The Method of Characteristics in an Identification Problem
We consider the problem of identifying the parameters of a dynamic system from a noisy history of measuring the phase trajectory. We propose a new approach to the solution of this problem based on the construction of an auxiliary optimal control problem such that its extremals approximate the measurement history with a given accuracy. Using the solutions of the corresponding characteristic system, we obtain estimates for the residual, which is the difference between the coordinates of the extremals and the measurements of the phase trajectory. An estimate for the result of identifying the parameters of the dynamic system is obtained. An illustrative numerical example is given.
Keywordsidentification residual functional Hamilton–Jacobi–Bellman equation characteristic system.
Unable to display preview. Download preview PDF.
- 2.Handbook of Automatic Control Theory, Ed. by A. Krasovskii (Nauka, Moscow, 1987) [in Russian].Google Scholar
- 3.N. N. Subbotina, E. A. Kolpakova, T. B. Tokmantsev, and L. G. Shagalova, The Method of Characteristics for Hamilton–Jacobi–Bellman Equations (Izd. UrO RAN, Yekaterinburg, 2013) [in Russian].Google Scholar
- 4.N. N. Subbotina and T. B. Tokmantsev, “Optimal synthesis to inverse problems of dynamics,” in Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, 2014 (Elsevier, New York, 2014), pp. 5866–5871.Google Scholar
- 7.N. N. Krasovskii, Theory of Motion Control (Nauka, Moscow, 1968) [in Russian].Google Scholar
- 9.A. N. Tikhonov, “On the stability of inverse problems,” C. R. (Doklady) Acad. Sci. URSS (N.S.) 39, 195–198 (1943).Google Scholar
- 10.L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1961; Wiley, New York, 1962).Google Scholar
- 11.A. I. Subbotin, Generalized Solutions of First-Order Partial Differential Equations: The Dynamical Optimization Perspective (Birkhäuser, Boston, 1995; Inst. Komp. Issled., Moscow–Izhevsk, 2003).Google Scholar