✦ LIBER ✦

Nonlinear estimation for partial differential equations

✍ Scribed by J.H. Seinfeld

Publisher: Elsevier Science
Year: 1969
Tongue: English
Weight: 551 KB
Volume: 24
Category: Article
ISSN: 0009-2509
DOI: 10.1016/0009-2509(69)80010-2

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✦ Synopsis

The sequential estimation of the states of a process described by a set of nonlinear hyperbolic or parabolic partial differential equations subject to both stochastic input disturbances and measurement errors is considered. A functional partial differential equation of Hamilton-Jacobi type is derived for the minimum least square estimate error, which is solved approximately in the region of the optimal estimate by a second-order expansion. The optimal estimate is given as the solution ofan initial value problem. In the linear case the estimator equations represent analogs of the well-known Kalman filter equations for lumped parameter systems. The determination of the state of a process governed by the one-dimensional heat equation from noisy measurements is considered.

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