Algorithm for the continuous estimation of a disturbance in a stochastic differential equation
Tóm tắt
Based on the approach of the theory of dynamic inversion, the problem of continuous estimation of an unknown deterministic disturbance in an Ito stochastic differential equation is investigated with the use of inaccurate measurements of the current phase state. An auxiliary model equation with a control approximating the unknown input is derived. The suggested solution algorithm is constructive; an estimate for its convergence rate is written explicitly.
Tài liệu tham khảo
A. V. Kryazhimskii and Yu. S. Osipov, Engrg. Cybernetics 21(2), 38 (1983).
Yu. S. Osipov, F. P. Vasil’ev, and M. M. Potapov, Foundations of the Dynamical Regularization Method (Mosk. Gos. Univ., Moscow, 1999) [in Russian].
Yu. S. Osipov and A. V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions (Gordon and Breach, London, 1995).
V. I. Maksimov, Dynamical Inverse Problems of Distributed Systems (Izd. UrO RAN, Yekaterinburg, 2000; VSP, Utrecht-Boston, 2002).
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1974; Wiley, New York, 1977).
V. I. Maksimov, J. Appl. Math. Mech. 70(5), 696 (2006).
Yu. S. Osipov and A. V. Kryazhimskii, in Proc. Internat. Conf. on Stochastic Optimization (Kiev, 1984), pp. 43–45 [in Russian].
A. N. Shiryaev, Probability, Statistics, and Random Processes (Izd. Mosk. Gos. Univ., Moscow, 1974) [in Russian].
B. Øksendal, Stochastic Differential Equations: An Introduction with Applications (Springer-Verlag, Berlin, 1985; Mir, Moscow, 2003).
V. S. Pugachev and I. N. Sinitsyn, Stochastic Differential Systems (Nauka, Moscow, 1990) [in Russian].
V. L. Rozenberg, Autom. Remote Control 68(11), 1959 (2007).
N. N. Krasovskii and A. N. Kotel’nikova, Proc. Steklov Inst. Math., Suppl. 1, S151 (2006).