Robust covariance control for perturbed stochastic multivariable system via variable structure control. (English) Zbl 0948.93008
Summary: Based on the concept of variable structure control, this paper investigates the steady state covariance assignment problem for perturbed stochastic multivariable systems. By using the invariance property of variable structure systems, the matched perturbation of the system disappears on the sliding mode. With the aid of Ito-formula, the controller \(u(t)\) is proposed. Combining the sliding phase and hitting phase of the system design, the control feedback gain matrix \(G\) is derived to satisfy the steady state covariance assignment.
Keywords:
robust state covariance assignment; variable structure control; switching function; semimartingaleReferences:
| [1] | Chung, H. Y.; Chang, W. J., Covariance control with variance constraints for continuous perturbed stochastic systems, System Control Lett., 19, 5, 413-417 (1992) · Zbl 0763.93079 |
| [2] | W.J. Chang, K.Y. Chang, Performance constrained variable structure control for ship yaw-motion systems with perturbations, Proceedings of the IFAC Conference on Control Applications in Marine Systems (CAMS’98), Fukuoka, Japan, October, 1998, pp. 23-28.; W.J. Chang, K.Y. Chang, Performance constrained variable structure control for ship yaw-motion systems with perturbations, Proceedings of the IFAC Conference on Control Applications in Marine Systems (CAMS’98), Fukuoka, Japan, October, 1998, pp. 23-28. |
| [3] | K.Y. Chang, W.J. Wang, Covariance assignment for stochastic model reference systems via sliding mode control concept, Proceedings of the American Control Conference, Philadelphia, PA, USA, June, 1998, pp. 289-290.; K.Y. Chang, W.J. Wang, Covariance assignment for stochastic model reference systems via sliding mode control concept, Proceedings of the American Control Conference, Philadelphia, PA, USA, June, 1998, pp. 289-290. |
| [4] | K.Y. Chang, W.J. Wang, Local state covariance assignment for stochastic large-scale systems, ASME J. Dyn. Systems Meas. Control 121 (1) (1999) 139-142.; K.Y. Chang, W.J. Wang, Local state covariance assignment for stochastic large-scale systems, ASME J. Dyn. Systems Meas. Control 121 (1) (1999) 139-142. |
| [5] | C. Dellacherie, P.A. Meyer, Probabilities and Potential B, North-Holland, Amsterdam, 1982.; C. Dellacherie, P.A. Meyer, Probabilities and Potential B, North-Holland, Amsterdam, 1982. · Zbl 0494.60002 |
| [6] | Drazenovic, B., The invariance conditions in variable structure systems, Automatica, 5, 287-295 (1969) · Zbl 0182.48302 |
| [7] | Hotz, A.; Skelton, R. E., Covariance control theory, Int. J. Control, 46, 1, 13-32 (1987) · Zbl 0626.93080 |
| [8] | Hung, J. Y.; Gao, W. B.; Hung, J. C., Variable structure control: A survey, IEEE Trans. Ind. Electron., 40, 2-22 (1993) |
| [9] | Lee, J. L.; Wang, W. J., Robust decentralized stabilization via sliding mode control, Control-Theory Adv. Technol., 9, 3, 721-732 (1993) |
| [10] | X. Mao, Stability of Stochastic Differential Equations with Respect to Semimartingales, Wiley, New York, 1991.; X. Mao, Stability of Stochastic Differential Equations with Respect to Semimartingales, Wiley, New York, 1991. · Zbl 0724.60059 |
| [11] | D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991.; D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1991. · Zbl 0731.60002 |
| [12] | Utkin, V. I., Variable structure control systems with sliding modes, IEEE Trans. Automat. Control, 22, 212-222 (1977) · Zbl 0382.93036 |
| [13] | V.I. Utkin, Discontinuous control systems: state of the art in theory and applications, Proceedings of the 10th IFAC Triennial World Congress, Munich, Vol. 1, 1987, pp. 25-44.; V.I. Utkin, Discontinuous control systems: state of the art in theory and applications, Proceedings of the 10th IFAC Triennial World Congress, Munich, Vol. 1, 1987, pp. 25-44. |
| [14] | Wang, W. J.; Lee, J. L., Hitting time reduction and chattering attenuation in multi-input variable structure systems, Control-Theory Adv. Technol., 9, 2, 491-500 (1993) |
| [15] | Xu, J. H.; Skelton, R. E.; Zhu, G., Upper and lower covariance bounds for perturbed linear systems, IEEE Trans. Automat. Control, 35, 8, 944-948 (1990) · Zbl 0723.93065 |
| [16] | Yasuda, K.; Skelton, R. E.; Grigoriadis, K. M., Covariance controllers: a new parametrization of the class of all stabilizing controllers, Automatica, 29, 3, 785-788 (1993) · Zbl 0771.93010 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
