Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
This work addresses the computational bottleneck in hybrid MPC for real-time applications, offering an incremental improvement by combining existing techniques like geometric insights, learning algorithms, and warm starts.
The paper tackles the challenge of slow online solving for hybrid model predictive control (MPC) using mixed-integer programming (MIP), and proposes a learning-control algorithm called LNMS that accelerates MIP with minimal computational cost while maintaining ease of implementation.
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement.