Real-Time Dynamic-Mode Scheduling Using Single-Integration Hybrid Optimization

This paper introduces and implements a method for real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of switched system algorithms is often prohibitive for real-time applications and typically may only be reduced at the expense of approximation accuracy. We address this tradeoff by taking advantage of system linearity to formulate a projection-based approach, such that no simulation is required during open-loop optimization. A numerical example shows how the proposed open-loop algorithm outperforms the methods employing common numerical integration techniques. In addition, we follow a receding-horizon scheme to schedule the modes of a customized experimental setup in real time, using the robot operating system. In particular, we demonstrate-both in Monte Carlo simulation and in experiment-that optimal mode scheduling efficiently regulates a cart and suspended mass system and rejects disturbances online.