TY - JOUR
T1 - Filtering of nonlinear stochastic feedback systems
AU - Carravetta, F.
AU - Germani, A.
AU - Liptser, R.
AU - Manes, C.
PY - 2002
Y1 - 2002
N2 - 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].
AB - 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].
KW - Closed-loop systems
KW - Girsanov theorem
KW - Kallianpur-Striebel formula
KW - Nonlinear filtering
UR - http://www.scopus.com/inward/record.url?scp=0036405509&partnerID=8YFLogxK
U2 - 10.1137/S0363012998347146
DO - 10.1137/S0363012998347146
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AN - SCOPUS:0036405509
SN - 0363-0129
VL - 40
SP - 1576
EP - 1584
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
IS - 5
ER -