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A Control Parameterization Approach with Variable Time Nodes for Optimal Control Problems
Author(s) -
Li Guodong,
Liu Ping,
Liu Xinggao
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1175
Subject(s) - parameterized complexity , parametrization (atmospheric modeling) , grid , partition (number theory) , interval (graph theory) , control variable , mathematical optimization , control (management) , variable (mathematics) , control theory (sociology) , optimal control , multivariable calculus , computer science , mathematics , algorithm , engineering , control engineering , statistics , artificial intelligence , geometry , physics , quantum mechanics , combinatorics , radiative transfer , mathematical analysis
This paper presents a novel computational approach to deal with optimal multivariable control problems using a control vector parameterization approach with multiple time grids, where each of the control variables has its own time grid of parametrization. Both the control parameters and time nodes in the grid partition are treated directly as variables to be optimized. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient formulae for parameters are presented. Compared with the existing approaches, for which all the control variables are parameterized on the same time grid, the proposed method is more general and flexible. To illustrate, two numerical cases are tested, and the results demonstrate that fewer parameters are needed to achieve the same level of optimization.