Improving model predictive controller turnaround time using restricted Lagrangians

We present a new application of proper orthogonal decomposition (POD) to optimal control. By restricting the Lagrangian of an optimal control problem to a suitable affine subspace, we can achieve a reduction in computational cost leading to faster turnaround times with minimal degradation in controller performance. An explicit algorithm for nonlinear model predictive control (NMPC) reduction using POD is presented along with some initial error analysis. To the best of our knowledge, this is the first time such an approach has been presented. We applied this approach to the control of a vehicle during a double lane change maneuver using NMPC and achieved 2 times faster turnaround times with excellent controller performance. This reduction approach for the development of real-time optimal controls is very promising and introduces some new research directions.