Distributed model predictive control without terminal cost under inexact distributed optimization

TL;DR

This work tackles distributed model predictive control for linear discrete-time networks with coupled constraints, proposing a stability condition that replaces terminal costs via relaxed dynamic programming (RDP). It develops a distributed synthesis framework that decouples the global problem into local agents using slack variables and doubly stochastic weights, and enforces feasibility during iterations through constraint tightening, yielding a violation-free, parallelizable optimization process. Theoretical guarantees include Lyapunov stability under the proposed horizon-end constraint, existence and convexity of local subproblems, and convergence of the distributed optimization procedure. A platoon example illustrates that the method achieves closed-loop stability with larger horizons improving performance at the cost of higher computation time, and confirms parallel computation across agents.

Abstract

This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.

Figures (3)

• Figure 1: Distributed MPC for connected and automated vehicles.
• Figure 2: Cost per step for different horizons.
• Figure 3: Speed and position tracking of each vehicle.