Newton projection with proportioning using iterative linear algebra for model predictive control with long prediction horizon

Otta, Pavel; Burant, Jiří; Šantin, Ondřej; Havlena, Vladimı́r

doi:10.1080/10556788.2019.1571588

Cited by 3 publications

(4 citation statements)

References 33 publications

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“…The feedback phase denotes the cost of problem ( 11) solution, in this paper, it is counted for NPPsparse solver [13]. This active-set-like method converges typically in several iterations.…”

Section: B Oscillating Massesmentioning

confidence: 99%

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On the Quadratic Programming Solution for Model Predictive Control with Move Blocking

Otta¹,

Šantin²,

Havlena³

2020

Preprint

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Model Predictive Control (MPC) is a popular optimization-based control technique. MPC is usually formulated as sparse or dense Quadratic Programming (QP). This paper reviews two well-known methods, namely, state condensing and move blocking, and brings them together. Their combination results in generalized QP that serves arbitrarily sparse (or dense) QP for MPC with move blocking. The proposed QP can be solved by a specialized solver capable of exploiting a sparsity structure of the problem. Numerical examples give inside in computational and memory requirements.

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Section: B Oscillating Massesmentioning

confidence: 99%

“…Nowadays, several structureexploiting methods tailored for sparse QP arising in MPC exist (e.g. [6], [13], [19], [20]). As the problem formulation proposed in this work is derived from the sparse QP, these algorithms can be applied with no additional modification required.…”

Section: Introductionmentioning

confidence: 99%

On the Quadratic Programming Solution for Model Predictive Control with Move Blocking

Otta¹,

Šantin²,

Havlena³

2020

Preprint

Self Cite

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“…Earlier work in References 14,15 studied the use of block‐diagonal preconditioners, in combination with numerical techniques that are tailored to an inexact interior‐point (IP) framework. More recently, the work in Reference 16 presents an active‐set strategy based on a sparse variant of the Newton projection with proportioning (NPP) algorithm and using an augmented Lagrangian‐based preconditioner for the MINRES method. Unlike IP methods, an active‐set quadratic programming algorithm can considerably benefit from the use of warm or hot‐starting techniques to reduce the computational effort when solving a sequence of closely related optimal control problems 5,17,18 .…”

Section: Introductionmentioning

confidence: 99%

“…Unlike IP methods, an active‐set quadratic programming algorithm can considerably benefit from the use of warm or hot‐starting techniques to reduce the computational effort when solving a sequence of closely related optimal control problems 5,17,18 . The cost per iteration of an active‐set QP solver is computationally cheaper by exploiting low‐rank updates of the matrix factorizations when changing the current guess for the active set, 6,19 compared with standard IP methods 17 or compared with the NPP algorithm in Reference 16. We propose block‐structured preconditioning techniques within a primal active‐set strategy for real‐time optimal control, following our initial investigation in References 20,21.…”

Section: Introductionmentioning

confidence: 99%

PRESAS: Block‐structured preconditioning of iterative solvers within a primal active‐set method for fast model predictive control

Quirynen

Cairano

2020

Optim Control Appl Methods

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Summary Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This article proposes a primal active‐set strategy, called PRESAS, for the efficient solution of such block‐sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank‐one factorization updates of the preconditioner result in a per‐iteration computational complexity of 𝒪(Nm2), where m denotes the number of state and control variables and N the number of control intervals. Three different block‐structured preconditioning techniques are presented and their numerical properties are studied further. In addition, an augmented Lagrangian based implementation is proposed to avoid a costly initialization procedure to find a primal feasible starting point. Based on a standalone C code implementation, we illustrate the computational performance of PRESAS against current state of the art QP solvers for multiple linear and nonlinear MPC case studies. We also show that the solver is real‐time feasible on a dSPACE MicroAutoBox‐II rapid prototyping unit for vehicle control applications, and numerical reliability is illustrated based on experimental results from a testbench of small‐scale autonomous vehicles.

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On the Quadratic Programming Solution for Model Predictive Control with Move Blocking

Otta

Šantin²,

Havlena

2021

2021 23rd International Conference on Process Control (PC)

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Newton projection with proportioning using iterative linear algebra for model predictive control with long prediction horizon

Cited by 3 publications

References 33 publications

On the Quadratic Programming Solution for Model Predictive Control with Move Blocking

On the Quadratic Programming Solution for Model Predictive Control with Move Blocking

PRESAS: Block‐structured preconditioning of iterative solvers within a primal active‐set method for fast model predictive control

On the Quadratic Programming Solution for Model Predictive Control with Move Blocking

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