A Dual Characterization of Observability for Stochastic Systems ⁎Financial support from the NSF grant 1761622 and the ARO grant W911NF1810334 is gratefully acknowledged. Issue 9 (2021)

• Record Type: Journal Article
• Authors: Kim, Jin Won; Mehta, Prashant G.
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 9(2021)
• Page Start: 659
• Page End: 664
• Publication Date: 2021
• Subjects: Observability -- Stochastic systems -- Duality -- Backward stochastic differential equations; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.06.126
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: 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).