Iterative Optimal Feedback Control for Time-based Switched Systems

This paper presents a data-driven iterative optimal feedback control approach to solve input constrained nonlinear optimal control problems with switching dynamics. We consider multi-stage optimal control problems where the switching sequence of the stages is known but the switching instants and the control inputs are both unknown and are optimized. The proposed approach relies on repetitive task execution and assumes inexact models for both continuous and discrete dynamics in between and at the switching events. Our key contribution is a novel algorithm which iteratively computes a local feedback control input along the measured trajectory of the controlled system, as opposed to computing the control input along the trajectory predicted by an inexact model. We conjecture that the proposed algorithm can significantly reduce the cost compared to alternative methods that use model-based future prediction. The benefit of the algorithm is illustrated with numerical simulation and demonstrated with an experiment using a three-link torque-controlled robot. The algorithm provides a new systematic method for real-time data-driven optimal control of complex robotic systems.