Extrapolation in discrete systems with multiplicative perturbations at incomplete information
The model with multiplicative perturbations and incomplete information is described by the equation: m x(k +1) = (A + AA)x(k) + (B + AB)u(k) + £Asx(k)9s (k) + /(k) + q(k), x(0) = x0, s=1 where x(k) e Rn is the state vector, u (k) e Rp is the known input, f(k) is an unknown input; x0 is a random vector (the covariance matrix N0 = M{(x0 - x0)(x0 - x0)T} and the expectation x0 = M{x0} are assumed to be known); A, B, A3(s = 1...m) are known matrices; AA, AB are matrices of unknown parameters; q(k) and 9 (k) are Gaussian vector random sequences with the following characteristics: M{q(k)} = 0 , M{q(k)qT(j)} = QS. , M{9f(k)} = 0 , M{9s(k)9sT(j)} = QS. The observation channel is described by the formula: y(k) = Sx(k) + v(k), where v(k) is a Gaussian random sequence with known characteristics. The problem solution is proposed to be performed on the basis of the separation principle using the optimal recurrent extrapolation, the least squares method with additional smoothing using the moving average algorithms and nonparametric estimators. It is shown that the use of smoothing algorithms for estimating an unknown input for a discrete model with multiplicative perturbations allows can improve the prediction accuracy.
Keywords
оценки экстраполяции,
дискретная система,
мультипликативные возмущения,
неизвестный вход,
extrapolation estimates,
discrete system,
multiplicative perturbations,
unknown input,
неизвестные параметры,
unknown parametersAuthors
| Kim Konstantin S. | Tomsk State University | kks93@rambler.ru |
| Smagin Valery I. | Tomsk State University | vsm@mail.tsu.ru |
Всего: 2
References
Mohanty N.C., Soong T.T. Linear filtering in multiplicative noise // Information and Control. 1977. V. 34, is. 2. P. 141-147.
Stoica A.-M., Yaesh I. Kalman-type filtering for discrete-time stochastic systems with state-dependent noise // Proc. Mathematical Theory of Networkand Systems-MTNS. 28 July - 1 August, Blacksburg, VA. 2008. P. 1-6.
Wu Y., Zhang Q., Shen Z. Kalman filtering with multiplicative and additive noises // Proc. 12th World Congress on Intelligent Control and Automation (WCICA). 12-15 June, 2016. P. 483-487.
Germani A., Manes C., Palumbo P. Linear filtering for bilinear stochastic differential systems with unknown inputs // IEEE Trans. on Automatic Control. 2002. V. 47, No. 10. P. 1726-1730.
Yang F., Wang Z., Hung Y.S. Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises // IEEE Trans. on Automatic Control. 2002. V. 47, No. 7. P. 1179-1183.
Smagin V.I. State estimation for nonstationary discrete systems with unknown input using compensations // Russian Physics Jour nal. 2015. V. 58, is. 7. P. 1010-1017.
Janczak D., Grishin Yu. State estimation of linear dynamic system with unknown input and uncertain observation using dynamic programming // Control and Cybernetics. 2006. No. 4. P. 851-862.
Gillijns S., Moor B. Unbiased minimum-variance input and state estimation for linear discrete-time systems // Automatica. 2007. V. 43. P. 111-116.
Hsien C.-S. On the optimality of two-stage Kalman filter for systems with unknown input // Asian J. of Control. 2010. V. 12, No. 4. P. 510-523.
Witczak M. Fault diagnosis and fault-tolerant control strategies for non-linear systems. Ch. 2: Unknown input observers and filters // Lecture Notes in Electrical Engineering. Springer International Publishing, 2014. P. 19-56.
Koshkin G.M., Smagin V.I. Filtering and prediction for discrete systems with unknown input using nonparametric algorithms // Proc. 10th International Conference on Digital Technologies. Zilina, Slovakia, July 9-11, 2014. P. 120-124.
Smagin V.I., Koshkin G.M. Kalman filtering and conrol algorithms for systems with unknown disturbances and parameters using nonparametric technique // Proc. 20th International Conference on Methods and Models in Automation and Robotics (MMAR 2015). 24-27 August, 2015, Miedzyzdroje, Poland. P. 247-251.
Koshkin G.M., Smagin V.I. Kalman filtering and forecasting algorithms with use of nonparametric functional estimators // Springer Proceeding in Mathematical Statistics / eds. R. Cao et al. 2016. Vol. 175. P. 75-84.
Athans M. The matrix minimum principle // Informat. and Contr. 1968. V. 11. P. 592-606.
