Galerkin approximation for optimal linear filtering of infinite- dimensional linar systems. (English) Zbl 0662.93073

Germani, A.; Jetto, L.; Piccioni, M.

SIAM J. Control Optimization 26, No. 6, 1287-1305 (1988).

An explicitly computable, finite-dimensional approximation to the infinite-dimensional Kalman filter is studied. The approximation consists in the replacement of the original infinite-dimensional system by a finite dimensional one whose state approximates the projection of the true state on a given finite-dimensional space and in the use of a suitable finite-rank transformation of the original output. The approximate solution is shown to converge to the optimal solution for each sample path of the observation process.

Reviewer: G.DiMasi

MSC:

93E11	Filtering in stochastic control theory
93E25	Computational methods in stochastic control (MSC2010)
93C25	Control/observation systems in abstract spaces
93C05	Linear systems in control theory

Keywords:

Galerkin approximation; finite-dimensional approximation; infinite- dimensional Kalman filter