Parametric Optimization Based MPC for Systems of Systems with Affine Coordination Constraints

TL;DR

This paper presents an efficient parametric MPC algorithm for large-scale systems of systems with affine coordination constraints, leveraging problem splitting and parametric solutions for real-time control.

Contribution

It introduces a novel splitting-based MPC approach that combines offline parametric optimization of local subsystems with online coordination solving, improving efficiency.

Findings

Coordination problem solvable in linear time for fixed constraints

Local parametric solutions enable fast online coordination

Algorithm applicable to systems with one-dimensional coordination parameters

Abstract

A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive control of a class of system of systems for which the overall objective function is the sum of convex quadratic cost functions of (locally) constrained linear subsystems that are coupled through a set of (global) linear constraints on the subsystems coordination parameters. The proposed control algorithm is based on parametrization and splitting of the underlying optimization problem into one global coordination problem and a set of local optimization problems pertaining to individual subsystems. The local optimization problems are solved off-line, via parametric optimization, while the coordination problem is solved on-line. The properties of the local parametric solutions are utilized to solve the coordination problem very efficiently. In particular, it is shown that, for a fixed number of coupling constraints, the coordination problem can be solved with a linear-time algorithm in a finite number of iterations if all subsystems have one-dimensional coordination parameters.