Fast NMPC of a chain of masses connected by springs

Wirsching, Leonard; Bock, Hans Georg; Diehl, Moritz

doi:10.1109/cacsd-cca-isic.2006.4776712

Cited by 18 publications

(24 citation statements)

References 13 publications

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“…Chain of masses. We consider the chain mass optimal control problem from [44,49]. The objective is to return a chain of n m masses connected with springs to its steady state, starting from a perturbed initial configuration.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Inexact Newton-Type Optimization with Iterated Sensitivities

Quirynen¹,

Gros²,

Diehl³

2018

SIAM J. Optim.

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This paper presents and analyzes an inexact Newton-type optimization method based on iterated sensitivities (INIS). A particular class of nonlinear programming (NLP) problems is considered, where a subset of the variables is defined by nonlinear equality constraints. The proposed algorithm considers any problem-specific approximation for the Jacobian of these constraints. Unlike other inexact Newton methods, the INIS-type optimization algorithm is shown to preserve the local convergence properties and the asymptotic contraction rate of the Newton-type scheme for the feasibility problem yielded by the same Jacobian approximation. The INIS approach results in a computational cost which can be made close to that of the standard inexact Newton implementation. In addition, an adjoint-free (AF-INIS) variant of the approach is presented which, under certain conditions, becomes considerably easier to implement than the adjoint based scheme. The applicability of these results is motivated specifically for dynamic optimization problems. In addition, the numerical performance of a corresponding open-source implementation is illustrated.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Similar to before, this discussion omits the presence of inequality constraints even though the above results on local Newton-type convergence can be extended. This will be illustrated based on numerical results for the chain mass example [49].…”

Section: 2mentioning

confidence: 99%

Inexact Newton-Type Optimization with Iterated Sensitivities

Quirynen¹,

Gros²,

Diehl³

2018

SIAM J. Optim.

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“…One end of the chain is fixed at the origin, while the other one is free and can be controlled by its velocities in x, y, and z direction. Note that, as in [40], we placed the wall closer to the equilibrium position than it has been considered in the original setting from [43]. This means that potentially a large amount of state constraints becomes active in the solution, and thus we yield a more challenging problem, particularly for the dual Newton strategy.…”

Section: Hanging Chainmentioning

confidence: 97%

“…To comment on the weaknesses of the dual Newton strategy, we consider a third problem, which has been used for benchmarking in several papers before, see [14,40, 43]. The problem features again a chain of masses, yet in three-dimensional space, connected by springs, that assumes its steady state very close to a wall, cf.…”

Section: Hanging Chainmentioning

confidence: 99%

“…As in [14] we perform linear MPC based on a linearization in the steady state, trying to stabilize the problem quickly at its equilibrium. For the detailed model equations we refer to [43]. We consider a chain of 5 Masses, which results in a system of 33 states (the free masses' positions and velocities) and 3 controls (the last masses' velocities), on a varying horizon length between 30 and 60 intervals.…”

Section: Hanging Chainmentioning

confidence: 99%

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A parallel quadratic programming method for dynamic optimization problems

2015

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Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstarting capabilities of active-set methods. We give details for an efficient implementation, including tailored numerical linear algebra, step size computation, parallelization, and infeasibility handling. We prove convergence of the algorithm for the considered problem class. A numerical study based on the open-source implementation qpDUNES shows that the algorithm outperforms both well-established general purpose QP solvers as well as state-of-the-art tailored control QP solvers significantly on the considered benchmark problems.

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Dominant speed factors of active set methods for fast MPC

Herceg

Jones

Morari

2014

Optim Control Appl Methods

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The paper presents a review of active set (AS) algorithms that have been deployed for implementation of fast model predictive control (MPC). The main purpose of the survey is to identify the dominant features of the algorithms that contribute to fast execution of online MPC and to study their influence on the speed. The simulation study is conducted on two benchmark examples where the algorithms are analyzed in the number of iterations and in the workload per iteration. The obtained results suggest directions for potential improvement in the speed of existing AS algorithms.

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Fast NMPC of a chain of masses connected by springs

Cited by 18 publications

References 13 publications

Inexact Newton-Type Optimization with Iterated Sensitivities

Inexact Newton-Type Optimization with Iterated Sensitivities

A parallel quadratic programming method for dynamic optimization problems

Dominant speed factors of active set methods for fast MPC

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