A Time Splitting Based Real-Time Iteration Scheme for Nonlinear MPC

This paper proposes a parallelizable real-time algorithm for model predictive control (MPC). In contrast to existing distributed and parallel optimization algorithms for linear MPC such as dual decomposition or the alternating direction method of multipliers (ADMM), the proposed algorithm can deal with nonlinear dynamic systems as well as non-convex stage costs. Existing real-time algorithms for MPC simulate and compute sensitivities of the predicted state trajectories on the whole prediction horizon. Different from this, the proposed method uses a reversed real-time scheme, where small-scale nonlinear MPC problems are solved on much shorter horizons and in parallel during the feedback phase, while a large equality constrained coupled QP is solved during the preparation step. This makes the proposed algorithm particularly suited for nonlinear MPC problems with long prediction horizons. The performance and advantages of the proposed method compared to existing real-time nonlinear MPC algorithms are illustrated by applying the method to a benchmark case study.

[1]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[2]  Moritz Diehl,et al.  A parallel quadratic programming method for dynamic optimization problems , 2015, Math. Program. Comput..

[3]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[4]  Victor M. Zavala,et al.  The advanced-step NMPC controller: Optimality, stability and robustness , 2009, Autom..

[5]  Moritz Diehl,et al.  A block based ALADIN scheme for highly parallelizable direct Optimal Control , 2016, 2016 American Control Conference (ACC).

[6]  Manfred Morari,et al.  Computational aspects of distributed optimization in model predictive control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  S. Joe Qin,et al.  An Overview of Nonlinear Model Predictive Control Applications , 2000 .

[8]  Moritz Diehl,et al.  An Augmented Lagrangian Based Algorithm for Distributed NonConvex Optimization , 2016, SIAM J. Optim..

[9]  Johan A. K. Suykens,et al.  Distributed nonlinear optimal control using sequential convex programming and smoothing techniques , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[10]  James B. Rawlings,et al.  Discrete-time stability with perturbations: application to model predictive control , 1997, Autom..

[11]  Dinh Quoc Tran,et al.  An Inexact Perturbed Path-Following Method for Lagrangian Decomposition in Large-Scale Separable Convex Optimization , 2011, SIAM J. Optim..

[12]  Moritz Diehl,et al.  An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range , 2011, Autom..

[13]  Abdelouahed Hamdi,et al.  Decomposition Methods Based on Augmented Lagrangians: A Survey , 2011 .

[14]  Manfred Morari,et al.  Towards computational complexity certification for constrained MPC based on Lagrange Relaxation and the fast gradient method , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  Melanie Nicole Zeilinger,et al.  Inexact fast alternating minimization algorithm for distributed model predictive control , 2014, 53rd IEEE Conference on Decision and Control.

[16]  Bart De Schutter,et al.  Accelerated gradient methods and dual decomposition in distributed model predictive control , 2013, Autom..

[17]  Moritz Diehl,et al.  A distributed method for convex quadratic programming problems arising in optimal control of distributed systems , 2013, 52nd IEEE Conference on Decision and Control.

[18]  Rolf Findeisen,et al.  Cooperative Distributed MPC Using the Alternating Direction Multiplier Method , 2012 .

[19]  M. Diehl,et al.  Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations , 2000 .

[20]  Stephen P. Boyd,et al.  A Splitting Method for Optimal Control , 2013, IEEE Transactions on Control Systems Technology.

[21]  Nicholas I. M. Gould,et al.  GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization , 2003, TOMS.

[22]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[23]  Stephen P. Boyd,et al.  Automatic code generation for real-time convex optimization , 2010, Convex Optimization in Signal Processing and Communications.

[24]  Matthias Albrecht Müller,et al.  Cost-to-travel functions: A new perspective on optimal and model predictive control , 2017, Syst. Control. Lett..

[25]  Convex Optimization in Signal Processing and Communications , 2010 .

[26]  Benjamin Pfaff,et al.  Perturbation Analysis Of Optimization Problems , 2016 .

[27]  Yuning Jiang,et al.  Parallel Explicit Model Predictive Control , 2019, 1903.06790.

[28]  João M. F. Xavier,et al.  Distributed ADMM for model predictive control and congestion control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).