Time-Optimal nonlinear model predictive control with minimal control interventions

This paper presents a novel approach for timeoptimal model predictive control. In contrast to a global uniform time scaling, the underlying optimal control problem rests upon a dynamic, local temporal discretization of the shooting grid. The approach seeks for a grid partition with minimum overall transition time. Furthermore, a multi-stage optimization iteratively adapts the number of grid points during runtime to achieve a minimum number of control interventions. A comparative analysis with previous approaches for three nonlinear control problems demonstrates the superiority of the proposed scheme. The feasibility is experimentally demonstrated for position control of a servo drive operated at 200 Hz.

[1]  Arthur Richards,et al.  Fast model predictive control with soft constraints , 2013, 2013 European Control Conference (ECC).

[2]  Robin S. Sharp,et al.  Time-optimal control of the race car: a numerical method to emulate the ideal driver , 2010 .

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

[4]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[5]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

[6]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[7]  Jan Swevers,et al.  Time-optimal motion planning for n-DOF robot manipulators using a path-parametric system reformulation , 2016, 2016 American Control Conference (ACC).

[8]  Denise Lam,et al.  A model predictive approach to optimal path-following and contouring control , 2012 .

[9]  Héctor J. Sussmann,et al.  The structure of time-optimal trajectories for single-input systems in the plane: the general real analytic case , 1987 .

[10]  Henrik Ohlsson,et al.  Sparse control using sum-of-norms regularized model predictive control , 2013, 52nd IEEE Conference on Decision and Control.

[11]  Torsten Bertram,et al.  Efficient trajectory optimization using a sparse model , 2013, 2013 European Conference on Mobile Robots.

[12]  Jie Zhao,et al.  Nonlinear Model Predictive Control of Robots Using Real-Time Optimization , 2004 .

[13]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[14]  Knut Graichen,et al.  A Real-Time Gradient Method for Nonlinear Model Predictive Control , 2012 .

[15]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[16]  Jan Swevers,et al.  A model predictive control approach for time optimal point-to-point motion control , 2011 .

[17]  Moritz Diehl,et al.  An efficient implementation of partial condensing for Nonlinear Model Predictive Control , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[18]  Torsten Bertram,et al.  Timed-Elastic-Bands for time-optimal point-to-point nonlinear model predictive control , 2015, 2015 European Control Conference (ECC).

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

[20]  Knut Graichen,et al.  Nonlinear model predictive control based on constraint transformation , 2016 .