Bilevel MPC for Linear Systems: A Tractable Reduction and Continuous Connection to Hierarchical MPC

TL;DR

This paper introduces a smooth reduction for bilevel MPC in linear systems, connecting hierarchical MPC to standard MPC through an interpolation framework, ensuring performance and computational efficiency.

Contribution

It proposes a tractable single-level reformulation of bilevel MPC and a continuous interpolation framework linking hierarchical and standard MPC.

Findings

The reduction maintains performance under a block-matrix nonsingularity condition.

In convex cases, the solution is unique and matches centralized MPC.

The interpolation framework enables performance guarantees and efficiency trade-offs.

Abstract

Model predictive control (MPC) has been widely used in many fields, often in hierarchical architectures that combine controllers and decision-making layers at different levels. However, when such architectures are cast as bilevel optimization problems, standard KKT-based reformulations often introduce nonconvex and potentially nonsmooth structures that are undesirable for real-time verifiable control. In this paper, we study a bilevel MPC architecture composed of (i) an upper layer that selects the reference sequence and (ii) a lower-level linear MPC that tracks such reference sequence. We propose a smooth single-level reduction that does not degrade performance under a verifiable block-matrix nonsingularity condition. In addition, when the problem is convex, its solution is unique and equivalent to a corresponding centralized MPC, enabling the inheritance of closed-loop properties. We further show that bilevel MPC is a natural extension of standard hierarchical MPC, and introduce an interpolation framework that continuously connects the two via move-blocking. This framework reveals optimal-value ordering among the resulting formulations and provides inexpensive a posteriori degradation certificates, thereby enabling a principled performance-computational efficiency trade-off.