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

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.

Mots clés: Variational data assimilation; Observers; Output error minimization; State estimation; Back and forth nudging

Domaines: Optimisation et contrôle [math.OC]

Atte Aalto. Output error minimizing back and forth nudging method for initial state recovery. Systems and Control Letters, 2016, 94, pp.111-117. ⟨10.1016/j.sysconle.2016.06.002⟩. ⟨hal-01216075v2⟩