Approximate controllability of semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control. (English) Zbl 1517.34109
Summary: The objective of this paper is to interpret the approximate controllability of a semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control in infinite-dimensional spaces. Sufficient conditions for the approximate controllability of semi-linear control system have been established. The results are obtained using the Banach fixed point theorem and the theory of resolvent operator developed in [R. C. Grimmer, Trans. Am. Math. Soc. 273, 333–349 (1982; Zbl 0493.45015)]. An example is introduced to show the effectiveness of the result.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 93B05 | Controllability |
Keywords:
approximate controllability; stochastic integrodifferential system; multiple delays; Poisson jumpsCitations:
Zbl 0493.45015References:
| [1] | Anguraj, A.; Ramkumar, K., Approximate controllability of semilinear stochastic integrodifferential system with nonlocal conditions, Fractal Fract., 2, 4, 29 (2018) |
| [2] | Balachandran, K.; Dauer, J. P., Controllability of nonlinear systems in Banach spaces:a survey, J. Optim. Theory Appl., 115, 1, 7-28 (2002) · Zbl 1023.93010 |
| [3] | Barnett, S., Introduction to Mathematical Control Theory (1975), Clarendon Press: Clarendon Press, Oxford · Zbl 0307.93001 |
| [4] | Da Prato, G.; Zabczyk, J., Stochastic Equations in Infinite Dimensions (1992), Cambridge: Cambridge University Press · Zbl 0761.60052 |
| [5] | Dhanalakshmi, K.; Balasubramaniam, P., Stability result of higher-order fractional neutral stochastic differential system with infinite delay driven by Poisson jumps and Rosenblatt process, Stoch. Anal. Appl., 38, 2, 352-372 (2019) · Zbl 1440.60049 |
| [6] | Grimmer, R., Resolvent operator for integral equations in Banach spaces, Trans. Am. Math. Soc., 273, 333-349 (1982) · Zbl 0493.45015 |
| [7] | Kalman, R. E., Controllability of linear systems, Contrib. Differ. Equ., 1, 190-213 (1963) |
| [8] | Klamka, J., Stochastic controllability of linear systems with delays in control, Bull. Pol. Acad. Sci.: Tech. Sci. 55 (1), 23-29 (2007) · Zbl 1203.93190 |
| [9] | Klamka, J., Stochastic controllability of systems with multiple delays in control, Int. J. Appl. Math. Comput. Sci., 19, 39-48 (2009) · Zbl 1169.93005 |
| [10] | Klamka, J.; Socha, L., Some remarks about stochastic controllability, IEEE. Trans. Automat. Contr., 22, 5, 880-881 (1977) · Zbl 0363.93048 |
| [11] | Long, H.; Hu, J.; Li, Y., Approximate controllability of stochastic PDE with infinite delays driven by Poisson jumps, IEEE Int. Conf. Inf. Sci. Technol. 12819678, 194-199 (2012) |
| [12] | Mahmudov, N. I., Controllability of linear stochastic systems in Hilbert spaces, J. Math. Anal. Appl., 259, 64-82 (2001) · Zbl 1031.93032 |
| [13] | Mahmudov, N. I., Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces, SIAM J. Control Optim., 42, 1604-1622 (2003) · Zbl 1084.93006 |
| [14] | Muthukumar, P.; Balasubramaniam, P., Approximate controllability of mixed stochastic Volterra-Fredholm type integrodifferential systems in Hilbert space, J. Franklin Inst., 348, 10, 2911-2922 (2011) · Zbl 1254.93028 |
| [15] | Naito, K., Controllability of semilinear control systems dominated by linear part, SIAM J. Control Optim., 25, 715-722 (1987) · Zbl 0617.93004 |
| [16] | Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer: Springer, New York · Zbl 0516.47023 |
| [17] | Ramkumar, K.; Ravikumar, K.; Anguraj, A., Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with fractional Brownian motion and Poisson jumps, Discontinuity Nonlinearity Complex, 10, 2, 227-235 (2021) · Zbl 1494.93019 |
| [18] | Ramkumar, K.; Ravikumar, K., Controllability of neutral impulsive stochastic integrodifferential equations driven by a Rosenblatt process and unbounded delay, Discontinuity Nonlinearity Complex, 10, 2, 311-321 (2021) · Zbl 1494.93018 |
| [19] | Ravikumar, K.; Ramkumar, K.; Anguraj, A., Null controllability of nonlocal Sobolev-type Hilfer fractional stochastic differential system driven by fractional Brownian motion and Poisson jumps, Discontinuity Nonlinearity Complex, 10, 4, 617-626 (2021) · Zbl 1478.93062 |
| [20] | Sakthivel, R.; Ren, Y., Complete controllability of stochastic evolution equations with jumps, Rep. Math. Phys., 68, 163-174 (2011) · Zbl 1244.93028 |
| [21] | Shukla, A.; Arora, U.; Sukavanam, N., Approximate controllability of semilinear stochastic system with multiple delays in control, Cogent Math., 3, 1 (2016) · Zbl 1438.93014 |
| [22] | Triggiani, R., Controllability and observability in Banach spaces with bounded operators, SIAM J. Control, 10, 462-491 (1975) · Zbl 0268.93007 |
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.
