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A semidefinite programming approach for polynomial switched optimal control problems
Author(s) -
Davoudi Ramtin,
Hosseini Seyed Mohammad
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2500
Subject(s) - conic section , semidefinite programming , polynomial , mathematics , optimal control , mathematical optimization , control theory (sociology) , projection (relational algebra) , linear programming , conic optimization , signal (programming language) , control (management) , computer science , algorithm , convex optimization , mathematical analysis , geometry , artificial intelligence , regular polygon , convex analysis , programming language
Summary This paper considers solving optimal control of switched systems with polynomial data globally, where the number of switches and the switching signal are not preassigned. The problem is transformed into an embedded polynomial form in which a continuous variable controls the switching policy. Then, using occupation measures, the embedded optimal control problem is formulated as an infinite‐dimensional linear programming (LP) over the space of measures. A polynomial sum‐of‐squares strengthening corresponding to conic dual of the measure LP problem provides an approximating optimal feedback control for both classical control and the switching signal. Furthermore, the optimal switching signal is calculated without mode projection. Finally, three simulation experiments are included to confirm the theoretical results in the paper.