A new approach to problem of stochastic optimization of linear dynamic systems with parametric uncertainties

Heading: 
Space Instruments
1Novikov, AV, 2Yatsenko, VA
1Yangel Yuzhnoye State Design Office, Dnipropetrovsk, Ukraine
2Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Kyiv, Ukraine
Kosm. nauka tehnol. 2006, 12 ;(2-3):083-097
https://doi.org/10.15407/knit2006.02.083
Publication Language: Russian
Abstract: 
We propose a new approach to solving a number of optimization problems of linear dynamic systems with parametric uncertainties. The approach is based on application of tensor formalism for construction of mathematical models of parametric uncertainties. Within the framework of the approach the following problems are considered: states prediction and data processing, optimal control etc. The efficiency of the methods proposed is illustrated by the results of computational simulation.
Keywords: optimization, parametric uncertainties, tensor formalism
Full text (PDF)
 
References: 
1. Anderson T. W. An Introduction to Multivariate Statistical Analysis, 500 p. (Fizmatgiz, Moscow, 1963) [in Russian].
2. Aoki M. Optimization of Stochastic Systems, 424 p. (Nauka, Moscow, 1971) [in Russian].
3. Athans M., Falb P. Optimal Control, 764 p. (Mashinostroenie, Moscow, 1968) [in Russian].
4. Bellman R. Processes of Control with Adaptation, 360 p. (Nauka, Moscow, 1964) [in Russian].
5. Bellman R. Introduction to Matrix Theory, 368 p. (Nauka, Moscow, 1969) [in Russian].
6. Bellman R., Kalaba R. Quasilinearization and Nonlinear Boundary-Value Problems, 184 p. (Mir, Moscow, 1968) [in Russian].
7. Bobrikov E. P., Yatsenko V. A. Local prediction, filtering and identification of linear dynamical systems under the conditions of a priori parametric uncertainty. In: Pribory i metody avtomatizacii jeksperimental'nyh issledovanij, 53—57 (Dnepropetrovsk, 1984) [in Russian].
8. Gantmacher F. R. Theory of Matrices, 576 p. (Nauka, Moscow, 1966) [in Russian].
9. Korn G. A., Korn Th. M. Mathematical handbook for scientists and engineers: definitions, theorems and formulas for reference and review, 832 p. (Nauka, Moscow, 1974) [in Russian].
10. Rashevsky P. K. Riemannian Geometry and Tensor Analysis, 664 p. (Nauka, Moscow, 1967) [in Russian].
11. Saridis G. N. Self-Organizing Control of Stochastic Systems, 400 p. (Nauka, Moscow, 1980) [in Russian].
12. Feldbaum A. A. Fundamentals of Optimal Automatic System Theory, 623 p. (Fizmatgiz, Moscow, 1963) [in Russian].
13. Leondes C. T. (Ed.) Filtering and stochastic control in dynamic systems, 350 p. (Mir, Moscow, 1980) [in Russian].
14. Tsypkin Ya. Z. Foundations of the Theory of Learning Systems, 252 p. (Nauka, Moscow, 1970) [in Russian].
15. Yatsenko V. A. Information prediction of solutions to the identification problem. In: Pribory i metody avtomatizacii jeksperimental'nyh issledovanij, 6—12 (Dnepropetrovsk, 1985) [in Russian].
16. Spooner J. T., Maggiore M., Ordonez R., Passino K. M. Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques, 509 p. (John Wiley & Sons, Inc., 2002).
https://doi.org/10.1002/0471221139

17. Tanaka K., Wang H. O. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, 305 p. (John Wiley & Sons, Inc., 2001).
https://doi.org/10.1002/0471224596