The separation principle in stochastic control, redux

Tryphon T Georgiou, Anders Lindquist

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Over the last 50 years, a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with 'real-life' engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded.

Original languageEnglish (US)
Article number6506982
Pages (from-to)2481-2494
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - 2013


  • Certainty equivalence
  • separation principle
  • stochastic control


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