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Robust output stabilization for a class of nonlinear uncertain stochastic systems under multiplicative and additive noises: The attractive ellipsoid method
1. | Departamento de Ingenieria Mecatronica, Universidad Autonoma del Carmen, Capmeche, Mexico |
2. | Centro de Investigacin y de Estudios Avanzados del I.P.N. (Cinvestav-IPN), Mexico |
References:
[1] |
H. Alazki and A. Poznyak, Inventory constraint control with uncertain stochastic demands: Attractive ellipsoid technique application, IMA Journal of Mathematical Control and Information, 29 (2012), 399-425.
doi: 10.1093/imamci/dnr038. |
[2] |
J. A. Appleby and A. Flynn, Stabilization of volterra equations by noise, The Journal of Applied Mathematics and Stochastic Analysis, (2006), Art. ID 89729, 29 pp.
doi: 10.1155/JAMSA/2006/89729. |
[3] |
L. Arnold and B. Schmalfuss, Lyapunov's second method for random dynamical systems, The Journal of Differential Equations, 177 (2001), 235-265.
doi: 10.1006/jdeq.2000.3991. |
[4] |
M. Bardi and D. I. Capuzzo, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems and Control: Foundations and Applications, Birkhauser, Boston, 1997.
doi: 10.1007/978-0-8176-4755-1. |
[5] |
D. P. Bertsekas, Infinite time reachability of state-space regions by using feedback control, IEEE Trans. on Automatic Control, 17 (1994), 604-613. |
[6] |
A. Bensoussan, Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge, 1992.
doi: 10.1017/CBO9780511526503. |
[7] |
F. Blanchini, Set invariance in control - a survey, Automatica J. IFAC, 35 (1999), 1747-1767.
doi: 10.1016/S0005-1098(99)00113-2. |
[8] |
F. Blanchini and S. Miani, Set Theoretic Methods in Control, Systems & Control: Foundations & Applications. Birkhauser Boston Inc., Boston, MA, 2008. |
[9] |
A. El Bouhtouri and K. El Hadri, Robust stabilization of jump linear systems with multiplicative noise, IMA Journal of Mathematical Control and Information, 20 (2003), 1-19.
doi: 10.1093/imamci/20.1.1. |
[10] |
M. Davis, Linear Estimation and Stochastic Control, Champman and Hall, New York, 1977. |
[11] |
T. Duncan and P. Varaiya, On the solution of a stochastic control system, SIAM J. Control, 9 (1971), 354-371.
doi: 10.1137/0309026. |
[12] |
W. Fleming and R. Rishel, Optimal Deterministic and Stochastic Control, Springer- Verlag, Berlin, 1975. |
[13] |
U. Haussman, Some examples of optimal control, Or: Stochastic maximum principal at work, SIAM Rev., 23 (1981), 292-307.
doi: 10.1137/1023062. |
[14] |
K. Holmstrom, A. Goran and M. Edvall, User's Guide for TOMLAB/CPLEX, v12.1, (2009). |
[15] |
N. V. Krylov, Controlled Diffusion Process, Springer, New York. 1980. |
[16] |
A. Kurzhanskii and I. Valyi, Ellipsoidal Calculus for Estimation and Control, Birkhauser, Boston, MA, 1997.
doi: 10.1007/978-1-4612-0277-6. |
[17] |
H. Kushner, Necessary condition for continuous parameter stochastic optimization problems, SIAM J. Control, 10 (1972), 550-565.
doi: 10.1137/0310041. |
[18] |
D. G. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, 16 (1971), 596-602. |
[19] |
S. A. Nazin, B. T. Polyak and M. V. Tpopunov, Rejection of bounded exogenous disturbances by the method of invariant ellipsoids, Autom. Remote Control, 68 (2007), 467-486.
doi: 10.1134/S0005117907030083. |
[20] |
Y. Nesterov and A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming, SIAM, 1994. |
[21] |
B. Polyak, A. V. Nazin, M. V. Topunov and S. A. Nazin, Rejection of bounded disturbances via invariant ellipsoids technique, In Proc. 45th IEEE Conf. Decision Contr., San Diego. USA, (2006), 1429-1434. |
[22] |
A. Polyakov and A. Poznyak, Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control, Automatica, 47 (2011), 1450-1454. |
[23] |
A. S. Poznyak, Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques, Vol. 1. Elsevier, London - New York, 2008. |
[24] |
A. S. Poznyak, Advanced Mathematical Tools for Automatic Control Engineers: Stochastic Techniques, Vol. 2. Elsevier, London - New York, 2009. |
[25] |
A. S. Poznyak, T. E. Duncan, B. Pasik-Duncan and V. G. Boltyanskii, Robust stochastic maximum principle for multi-model worst case optimization, International Journal of Control, 75 (2002), 1032-1048.
doi: 10.1080/00207170210156251. |
[26] |
F. Schweppe, Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, N.J., 1973. |
[27] |
V. A. Ugrinovskii, Robust H infinity control in the presence of stochastic uncertainty, International Journal of Control, 71 (1998), 219-237.
