A Dual Characterization of Observability for Stochastic Systems

Jin Won Kim, Prashant G. Mehta

Research output: Contribution to journalConference articlepeer-review


This paper is concerned with the definition and characterization of the observability for a continuous-time hidden Markov model where the state evolves as a continuous-time Markov process on a compact state space and the observation process is modeled as nonlinear function of the state corrupted by a Gaussian measurement noise. The main technical tool is based on the recently discovered duality relationship between minimum variance estimation and stochastic optimal control: The observability is defined as a dual of the controllability for a certain backward stochastic differential equation. Based on the dual formulation, a test for observability is presented and related to literature. The proposed duality-based framework allows one to easily relate and compare the linear and the nonlinear systems. A side-by-side summary of this relationship is given in a tabular form (Table 1).

Original languageEnglish (US)
Pages (from-to)659-664
Number of pages6
Issue number9
StatePublished - Jun 1 2021
Event24th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2020 - Cambridge, United Kingdom
Duration: Aug 23 2021Aug 27 2021


  • 60g35
  • 93b28
  • Backward stochastic differential equations msc 2010: 93b07
  • Observability
  • Stochastic systems. duality

ASJC Scopus subject areas

  • Control and Systems Engineering


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