Abstract
The input reconstruction problem for a stochastic differential equation is investigated by means of the approach of the theory of dynamic inversion. The statement when the simultaneous reconstruction of disturbances in both the deterministic and stochastic terms of the equation is performed from the discrete information on several realizations of the stochastic process is considered. A finite-step software-oriented solving algorithm based on the method of auxiliary feedback controlled models is designed; an estimate for its convergence rate with respect to the number of measurable realizations is obtained. An empirical procedure for the automatic tuning of algorithm's parameters in order to get best approximation results for a specific dynamical system is proposed. To optimize this time-taking process, the parallelization of calculations is applied. A model example illustrating the method proposed is given.
Highlights
The problems of reconstructing unknown input parameters of controlled systems based on inaccurate/incomplete information on the phase state arise in many scientific studies and applications and attract a great attention in recent time
The statement when the simultaneous reconstruction of disturbances in both the deterministic and stochastic terms of the equation is performed from the discrete information on several realizations of the stochastic process is considered
The inverse problem for a quasi-linear diffusion stochastic differential equation (SDE) consisting in the dynamical reconstruction of two unknown nonrandom disturbances in the deterministic and stochastic terms of the equation is investigated
Summary
The problems of reconstructing unknown input parameters of controlled systems based on inaccurate/incomplete information on the phase state arise in many scientific studies and applications (in flight mechanics and guidance theory, in financial and actuarial mathematics, for designing engineering and production processes, in ecology and medicine, etc.) and attract a great attention in recent time. The inverse problem for a quasi-linear system with diffusion depending on the phase state in the statement assuming the simultaneous reconstruction of disturbances both in the deterministic and stochastic terms was discussed in [22] The latter problem is under further investigation in the present paper. The matter is that up to now there is no a universal procedure for fitting parameters of algorithms of dynamical reconstruction even in the case of ODEs, see the discussions on numerical examples in [10, 11, 16] This important applied aspect of the theory of dynamic inversion remains vague. In Conclusion, we resume the results obtained and outline some directions for perspective investigations
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