A block based ALADIN scheme for highly parallelizable direct Optimal Control

Nonlinear Model Predictive Control (NMPC) requires the online solution of a nonlinear Optimal Control Problem (OCP) at each sampling instant. This paper presents a novel, block based and highly parallelizable algorithm which solves nonlinear OCPs using a recently proposed Augmented Lagrangian based method (ALADIN). The latter employs techniques from standard Sequential Quadratic Programming (SQP) methods within a more parallelizable framework. An implementation tailored to optimal control is proposed where Nonlinear Programs (NLPs) are solved approximately and concurrently on each stage while a centralized consensus step is used to update the dual variables of the coupling constraints. The implementation also comprises algorithmic concepts to extend the parallelizability of the consensus step and a blocking technique to accelerate convergence. The performance of the resulting scheme is illustrated using as benchmark example the control of an overhead crane.

[1]  H. Bock,et al.  Recent Advances in Parameteridentification Techniques for O.D.E. , 1983 .

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

[3]  Stephen J. Wright.  Partitioned Dynamic Programming for Optimal Control , 1991, SIAM J. Optim..

[4]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[5]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[6]  MORITZ DIEHL,et al.  A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control , 2005, SIAM J. Control. Optim..

[7]  Johan A. K. Suykens,et al.  Application of a Smoothing Technique to Decomposition in Convex Optimization , 2008, IEEE Transactions on Automatic Control.

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

[9]  Jan Swevers,et al.  Experimental validation of nonlinear MPC on an overhead crane using automatic code generation , 2012, 2012 American Control Conference (ACC).

[10]  Dinh Quoc Tran,et al.  A dual decomposition algorithm for separable nonconvex optimization using the penalty function framework , 2013, 52nd IEEE Conference on Decision and Control.

[11]  Janick V. Frasch.  Parallel algorithms for optimization of dynamic systems in real-time , 2014 .

[12]  Christian Kirches,et al.  qpOASES: a parametric active-set algorithm for quadratic programming , 2014, Mathematical Programming Computation.

[13]  Daniel Axehill,et al.  Controlling the level of sparsity in MPC , 2014, Syst. Control. Lett..

[14]  Moritz Diehl,et al.  Autogenerating microsecond solvers for nonlinear MPC: A tutorial using ACADO integrators , 2015 .

[15]  Moritz Diehl,et al.  Block Condensing for Fast Nonlinear MPC with the Dual Newton Strategy , 2015 .

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

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

[18]  Colin Neil Jones,et al.  A Parametric Nonconvex Decomposition Algorithm for Real-Time and Distributed NMPC , 2016, IEEE Transactions on Automatic Control.