Efficient and accurate computation of model predictive control using pseudospectral discretization

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The model predictive control (MPC) is implemented by repeatedly solving an open loop optimal control problem (OCP). For the real-time implementation, the OCP is often discretized with evenly spaced time grids. This evenly spaced discretization, however, is accurate only if sufficiently small sampling time is used, which leads to heavy computational load. This paper presents a method to efficiently and accurately compute the continuous-time MPC problem based on the pseudospectral discretization, which utilizes unevenly spaced collocation points. The predictive horizon is virtually doubled by augmenting a mirrored horizon such that denser collocation points can be used towards the current time step, and sparser points can be used towards the end time of predictive horizon. Then, both state and control variables are approximated by Lagrange polynomials at only a half of LGL (Legendre-Gauss-Lobatto) collocation points. This implies that high accuracy can be achieved with a much less number of collocation points, which results in much reduced computational load. Examples are used to demonstrate its advantages over the evenly spaced discretization.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2016-02
Language
English
Article Type
Article
Keywords

DIRECT TRAJECTORY OPTIMIZATION; TIME NONLINEAR-SYSTEMS; COSTATE ESTIMATION; STABILITY; FRAMEWORK

Citation

NEUROCOMPUTING, v.177, pp.363 - 372

ISSN
0925-2312
DOI
10.1016/j.neucom.2015.11.020
URI
http://hdl.handle.net/10203/207977
Appears in Collection
GT-Journal Papers(저널논문)
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