Safely Learning Dynamical Systems from Short Trajectories

Amir Ali Ahmadi, Abraar Chaudhry, Vikas Sindhwani, Stephen Tu

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


A fundamental challenge in learning to control an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the system is required to stay within a given safety region under the (possibly repeated) action of all dynamical systems that are consistent with the information gathered so far. For our first two results, we consider the setting of safely learning linear dynamics. We present a linear programming-based algorithm that either safely recovers the true dynamics from trajectories of length one, or certifies that safe learning is impossible. We also give an efficient semidefinite representation of the set of initial conditions whose resulting trajectories of length two are guaranteed to stay in the safety region. For our final result, we study the problem of safely learning a nonlinear dynamical system. We give a second-order cone programming based representation of the set of initial conditions that are guaranteed to remain in the safety region after one application of the system dynamics.

Original languageEnglish (US)
Pages (from-to)498-509
Number of pages12
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event3rd Annual Conference on Learning for Dynamics and Control, L4DC 2021 - Virtual, Online, Switzerland
Duration: Jun 7 2021Jun 8 2021

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


  • conic programming
  • learning dynamical systems
  • robust optimization
  • safe learning
  • uncertainty quantification


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