Parallel Shooting Sequential Quadratic Programming for Nonlinear MPC Problems

In this paper, we propose a parallel shooting algorithm for solving nonlinear model predictive control problems using sequential quadratic programming. This algorithm is built on a two-phase approach where we first test and assess sequential convergence over many initial trajectories in parallel. However, if none converge, the algorithm starts varying the Newton step size in parallel instead. Through this parallel shooting approach, it is expected that the number of iterations to converge to an optimal solution can be decreased. Furthermore, the algorithm can be further expanded and accelerated by implementing it on GPUs. We illustrate the effectiveness of the proposed Parallel Shooting Sequential Quadratic Programming (PS-SQP) method in some benchmark examples for nonlinear model predictive control. The developed PS-SQP parallel solver converges faster on average and especially when significant nonlinear behaviour is excited in the NMPC horizon.

I. Introduction

Model Predictive Control (MPC) is a control strategy that computes the control input by optimizing the predicted response over a finite time horizon while respecting system constraints [1]. Due to this explicit form of computing the control law, MPC problems are significantly more complex compared to classical frequency domain or state feedback controllers. However, the MPC framework is not limited to LTI systems and can be extended to control nonlinear systems.