### Abstract

Andy Packard, an expert from University of California at Berkeley (UCB) Mechanical Engineering Department shares views on the use of sum-of-squares (SOS) methods to determine the region of attraction (ROA). SOS applies to polynomials in several real variables and a polynomial is a finite linear combination of monomials. The ROA can be visualized by simulating the system from many initial conditions and plotting the trajectories in a phase plane plot for systems with two or three states. SOS techniques can be used to perform nonlinear analyses, including computation of input/output gains, estimation of reachable sets, and computation of robustness margins. The approaches that apply to SOS methods includes the computational requirements that grow rapidly in the number of variables and polynomial degree, which roughly limits SOS-based analysis to systems with at most eight to ten states, one to two inputs, and polynomial vector fields of degree 3.

Original language | English (US) |
---|---|

Article number | 5510720 |

Pages (from-to) | 18-23 |

Number of pages | 6 |

Journal | IEEE Control Systems Magazine |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - Aug 1 2010 |

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### Cite this

*IEEE Control Systems Magazine*,

*30*(4), 18-23. [5510720]. https://doi.org/10.1109/MCS.2010.937045

**Help on SOS.** / Packard, Andy; Topcu, Ufuk; Seiler Jr, Peter J; Balas, Gary.

Research output: Contribution to journal › Review article

*IEEE Control Systems Magazine*, vol. 30, no. 4, 5510720, pp. 18-23. https://doi.org/10.1109/MCS.2010.937045

}

TY - JOUR

T1 - Help on SOS

AU - Packard, Andy

AU - Topcu, Ufuk

AU - Seiler Jr, Peter J

AU - Balas, Gary

PY - 2010/8/1

Y1 - 2010/8/1

N2 - Andy Packard, an expert from University of California at Berkeley (UCB) Mechanical Engineering Department shares views on the use of sum-of-squares (SOS) methods to determine the region of attraction (ROA). SOS applies to polynomials in several real variables and a polynomial is a finite linear combination of monomials. The ROA can be visualized by simulating the system from many initial conditions and plotting the trajectories in a phase plane plot for systems with two or three states. SOS techniques can be used to perform nonlinear analyses, including computation of input/output gains, estimation of reachable sets, and computation of robustness margins. The approaches that apply to SOS methods includes the computational requirements that grow rapidly in the number of variables and polynomial degree, which roughly limits SOS-based analysis to systems with at most eight to ten states, one to two inputs, and polynomial vector fields of degree 3.

AB - Andy Packard, an expert from University of California at Berkeley (UCB) Mechanical Engineering Department shares views on the use of sum-of-squares (SOS) methods to determine the region of attraction (ROA). SOS applies to polynomials in several real variables and a polynomial is a finite linear combination of monomials. The ROA can be visualized by simulating the system from many initial conditions and plotting the trajectories in a phase plane plot for systems with two or three states. SOS techniques can be used to perform nonlinear analyses, including computation of input/output gains, estimation of reachable sets, and computation of robustness margins. The approaches that apply to SOS methods includes the computational requirements that grow rapidly in the number of variables and polynomial degree, which roughly limits SOS-based analysis to systems with at most eight to ten states, one to two inputs, and polynomial vector fields of degree 3.

UR - http://www.scopus.com/inward/record.url?scp=77954779894&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954779894&partnerID=8YFLogxK

U2 - 10.1109/MCS.2010.937045

DO - 10.1109/MCS.2010.937045

M3 - Review article

VL - 30

SP - 18

EP - 23

JO - IEEE Control Systems

JF - IEEE Control Systems

SN - 1066-033X

IS - 4

M1 - 5510720

ER -