Sum-of-Squares-Based Region of Attraction Analysis for Gain-Scheduled Three-Loop Autopilot

  • Min-Won Seo
  • Hyuck-Hoon Kwon
  • Han-Lim Choi
Original Paper


A conventional method of designing a missile autopilot is to linearize the original nonlinear dynamics at several trim points, then to determine linear controllers for each linearized model, and finally implement gain-scheduling technique. The validation of such a controller is often based on linear system analysis for the linear closed-loop system at the trim conditions. Although this type of gain-scheduled linear autopilot works well in practice, validation based solely on linear analysis may not be sufficient to fully characterize the closed-loop system especially when the aerodynamic coefficients exhibit substantial nonlinearity with respect to the flight condition. The purpose of this paper is to present a methodology for analyzing the stability of a gain-scheduled controller in a setting close to the original nonlinear setting. The method is based on sum-of-squares (SOS) optimization that can be used to characterize the region of attraction of a polynomial system by solving convex optimization problems. The applicability of the proposed SOS-based methodology is verified on a short-period autopilot of a skid-to-turn missile.


Sum-of-squares optimization Nonlinear stability analysis Region of attraction Autopilot 



This work was supported by “Core Technology Research for the Next Generation of Precision Guided Munitions” Project funded by LIG Nex1.


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Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Pangyo R&D Center of LIG Nex1 Corp.SeongnamRepublic of Korea
  2. 2.Department of Aerospace EngineeringKAISTDaejeonRepublic of Korea

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