Second-Order Switching Time Optimization for Switched Dynamical Systems

Bartolomeo Stellato, Sina Ober-Blöbaum, Paul J. Goulart

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient, and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We have implemented the algorithm in the Julia package SwitchTimeOpt, allowing users to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few millisecond. In the case of nonlinear dynamics, our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches.

Original languageEnglish (US)
Article number7908990
Pages (from-to)5407-5414
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - Oct 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Hybrid systems
  • optimal control
  • optimal switching times
  • optimization algorithms
  • switched systems


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