Filtering of nonlinear stochastic feedback systems

F. Carravetta*, A. Germani, R. Liptser, C. Manes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper concerns the filtering problem for a class of stochastic nonlinear systems where the drift term may depend either on some external function (open-loop system) or on the system output (closed-loop system), through a controller. Such systems are denoted feedback systems. The following result is proven: for feedback systems, the optimal filter in the open-loop case remains optimal when the feedback is closed. The proof is obtained by showing equivalence of suitable expressions for the estimators of the open-loop and closed-loop systems, obtained using the Kallianpur-Striebel formula [G. Kallianpur and C. Striebel, Ann. Math. Statist., 39 (1968), pp. 785-801].

Original languageEnglish
Pages (from-to)1576-1584
Number of pages9
JournalSIAM Journal on Control and Optimization
Issue number5
StatePublished - 2002
Externally publishedYes


  • Closed-loop systems
  • Girsanov theorem
  • Kallianpur-Striebel formula
  • Nonlinear filtering


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