Benchmark Dataset: Distributed Model Predictive Control (DMPC)

Overview

This dataset contains 18,000 randomly generated distributed model predictive control (DMPC) instances for benchmarking algorithms for distributed convex optimization via dual decomposition.

The benchmark structure follows Yfantis et al. (2024), where the original benchmark is publicly available on Zenodo. This dataset was generated using the same procedure with a larger and more varied set of instances.

Problem Formulation

Each instance is a constraint-coupled MPC problem of the form:

min sum_i=1^N_s [ J_i^f(x_i^N_p) + sum_k=0^N_p-1 J_i(x_i^k, u_i^k) ]
x_i^0:N_p, u_i^0:N_p-1

s.t. x_i^k+1 = A_i x_i^k + B_i u_i^k, for all i, k = 0,...,N_p-1
 x_i^0 = x_tilde(t_0), for all i
 x_i^k in X_i, for all i, k = 0,...,N_p
 u_i^k in U_i, for all i, k = 0,...,N_p-1
 sum_i R_i u_i^k <= r_max^k, for k = 0,...,N_p-1

where:

• N_s is the number of subsystems
• N_p is the prediction horizon
• A_i, B_i are the system and input matrices of subsystem i
• X_i, U_i are the local state and input constraint sets
• R_i maps the inputs of subsystem i to its resource consumption or production
• r_max^k is the total resource availability at time step k

The resource constraint takes the role of the coupling constraint and links all subsystems, while the local dynamics and constraints are handled independently per subsystem.

Stage and Terminal Cost

A quadratic tracking objective is used for stage and terminal costs:

J_i(x_i^k, u_i^k) = (x_i^k - x_i^ref,k)^T H_x (x_i^k - x_i^ref,k) + u_i^k,T H_u u_i^k

with symmetric positive-definite weighting matrices H_x and H_u.

Parameter Space

All combinations of the following parameters were generated, with 100 instances per combination, resulting in 18,000 instances in total.