility and stability, even when SCP is stopped early. Finally, simulations demonstrate that the proposed methods reduce conservatism in closed-loop trajectories, particularly for higher order concave inequality constraints.