A Parallel Quadratic Programming Algorithm for Model Predictive Control

Brand, Matthew; Shilpiekandula, Vijay; Chen, Yao; Bortoff, Scott A.; Nishiyama, Takehiro; Yoshikawa, Shoji; Iwasaki, Takashi

doi:10.3182/20110828-6-it-1002.03222

Cited by 28 publications

(16 citation statements)

References 21 publications

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“…and hence (28) holds, (29) (30) does not account for the case where J p (U (h) ) > 0 and J d (Y (h) ) < 0, which may occur. However, for this to occur close to the optimum, J p (U * ) ≈ 0, and hence, due to the max operator in (25b), the termination condition to be considered is the absolute error.…”

Section: A Pqp-based Solution Of Mpc Quadratic Programsmentioning

confidence: 99%

“…Termination conditions (28), (30) are valid only for solutions that are primal and dual feasible. While dual feasibility is guaranteed by the PQP properties, primal feasibility of U (h) has to be verified before checking (28), (30). By checking feasibility according to (25) an error is induced in (25b), because only ε-feasibility is verified.…”

Section: A Pqp-based Solution Of Mpc Quadratic Programsmentioning

confidence: 99%

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Projection-free parallel quadratic programming for linear model predictive control

Cairano

Brand

Bortoff

2013

International Journal of Control

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Brand, M.; Bortoff, S. TR2013-059 July 2013Abstract A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace and factory automation is the availability of low-complexity fast optimization algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper we introduce a projection-free iterative optimization algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimized by pre-computing the matrices in a parametric form.We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers. International Journal of ControlThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. AbstractA key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace and factory automation is the availability of low-complexity fast optimization algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper we introduce a projection-free iterative optimization algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projectionfree line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algo...

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Section: A Pqp-based Solution Of Mpc Quadratic Programsmentioning

confidence: 99%

Section: A Pqp-based Solution Of Mpc Quadratic Programsmentioning

confidence: 99%

Projection-free parallel quadratic programming for linear model predictive control

Cairano

Brand

Bortoff

2013

International Journal of Control

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“…(1) and, by extension, Eq. A variational proof is given in a companion paper [2] where the update is used for high-speed optimal control of machinery. The role of r is to guarantee that the update gives a contraction even in the nullspace of semidefinite Q.…”

Section: Introductionmentioning

confidence: 99%

Parallel quadratic programming for image processing

Brand

Chen

2011

2011 18th IEEE International Conference on Image Processing

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Many image processing and computer vision problems can be solved as quadratic programs in the non-negative cone. This paper develops a provably convergent multiplicative update that has a simple form and is amenable to fine-grained data parallelism. Classic algorithms for deblurring, matrix factorization, and tomography are recovered as special cases. This paper also demonstrates applications to super-resolution, labeling and segmentation. IEEE International Conference on Image Processing (ICIP)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. ABSTRACT Many image processing and computer vision problems can be solved as quadratic programs in the nonnegative cone. This paper develops a provably convergent multiplicative update that has a simple form and is amenable to fine-grained data parallelism. Classic algorithms for deblurring, matrix factorization, and tomography are recovered as special cases. This paper also demonstrates applications to super-resolution, labeling and segmentation.Index Terms-parallel quadratic programming, image super-resolution, image segmentation, Markov random field

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“…(5) is transformed into a QP problem [38], and solved using a publicly available MATLAB-based solver. The QP solver outputs the required control inputs for the entire horizon.…”

Section: Linear-quadratic Model Predictive Control (Lq-mpc)mentioning

confidence: 99%

“…This problem formulation results in a convex QP problem that can be solved using readily available solvers [38]. The obstacle avoidance constraint is linearized through a rotating hyperplane method [37].…”

Section: Linear-quadratic Model Predictive Control (Lq-mpc)mentioning

confidence: 99%

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

et al. 2017

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Ground-based experimental evaluations of emerging guidance, navigation, and control (GNC) approaches may be used to raise their technological readiness level and determine their performance and limitations on flight-equivalent hardware (i.e., sensors, actuators, and computational systems) [2].An experimental campaign to evaluate the performance of the model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD) guidance methods has been performed at the Naval Postgraduate School POSEI-DYN 1 air-bearing test bed [4]. The focus of this research is limited in scope to the guidance and control of the simulated spacecraft. The navigation problem is solved by the POSEIDYN test bed motion capture system, which, augmented by onboard sensors, is used to provide accurate navigation data. The test vehicles operating in the POSEI-DYN test bed float on top of a 4-by-4 m granite table and exhibit a drag-free and weightless motion on a plane [4]. These test vehicles are referred to as floating spacecraft simulators, or simply as FSS.A spacecraft docking problem is selected for the experimental evaluation of these two different control approaches. A keep-out zone, an entry cone, and a maximum force constraint are added to the docking scenario to evaluate the constraint handling abilities of the two different controllers. A linear-quadratic MPC (LQ-MPC) algorithm with a quadratic programming (QP) solver and an IDVD algorithm with a nonlinear programming (NLP) solver have been chosen for this comparative study. These two controllers have been implemented and, when executed in real-time on board the FSS, they are successful in 1 POSEIDYN stands for Proximity Operation of Spacecraft: Experimental hardware-In-the-loop DYNamic simulator Abstract An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a groundbased air-bearing test bed, using spacecraft simulators that float over a granite table.Keywords Rendezvous and proximity operations · Model predictive control · Inverse dynamics · Hardware-in-theloop

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A Parallel Quadratic Programming Algorithm for Model Predictive Control

Cited by 28 publications

References 21 publications

Projection-free parallel quadratic programming for linear model predictive control

Projection-free parallel quadratic programming for linear model predictive control

Parallel quadratic programming for image processing

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

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