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

Research output: Contribution to journalJournal articleResearchpeer-review

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
Number of pages12
ISSN0142-3312
DOIs
Publication statusPublished - 2019

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polynomials
Polynomials
Liapunov functions
Chaotic systems
Lyapunov functions
matrices
programming
State feedback
permanent magnets
Permanent magnets
controllers
Derivatives
Decomposition
computer programs
decomposition
Controllers
simulation

Keywords

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

Cite this

Rakhshan, Mohsen ; Vafamand, Navid ; Mardani, Mohammad Mehdi ; Khooban, Mohammad Hassan ; Dragicevic, Tomislav. / Polynomial control design for polynomial systems: A non-iterative sum of squares approach. In: Transactions of the Institute of Measurement and Control. 2019 ; Vol. 41, No. 7.
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abstract = "This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum ofsquares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound onthe time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computedthrough semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a widerange of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tankreactor, 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.",
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Polynomial control design for polynomial systems: A non-iterative sum of squares approach. / Rakhshan, Mohsen; Vafamand, Navid; Mardani, Mohammad Mehdi; Khooban, Mohammad Hassan; Dragicevic, Tomislav.

In: Transactions of the Institute of Measurement and Control, Vol. 41, No. 7, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Polynomial control design for polynomial systems: A non-iterative sum of squares approach

AU - Rakhshan, Mohsen

AU - Vafamand, Navid

AU - Mardani, Mohammad Mehdi

AU - Khooban, Mohammad Hassan

AU - Dragicevic, Tomislav

PY - 2019

Y1 - 2019

N2 - This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum ofsquares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound onthe time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computedthrough semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a widerange of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tankreactor, 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.

AB - This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum ofsquares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound onthe time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computedthrough semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a widerange of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tankreactor, 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.

KW - Polynomial chaotic system

KW - Polynomial CSTR plant

KW - Polynomial PMSM system

KW - Sum of squares (SOS) decomposistion

KW - Polynomial Lyapunov function

KW - Software-in-the-loop (SiL)

U2 - 10.1177/0142331218793476

DO - 10.1177/0142331218793476

M3 - Journal article

VL - 41

JO - Transactions of the Institute of Measurement and Control

JF - Transactions of the Institute of Measurement and Control

SN - 0142-3312

IS - 7

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