Polynomial control design for polynomial systems: A non-iterative sum of squares approach

Mohsen Rakhshan, Navid Vafamand, Mohammad Mehdi Mardani, Mohammad Hassan Khooban*, Tomislav Dragicevic

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

3 Citations (Scopus)

Abstract

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of
squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on
the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed
through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide
range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank
reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.
Original languageEnglish
JournalTransactions of the Institute of Measurement and Control
Volume41
Issue number7
Pages (from-to)1993-2004
Number of pages12
ISSN0142-3312
DOIs
Publication statusPublished - 1 Apr 2019

Keywords

  • Polynomial chaotic system
  • Polynomial CSTR plant
  • Polynomial PMSM system
  • Sum of squares (SOS) decomposistion
  • Polynomial Lyapunov function
  • Software-in-the-loop (SiL)
  • sum of squares (SOS) decomposition
  • polynomial PMSM system
  • software-in-the-loop (SiL)

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