Convex Synthesis of Control Barrier Functions Under Input Constraints

Pan Zhao, Reza Ghabcheloo, Yikun Cheng, Hossein Abdi, Naira Hovakimyan

Research output: Contribution to journalArticlepeer-review


This letter presents a systematic method based on the sum of square (SOS) optimization to synthesize control barrier functions (CBFs) for nonlinear polynomial systems subject to input constraints. The approach consists of two design steps. In the first step, using a linear-like representation of the nonlinear dynamics, an SOS optimization problem is formulated to search for an initial CBF and controller jointly. In the second step, an iterative optimization procedure involving the solution of a series of SOS problems is proposed to alternatively update the CBF and the controller to increase the invariant set defined by the CBF. The efficacy of the proposed approach is validated using numerical examples.

Original languageEnglish (US)
Pages (from-to)3102-3107
Number of pages6
JournalIEEE Control Systems Letters
StatePublished - 2023


  • Constrained control
  • nonlinear systems
  • optimization
  • safety

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization


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