Abstract
A parallel Newton-type method for nonlinear model predictive control is presented that exploits the particular structure of the associated discrete-time Euler–Lagrange equations obtained by utilizing an explicit discretization method in the reverse-time direction. These equations are approximately decoupled into single-step subproblems along the prediction horizon for parallelization. The coupling variable of each subproblem is approximated to its optimal value using a simple, efficient, and effective method at each iteration. The rate of convergence of the proposed method is proved to be superlinear under mild conditions. Numerical simulation of using the proposed method to control a quadrotor showed that the proposed method is highly parallelizable and converges in only a few iterations, even to a high accuracy. Comparison of the proposed method’s performance with that of several state-of-the-art methods showed that it is faster.
Highlights
Nonlinear model predictive control (NMPC) is an optimal control method for controlling nonlinear systems
First-order methods such as the alternating direction method of multipliers (Jerez et al, 2014; O’Donoghue, Stathopoulos, & Boyd, 2013) and the fast gradient method (Jerez et al, 2014) can be parallelized and efficiently implemented for linear MPC, they suffer from slow rates of convergence compared with the Newton-type methods, dealing with complicated constraints, and time-varying dynamics in the underlying linearized problems when using sequential quadratic programming (SQP) for NMPC
An augmented Lagrangian-based method tailored to nonlinear OCPs has been reported (Kouzoupis, Quirynen, Houska, & Diehl, 2016) that concurrently solves subproblems along the prediction steps and solves a centralized consensus quadratic programming (QP) to update the dual variables at each iteration
Summary
Nonlinear model predictive control (NMPC) is an optimal control method for controlling nonlinear systems. First-order methods such as the alternating direction method of multipliers (Jerez et al, 2014; O’Donoghue, Stathopoulos, & Boyd, 2013) and the fast gradient method (Jerez et al, 2014) can be parallelized and efficiently implemented for linear MPC, they suffer from slow rates of convergence compared with the Newton-type methods, dealing with complicated constraints, and time-varying dynamics in the underlying linearized problems when using SQP for NMPC. An augmented Lagrangian-based method tailored to nonlinear OCPs has been reported (Kouzoupis, Quirynen, Houska, & Diehl, 2016) that concurrently solves subproblems along the prediction steps and solves a centralized consensus QP to update the dual variables at each iteration This method has a linear rate of convergence and its speed-up depends on the computation time of the consensus step in accordance with Amdahl’s law (Amdahl, 1967).
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