Analytical results for the multi-objective design of model-predictive control

TL;DR

This paper introduces a multi-objective design framework for model-predictive control that balances control performance with computational resource requirements, providing a systematic tuning method and validated guarantees.

Contribution

It extends existing MPC design methods by jointly optimizing sampling time and prediction horizon, with theoretical analysis and a specialized solver for multi-objective optimization.

Findings

The design objectives are smooth and bounded, enabling effective optimization.

Necessary and sufficient conditions for solver effectiveness are established.

Real-world control problems demonstrate the approach's practical benefits.

Abstract

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem.