Mixed integer predictive control and shortest path reformulation

TL;DR

This paper introduces a decomposition approach for mixed integer predictive control problems, transforming them into independent shortest path problems solved via linear programming, enhancing tractability for larger systems.

Contribution

It presents a novel decomposition method that simplifies high-dimensional mixed integer control problems into scalar shortest path problems, improving computational efficiency.

Findings

Decomposition reduces problem complexity.

Reformulation as shortest path enables efficient LP solutions.

Method improves scalability of mixed integer predictive control.

Abstract

Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this little issue, we propose a decomposition method which turns the original $n$-dimensional problem into $n$ indipendent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. The approximation introduced by the decomposition can be lowered if we operate in accordance with the predictive control technique: i) optimize controls over the horizon ii) apply the first control iii) provide measurement updates of other states and repeat the procedure.