A warm-start interior-point method for predictive control

Shahzad, Amir; Kerrigan, Eric C.; Constantinides, George A.

doi:10.1049/ic.2010.0409

Cited by 22 publications

(28 citation statements)

References 13 publications

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“…In this section we discuss an acceleration method that is common for certain optimization methods such as Sequential Quadratic Programming [28] and Interior-Point methods [22] warm-starting. In the CG-VAMP algorithm, at each outer-loop iteration we have to approximate a solution to the updated SLE W t µ t = z t and a natural question arises: how different are these SLE at two consecutive iterations?…”

Section: Warm-starting the Cg Algorithm In Cg-vampmentioning

confidence: 99%

Upscaling Vector Approximate Message Passing

Skuratovs

Davies

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Recently proposed Vector Approximate Message Passing (VAMP) demonstrates a great reconstruction potential at solving compressed sensing related linear inverse problems. VAMP provides high per-iteration improvement, can utilize powerful denoisers like BM3D, has rigorously defined dynamics and is able to recover signals sampled by highly undersampled and ill-conditioned linear operators. Yet, its applicability is limited to relatively small problem sizes due to necessity to compute the expensive LMMSE estimator at each iteration. In this work we consider the problem of upscaling VAMP by utilizing Conjugate Gradient (CG) to approximate the intractable LMMSE estimator and propose a CG-VAMP algorithm that can efficiently recover large-scale data. We derive evolution models of certain key parameters of CG-VAMP and use the theoretical results to develop fast and practical tools for correcting, tuning and accelerating the CG algorithm within CG-VAMP to preserve all the main advantages of VAMP, while maintaining reasonable and controllable computational cost of the algorithm.

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Section: Warm-starting the Cg Algorithm In Cg-vampmentioning

confidence: 99%

Upscaling Vector Approximate Message Passing

Skuratovs

Davies

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…1 we show the result of a convergence test for the duality measure in case of single, double and mixed precision used in the computation of the search direction, for both primal-dual and predictor-corrector IP methods. The fact that the single precision solution behaves as the higher precision ones till approximately 10 −6 suggest that we can implement an inexact IP method (proposed for MPC problems by Shahzad et al [2010], with MINRES to compute the search direction), where the inexact search direction is computed by solving the LQCP subproblems using Algorithm 1 in single precision, exploiting the higher performance of single precision computation. Numerical tests shows that a value of the duality measure of 10 −5 is a good threshold value between single and higher precision.…”

Section: Inexact Ip Methodsmentioning

confidence: 99%

A Family of High-Performance Solvers for Linear Model Predictive Control

Frison¹,

Sokoler²,

Jørgensen³

2014

IFAC Proceedings Volumes

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In Model Predictive Control (MPC), an optimization problem has to be solved at each sampling time, and this has traditionally limited the use of MPC to systems with slow dynamic. In this paper, we propose an efficient solution strategy for the unconstrained subproblems that give the search-direction in Interior-Point (IP) methods for MPC, and that usually are the computational bottleneck. This strategy combines a Riccati-like solver with the use of high-performance computing techniques: in particular, in this paper we explore the performance boost given by the use of single precision computation, and techniques such as inexact search direction and mixed precision computation. Finally, we test our HPMPC toolbox, a family of high-performance solvers tailored for MPC and implemented using these techniques, that is shown to be several times faster than current state-of-the-art solvers for linear MPC.

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“…There are several ways to reduce the complexity and thus the computational burden in model predictive control. The methods that can be highlighted are move blocking, 10,11 warm‐starting in interior‐point method, 12,13 active‐set approach, 14,15 and fast gradient method 16 . In addition, the Laguerre function also has potential benefits to achieve low computational loads with good feasibility and good performance in MPC design 17,18 .…”

Section: Introductionmentioning

confidence: 99%

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

Pinheiro

Silveira

2020

Optim Control Appl Methods

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SummaryThis work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case. The Laguerre functions are used to simplify and enhance the control horizon effect through parsimonious control trajectory, thus reducing the computational load required to find the optimal control solution. Furthermore, these results can be confirmed by simulations and experimental tests on the manipulator and comparing it to the traditional DMPC approach and the discrete linear quadratic regulator.

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A warm-start interior-point method for predictive control

Cited by 22 publications

References 13 publications

Upscaling Vector Approximate Message Passing

Upscaling Vector Approximate Message Passing

A Family of High-Performance Solvers for Linear Model Predictive Control

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

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