Minimum time observer designs for n + m linear hyperbolic systems with unilateral, bilateral or pointwise in-domain sensing

摘要

In this paper we derive minimum time convergent observers for n + m (1) systems of linear coupled first-order 1-D hyperbolic PDEs, that use either unilateral (single boundary measured), bilateral (both boundaries measured) or pointwise in-domain sensing. First, a Volterra integral transformation is combined with a Fredholm integral transformation to derive a minimum time unilateral observer for n m systems. Then, it is shown that an n m system with bilateral sensing can be transformed to an (1+ m) (ti m) system with unilateral sensing via an invertible coordinate transformation. The n m bilateral observer is subsequently obtained from the (n+ m) (n+ m) minimum time unilateral observer, and it is shown that it converges in a theoretical minimum time for bilateral sensing. In a similar fashion, the observer using pointwise in-domain measurement is derived using the same techniques. The performances of the n m bilateral and unilateral observers are demonstrated in simulations. (C) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved.