Density Functions for Mesh Refinement in Numerical Optimal Control

Zhao, Yiming; Tsiotras, Panagiotis

doi:10.2514/1.45852

Cited by 74 publications

(59 citation statements)

References 11 publications

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“…In [2] and [3] the authors developed a mesh refinement procedure for changing the discretisation involving an integer programming technique. In [15] a density function to generate a fixed-order mesh is used.…”

Section: Introductionmentioning

confidence: 99%

Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

Paiva

Fontes

2014

Procedia Technology

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Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are most frequently used. However, in some cases, these meshes cannot cope accurately with nonlinear behaviour unless a very large number of mesh nodes is used. One way to improve the solution involves adaptive mesh refinement algorithms which allow a non uniform node collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. The technique was applied to solve two problems involving nonholonomic vehicles and it led to results with higher accuracy and yet with lower overall computational time when compared to a mesh having equidistant nodes.

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Section: Introductionmentioning

confidence: 99%

Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

Paiva

Fontes

2014

Procedia Technology

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“…At the beginning of the time horizon the element size is mainly determined by the required update interval, whereas at the horizon end only numerical accuracy remains important. An example of mesh relocation is given in (Zhao and Tsiotras, 2011). 3 JModelica.org Enhancements to…”

Section: Optimizermentioning

confidence: 99%

A Framework for Nonlinear Model Predictive Control in JModelica.org

Axelsson

Magnusson

Henningsson

2015

Linköping Electronic Conference Proceedings

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In the past JModelica.org was successfully applied for generating optimal trajectories. Using it for Nonlinear Model Predictive Control (NMPC) is the natural next step and sets high requirements on calculation time. To improve real time capabilities warmstarting of the optimization and elimination of algebraic variables based on Block Lower Triangular (BLT) form were implemented. In performance comparisons, using the example of steam temperature control, a speed-up of the optimization time by a factor of five and of two respectively was measured. The increased efficiency allows application of NMPC to faster systems than before.

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“…Then, this initial mesh is repeatedly refined according to a chosen strategy until some stopping criterion is attained. Several mesh refinement methods employing direct collocation methods have been described in the recent years [1,2,22,29].…”

Section: Introductionmentioning

confidence: 99%

Sampled–Data Model Predictive Control Using Adaptive Time–Mesh Refinement Algorithms

Paiva

Fontes

2016

Lecture Notes in Electrical Engineering

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Abstract. We address sampled-data nonlinear Model Predictive Control (MPC) schemes, in particular we address methods to e ciently and accurately solve the underlying continuous-time optimal control problems (OCP). In nonlinear OCPs, the number of discretization points is a major factor a↵ecting the computational time. Also, the location of these points is a major factor a↵ecting the accuracy of the solutions. We propose the use of an algorithm that iteratively finds the adequate timemesh to satisfy some pre-defined error estimate on the obtained trajectories. The proposed adaptive time-mesh refinement algorithm provides local mesh resolution considering a time-dependent stopping criterion, enabling an higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. The results show the advantage of the proposed adaptive mesh strategy, which leads to results obtained approximately as fast as the ones given by a coarse equidistant-spaced mesh and as accurate as the ones given by a fine equidistant-spaced mesh.

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Density Functions for Mesh Refinement in Numerical Optimal Control

Cited by 74 publications

References 11 publications

Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

Time–mesh Refinement in Optimal Control Problems for Nonholonomic Vehicles

A Framework for Nonlinear Model Predictive Control in JModelica.org

Sampled–Data Model Predictive Control Using Adaptive Time–Mesh Refinement Algorithms

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