| Citation: | K. Fujita, D. Tsubakino, and S. Hara, “A stochastic optimal control for a class of LTI systems with a state-dependent wiener process: An algebraic approach,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 2, pp. 489–491, Feb. 2026. doi: 10.1109/JAS.2026.125750 |
| [1] |
A. Böttcher, “The algebraic Riccati equation with Toeplitz matrices as coefficients,” Electronic J. Linear Algebra, vol. 22, pp. 348–362, 2011.
|
| [2] |
N. Motee and Q. Sun, “Sparsity and spatial localization measures for spatially distributed systems,” SIAM J. Control and Optimization, vol. 55, no. 1, pp. 200–235, 2017. doi: 10.1137/15M1049294
|
| [3] |
I. Lasiecka and A. Tuffaha, “Riccati theory and singular estimates for a Bolza control problem arising in linearized fluid structure interaction,” Systems & Control Letters, vol. 58, no. 7, pp. 499–509, 2009.
|
| [4] |
K. Fujita and D. Tsubakino, “Hierarchical optimal control with information aggregation for groups including different numbers of agents,” in Proc. American Control Conf., 2022, pp. 1595–1600.
|
| [5] |
W. M. Wonham, “Optimal stationary control of a linear system with state-dependent noise,” SIAM Journal on Control, vol. 5, pp. 3–500, 1967.
|
| [6] |
Y. Zheng, L. Furieri, M. Kamgarpour, and N. Li, “Sample complexity of linear quadratic gaussian (LQG) control for output feedback systems,” in Proc. 3rd Conf. Learning for Dynamics and Control, 2021, vol. 144. pp. 559–570.
|
| [7] |
M. D. Fragoso, O. L. V. Costa, and C. E. de Souza, “A new approach to linearly perturbed Riccati equations arising in stochastic control,” Applied Math. and Optimization, vol. 37, no. 1, pp. 99–126, 1998. doi: 10.1007/s002459900070
|
| [8] |
R. Khasminskii, Stochastic Stability of Differential Equations. Berlin, Heidelberg, Germany: Springer, 2012.
|
| [9] |
M. A. Rami and X. Y. Zhou, “Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls,” IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1131–1143, 2000. doi: 10.1109/9.863597
|
| [10] |
W. M. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM J. Control, vol. 6, no. 4, pp. 681–697, 1968. doi: 10.1137/0306044
|
| [11] |
N. Motee, A. Jadbabaie, and B. Bamieh, “On decentralized optimal control and information structures,” in Proc. American Control Conf., 2008, pp. 4985–4990.
|
| [12] |
J. Sang, D. Ma, and Y. Zhou, “Group-consensus of hierarchical containment control for linear multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1462–1474, 2023. doi: 10.1109/JAS.2023.123528
|