Switch-Time-Aware Hybrid Model Predictive Control Using the Hybrid Minimum Principle

Key points

• Rather than relying on a fixed time grid, the switching instant is lifted into the decision vector and treated as an explicit optimization variable.1
• The resulting transcription is a smooth nonlinear program whose Karush-Kuhn-Tucker (KKT) conditions are consistent with the Hybrid Minimum Principle (HMP) event-time stationarity condition, so first-order hybrid sensitivities are recovered implicitly through the KKT system rather than by evaluating saltation matrices.1
• Each MPC step solves a single sparse Quadratic Program (QP), jointly optimizing control inputs and impact timing in real time.1
• On a bouncing mass landing on an oscillating platform, the method attaches in half the time of fixed-grid saltation MPC, reduces cumulative control effort by 30%, and removes the post-impact rebounds, at a 15% increase in per-cycle solve time.1

Sources (1)

• [1]Switch-Time-Aware Hybrid Model Predictive Control Using the Hybrid Minimum Principle
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 16, 06:53 PM

  This article presents a time-aware hybrid model predictive control (MPC) framework that simultaneously optimizes the objective with respect to both continuous control inputs and event switching times.

  Rather than relying on a fixed time grid, the switching instant is lifted into the decision vector and treated as an explicit optimization variable.

Extractive summary: sentences quoted from the sources.