A Linear Quadratic Control for Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimization

Automation and Remote Control

Volumn 64, Issue 10, 2003, Pages 1558-1570

  Dombrovskii, V V ^a   Lyashenko, E A ^a  

^a TOMSK STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK CONTROL; LINEAR CONTROL SYSTEMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; STOCHASTIC CONTROL SYSTEMS; THEOREM PROVING; VECTORS;

DISCRETE STOCHASTIC SYSTEMS; LINEAR QUADRATIC CONTROL;

DISCRETE TIME CONTROL SYSTEMS;

EID: 84904240224     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026057305653     Document Type: Article

References (23)

1. Sworder, D.D., Feedback Control of a Class of Linear Systems with Jump Parameters, IEEE Trans. Autom. Control, 1969, vol. 14, no. 1, pp. 9-14.
2. Bonhem, V.M., Stochastic Differential Equations in Control Theory, Mat. Sb. Perevodov, 1973, vol. 17, no. 5, pp. 82-114.
3. Kazakov, I.E. and Artem'ev, V.M., Optimizatsiya dinamicheskikh sistem sluchainoi struktury (Optimization of Random-Structure Dynamic Systems), Moscow: Nauka, 1980.
4. Pakshin, P.V., Optimal Linear Control for Discrete Systems under Random Jump Changes of Their Parameters, Probl. Upravlen. Tear. Inf., 1982, vol. 11, no. 3, pp. 179-193.
5. Pakshin, P.V., Stability of Discrete Random-Structure Systems under Constant Perturbations, Avtom. Telemekh., 1983, no. 6, pp. 75-85.
6. Hopkins, W.E., Optimal Stabilization of Families of Linear Differential Equations with Jump Coefficients and Multiplicative Noise, SIAM J. Control Optim., 1987, vol. 25, no. 6, pp. 1587-1600.
7. Li, X., Zhou, X., and Rami, M., Indefinite Stochastic LQ Control with Jumps, Proc. 40 IEEE Conf. Decision and Control, 2001, pp. 1693-1698.
8. De Koning, W.L., Infinite Horizon Optimal Control of Linear Discrete-Time Systems with Stochastic Parameters, Automatica, 1982, vol. 18, no. 4, pp. 503-514.
9. Dombrovskii, V.V. and Smagin, V.I., Robust Local Optimal Tracking Control Systems, Izv. Vuzov. Fiz., 1995, no. 9, pp. 96-99.
10. Dombrovskii, V.V. and Chikunova, E.V., Design of Dynamic Reduced-Order Controllers for Systems with Random Parameters, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 2, pp. 97-101.
11. Runolfsson, T., Risk-Sensitive and Robust Control of Discrete Time Hybrid Systems, Proc. 39 IEEE Conf. Decision and Control, 2000, pp. 1055-1060.
12. Chen, S. and Yong, J., Stochastic Linear Quadratic Optimal Control Problems, Appl. Math. Optim., 2001, vol. 43, pp. 21-45.
13. Malyshev, V.V. and Pakshin, P.V., Applied Theory of Stochastic Stability and Optimal Stationary Control: A Review, Part II, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1990, no. 2, pp. 97-119.
14. Merton, R.C., Continuous- Time Finance, Cambridge: Blackwell, 1990.
15. Mel'nikov, A.V., Volkov, S.N., and Nechaev, M.L., Matematika finansovykh obyazatel'stv (Mathematics of Pecuniary Liabilities), Moscow: Vysshaya Shkola Ekonomiki, 2001.
16. Shepard, N., Statistical Aspects of ARCH Models and Stochastic Volatility, Obozrenie Prikl. Prom. Mat., 1996, vol. 3, pp. 764-826.
17. Pakshin, P.V., State Estimation and Control Design for Discrete Linear Systems with Additive and Multiplicative Noise, Avtom. Telemekh., 1978, no. 4, pp. 75-85.
18. Phillis, Y.A., Estimation and Control of Systems with Unknown Covariance and Multiplicative Noise, IEEE Trans. Autom. Control, 1989, vol. 34, no. 10, pp. 1075-1078.
19. Dombrovskii, V.V., Design of Optimal Dynamic Reduced Order Controllers for Time-varying Linear Discrete Stochastic Systems, Avtom. Telemekh., 1996, no. 4, pp. 79-86.
20. Levine, W.S., Johnson, T.L., and Athans, M., Optimal Limited State Variable Feedback Controllers for Linear Systems, IEEE Trans. Autom. Control, 1971, vol. 16, no. 6, pp. 785-793.
21. Dombrovsky, V.V. and Gerasimov, E.S., Dynamic Network Model of Control Investment Portfolio in Continuous Time, Proc. 5 Russian-Korean Sympos. Sci. Technol. (KORUS-2001), 2001, Tomsk, pp. 304-308.
22. Gerasimov, E.S. and Dombrovskii, V.V., A Dynamic Network Model for Investment Control under Quadratic Risk Function, Avtom. Telemekh., 2002, no. 2, pp. 119-128.
23. Athans, M., The Matrix Minimum Principle, Inf. Control, 1968, vol. 11, pp. 592-606.