A hierarchical time-splitting approach for solving finite-time optimal control problems

Stathopoulos, Georgios T.; Keviczky, Tamás; Wang, Yang

doi:10.23919/ecc.2013.6669702

Cited by 17 publications

(42 citation statements)

References 21 publications

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“…is the dual cost defined in (5). In addition, let L Π := max t (π t σ f ) −1 eig min (H y ), π t ∈ Π.…”

Section: Stochastic Ama With Variance Reductionmentioning

confidence: 99%

“…These solvers are relatively easy to certify (in terms of level of suboptimality of the solution), use only simple algebraic operations, and require little memory. In [5]- [7], operator-splitting methods, such as the alternating minimization method of multipliers (ADMM) [8] and the fast alternating minimization algorithm (FAMA) [9], have been used to exploit the MPC problem structure and speed-up the computation of the solution. These algorithms most of the time require frequent exchanges of information at given synchronization points.…”

Section: Introductionmentioning

confidence: 99%

“…The idea of the time splitting has been previously proposed in [5]. Their work relies on a synchronous ADMM algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Asynchronous splitting design for Model Predictive Control

Ferranti

Jones

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-This paper focuses on the design of an asynchronous dual solver suitable for embedded model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the context of stochastic proximal gradient methods, and on the alternating minimization algorithm (AMA). The resultant algorithm, a stochastic AMA with VR, shows geometric convergence (in the expectation) to a suboptimal solution of the MPC problem and, compared to other state-of-the-art dual asynchronous algorithms, allows to tune the probability of the asynchronous updates to improve the quality of the estimates. We apply the proposed algorithm to a specific class of splitting methods, i.e., the decomposition along the length of the prediction horizon, and provide preliminary numerical results on a practical application, the longitudinal control of an Airbus passenger aircraft.

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“…is the dual cost defined in (5). In addition, let L Π := max t (π t σ f ) −1 eig min (H y ), π t ∈ Π.…”

Section: Stochastic Ama With Variance Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asynchronous splitting design for Model Predictive Control

Ferranti

Jones

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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“…In [12] a splitting method based on Alternating Direction Method of Multipliers (ADMM) is used, where some steps of the algorithm can be computed in parallel. In [13] an iterative three-set splitting quadratic programming (QP) solver is developed. In this method several simpler subproblems are computed in parallel and a consensus step using ADMM is performed to obtain the final solution.…”

Section: Introductionmentioning

confidence: 99%

A parallel structure exploiting factorization algorithm with applications to Model Predictive Control

Nielsen

Axehill

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-In Model Predictive Control (MPC) the control signal is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The CFTOC problem can be solved by, e.g., interior-point or active-set methods, where the main computational effort in both methods is known to be the computation of the search direction, i.e., the Newton step. This is often done using generic sparsity exploiting algorithms or serial Riccati recursions, but as parallel hardware is becoming more commonly available the need for parallel algorithms for computing the Newton step is increasing. In this paper a tailored, non-iterative parallel algorithm for computing the Newton step using the Riccati recursion is presented. The algorithm exploits the special structure of the Karush-Kuhn-Tucker system for a CFTOC problem. As a result it is possible to obtain logarithmic complexity growth in the prediction horizon length, which can be used to reduce the computation time for popular state-of-the-art MPC algorithms when applied to what is today considered as challenging control problems.

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“…Since in recent years MPC has been increasingly applied to systems raghunathan,dicairano@merl.com with fast dynamics and low computing power embedded processors [8], [9], [10] low complexity fast optimization algorithms have been investigated in the MPC context, see e.g., [11], [12], [13] and the references therein. ADMM has been previously explored in the context of MPC in [14], [15], in particular for solving the QP via different decompositions. As mentioned earlier, the assumptions required by [6] for optimal ADMM step size selection do not hold in general for the QPs of MPC.…”

Section: Introductionmentioning

confidence: 99%

Alternating direction method of multipliers for strictly convex quadratic programs: Optimal parameter selection

Raghunathan¹,

Cairano²

2014

2014 American Control Conference

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We consider an approach for solving strictly convex quadratic programs (QPs) with general linear inequalities by the alternating direction method of multipliers (ADMM). In particular, we focus on the application of ADMM to the QPs of constrained Model Predictive Control (MPC). After introducing our ADMM iteration, we provide a proof of convergence closely related to the theory of maximal monotone operators. The proof relies on a general measure to monitor the rate of convergence and hence to characterize the optimal step size for the iterations. We show that the identified measure converges at a Q-linear rate while the iterates converge at a 2-step Q-linear rate. This result allows us to relax some of the existing assumptions in optimal step size selection, that currently limit the applicability to the QPs of MPC. The results are validated through a large public benchmark set of QPs of MPC for controlling a four tank process. American Control Conference (ACC), 2014This 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-We consider an approach for solving strictly convex quadratic programs (QPs) with general linear inequalities by the alternating direction method of multipliers (ADMM). In particular, we focus on the application of ADMM to the QPs of constrained Model Predictive Control (MPC). After introducing our ADMM iteration, we provide a proof of convergence closely related to the theory of maximal monotone operators. The proof relies on a general measure to monitor the rate of convergence and hence to characterize the optimal step size for the iterations. We show that the identified measure converges at a Q-linear rate while the iterates converge at a 2-step Q-linear rate. This result allows us to relax some of the existing assumptions in optimal step size selection, that currently limit the applicability to the QPs of MPC. The results are validated through a large public benchmark set of QPs of MPC for controlling a four tank process.

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A hierarchical time-splitting approach for solving finite-time optimal control problems

Cited by 17 publications

References 21 publications

Asynchronous splitting design for Model Predictive Control

Asynchronous splitting design for Model Predictive Control

A parallel structure exploiting factorization algorithm with applications to Model Predictive Control

Alternating direction method of multipliers for strictly convex quadratic programs: Optimal parameter selection

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