Output error minimizing back and forth nudging method for initial state recovery

Atte Aalto 1
1 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and simulated outputs — given that the observer gains are chosen suitably and the system is exactly observable. If the system's generator A is essentially skew-adjoint and dissipative (with not too much dissipation), the colocated feedback has to be corrected by the operator e^{At}e^{A*t} in order to obtain such convergence. In some special cases, a feasible approximation for this operator can be found analytically. The case with wave equation with constant dissipation will be demonstrated.
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Atte Aalto. Output error minimizing back and forth nudging method for initial state recovery. Systems and Control Letters, Elsevier, 2016, 94, pp.111-117. 〈http://www.sciencedirect.com/science/article/pii/S0167691116300597〉. 〈10.1016/j.sysconle.2016.06.002〉. 〈hal-01216075v2〉

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