doi: 10.1080/002071798221849. |
[28] |
J. Yong and X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, 1999.
doi: 10.1007/978-1-4612-1466-3. |
show all references
References:
[1] |
H. Alazki and A. Poznyak, Inventory constraint control with uncertain stochastic demands: Attractive ellipsoid technique application, IMA Journal of Mathematical Control and Information, 29 (2012), 399-425.
doi: 10.1093/imamci/dnr038. |
[2] |
J. A. Appleby and A. Flynn, Stabilization of volterra equations by noise, The Journal of Applied Mathematics and Stochastic Analysis, (2006), Art. ID 89729, 29 pp.
doi: 10.1155/JAMSA/2006/89729. |
[3] |
L. Arnold and B. Schmalfuss, Lyapunov's second method for random dynamical systems, The Journal of Differential Equations, 177 (2001), 235-265.
doi: 10.1006/jdeq.2000.3991. |
[4] |
M. Bardi and D. I. Capuzzo, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems and Control: Foundations and Applications, Birkhauser, Boston, 1997.
doi: 10.1007/978-0-8176-4755-1. |
[5] |
D. P. Bertsekas, Infinite time reachability of state-space regions by using feedback control, IEEE Trans. on Automatic Control, 17 (1994), 604-613. |
[6] |
A. Bensoussan, Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge, 1992.
doi: 10.1017/CBO9780511526503. |
[7] |
F. Blanchini, Set invariance in control - a survey, Automatica J. IFAC, 35 (1999), 1747-1767.
doi: 10.1016/S0005-1098(99)00113-2. |
[8] |
F. Blanchini and S. Miani, Set Theoretic Methods in Control, Systems & Control: Foundations & Applications. Birkhauser Boston Inc., Boston, MA, 2008. |
[9] |
A. El Bouhtouri and K. El Hadri, Robust stabilization of jump linear systems with multiplicative noise, IMA Journal of Mathematical Control and Information, 20 (2003), 1-19.
doi: 10.1093/imamci/20.1.1. |
[10] |
M. Davis, Linear Estimation and Stochastic Control, Champman and Hall, New York, 1977. |
[11] |
T. Duncan and P. Varaiya, On the solution of a stochastic control system, SIAM J. Control, 9 (1971), 354-371.
doi: 10.1137/0309026. |
[12] |
W. Fleming and R. Rishel, Optimal Deterministic and Stochastic Control, Springer- Verlag, Berlin, 1975. |
[13] |
U. Haussman, Some examples of optimal control, Or: Stochastic maximum principal at work, SIAM Rev., 23 (1981), 292-307.
doi: 10.1137/1023062. |
[14] |
K. Holmstrom, A. Goran and M. Edvall, User's Guide for TOMLAB/CPLEX, v12.1, (2009). |
[15] |
N. V. Krylov, Controlled Diffusion Process, Springer, New York. 1980. |
[16] |
A. Kurzhanskii and I. Valyi, Ellipsoidal Calculus for Estimation and Control, Birkhauser, Boston, MA, 1997.
doi: 10.1007/978-1-4612-0277-6. |
[17] |
H. Kushner, Necessary condition for continuous parameter stochastic optimization problems, SIAM J. Control, 10 (1972), 550-565.
doi: 10.1137/0310041. |
[18] |
D. G. Luenberger, An introduction to observers, IEEE Transactions on Automatic Control, 16 (1971), 596-602. |
[19] |
S. A. Nazin, B. T. Polyak and M. V. Tpopunov, Rejection of bounded exogenous disturbances by the method of invariant ellipsoids, Autom. Remote Control, 68 (2007), 467-486.
doi: 10.1134/S0005117907030083. |
[20] |
Y. Nesterov and A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming, SIAM, 1994. |
[21] |
B. Polyak, A. V. Nazin, M. V. Topunov and S. A. Nazin, Rejection of bounded disturbances via invariant ellipsoids technique, In Proc. 45th IEEE Conf. Decision Contr., San Diego. USA, (2006), 1429-1434. |
[22] |
A. Polyakov and A. Poznyak, Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control, Automatica, 47 (2011), 1450-1454. |
[23] |
A. S. Poznyak, Advanced Mathematical Tools for Automatic Control Engineers: Deterministic Techniques, Vol. 1. Elsevier, London - New York, 2008. |
[24] |
A. S. Poznyak, Advanced Mathematical Tools for Automatic Control Engineers: Stochastic Techniques, Vol. 2. Elsevier, London - New York, 2009. |
[25] |
A. S. Poznyak, T. E. Duncan, B. Pasik-Duncan and V. G. Boltyanskii, Robust stochastic maximum principle for multi-model worst case optimization, International Journal of Control, 75 (2002), 1032-1048.
doi: 10.1080/00207170210156251. |
[26] |
F. Schweppe, Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, N.J., 1973. |
[27] |
V. A. Ugrinovskii, Robust H infinity control in the presence of stochastic uncertainty, International Journal of Control, 71 (1998), 219-237.
doi: 10.1080/002071798221849. |
[28] |
J. Yong and X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, 1999.
doi: 10.1007/978-1-4612-1466-3. |
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