Efficient solution of second order cone program for model predictive control

Åkerblad, Magnus; Hansson, Anders

doi:10.1080/00207170310001643221

Cited by 29 publications

(25 citation statements)

References 23 publications

(6 reference statements)

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“…For ease of notation we label the nodes with the states and control signals. 1 The cliques for this graph are…”

Section: Backward Dynamic Programmingmentioning

confidence: 99%

“…for given x k starting with k = N − 1 going down to k = 0, where m N,N−1 (x N ) = 1 2 x T N Sx N . The optimality conditions are for k = N − 1 1 Here we use a supernode for all components of a state and a control signal, respectively. In case there is further structure in the dynamic equations such that not all components of the control signal and the states are coupled, then more detailed modeling could potentially be benificial.…”

Section: Backward Dynamic Programmingmentioning

confidence: 99%

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Exploiting Chordality in Optimization Algorithms for Model Predictive Control

Hansson

Pakazad²

2018

Large-Scale and Distributed Optimization

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In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for distributing all the other computations in an interior-point method for solving the problem. The chordal structure can stem both from the sequential nature of the problem as well as from distributed formulations of the problem related to scenario trees or other formulations. The framework enables efficient parallel computations.

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“…For ease of notation we label the nodes with the states and control signals. 1 The cliques for this graph are…”

Section: Backward Dynamic Programmingmentioning

confidence: 99%

Section: Backward Dynamic Programmingmentioning

confidence: 99%

Exploiting Chordality in Optimization Algorithms for Model Predictive Control

Hansson

Pakazad²

2018

Large-Scale and Distributed Optimization

Self Cite

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“…The algorithms can be used to compute the Newton step which is defined by the solution to (3). This is where most computational effort is needed when solving (1). The computations can be performed using several processors, and the level of parallelism can be tuned to fit the hardware, i.e.…”

Section: Parallel Computation Of Newton Stepmentioning

confidence: 99%

An Ô (log N ) Parallel Algorithm for Newton Step Computation in Model Predictive Control

Nielsen

Axehill

2014

IFAC Proceedings Volumes

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The use of Model Predictive Control is steadily increasing in industry as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively high computational complexity. Hence, much research has been performed to find efficient algorithms that solve the optimization problem. As parallel hardware is becoming more commonly available, the demand of efficient parallel solvers for Model Predictive Control has increased. In this paper, a tailored parallel algorithm that can adopt different levels of parallelism for solving the Newton step is presented. With sufficiently many processing units, it is capable of reducing the computational growth to logarithmic in the prediction horizon. Since the Newton step computation is where most computational effort is spent in both interior-point and active-set solvers, this new algorithm can significantly reduce the computational complexity of highly relevant solvers for Model Predictive Control.

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“…It is well-known that the resulting optimization problem obtains a special structure that can be exploited to obtain high-performance linear algebra for computing Newton steps in various setups, see e.g. [1][2][3][4][5][6][7][8][9][10][11][12]. A problem which turns out to have similar problem structure is the Moving Horizon Estimation (mhe) problem, [13,14].…”

Section: Introductionmentioning

confidence: 99%

An O (log N) parallel algorithm for newton step computations with applications to moving horizon estimation

Nielsen

Axehill

2016

2016 European Control Conference (ECC)

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In Moving Horizon Estimation (mhe) the computed estimate is found by solving a constrained finite-time optimal estimation problem in realtime at each sample in a receding horizon fashion. The constrained estimation problem can be solved by, e.g., interior-point (ip) or active-set (as) 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 the optimal estimation problem. As a result it is possible to obtain logarithmic complexity growth in the estimation horizon length, which can be used to reduce the computation time for ip and as methods when applied to what is today considered as challenging estimation problems. Promising numerical results have been obtained using an ansi-c implementation of the proposed algorithm running on true parallel hardware. Beyond mhe, due to similarities in the problem structure, the algorithm can be applied to various forms of on-line and off-line smoothing problems. * I. Nielsen and D. Axehill are with the Division

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Efficient solution of second order cone program for model predictive control

Cited by 29 publications

References 23 publications

Exploiting Chordality in Optimization Algorithms for Model Predictive Control

Exploiting Chordality in Optimization Algorithms for Model Predictive Control

An Ô (log N ) Parallel Algorithm for Newton Step Computation in Model Predictive Control

An O (log N) parallel algorithm for newton step computations with applications to moving horizon estimation

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