Projection-Based Iterative Mode Scheduling for Switched Systems

TL;DR

This paper introduces a projection-based iterative method for optimal mode scheduling in switched systems, offering guarantees on convergence and feasibility without requiring time discretization, suitable for complex real-time applications.

Contribution

The proposed approach provides a novel iterative optimization method for mode scheduling that guarantees convergence and feasibility, outperforming mixed integer and relaxation-based methods in efficiency and applicability.

Findings

Successfully applied to vehicle tracking and power network synchronization.

Prevents instability in high-dimensional systems at near real-time speeds.

No need for time or state discretization in the optimization process.

Abstract

This paper describes a method for scheduling the events of a switched system to achieve an optimal performance. The approach has guarantees on convergence and computational complexity that parallel derivative-based iterative optimization but in the infinite dimensional, integer constrained setting of mode scheduling. In comparison to methods relying on mixed integer programming, the presented approach does not require a priori discretizations of time or state. Furthermore, in comparison to embedding and relaxation methods, every iteration of the algorithm returns a dynamically feasible solution. A large class of problems call for optimal mode scheduling. This paper considers a vehicle tracking problem and a high dimensional multimachine power network synchronization problem. For the power network example, both single horizon and receding horizon approaches prevent instability of the network, and the receding horizon approach does so at near real-time speeds on a single processor.