Details

Autor(en) / Beteiligte

• Zhang, Huanshui
• Xu, Juanjuan

Titel

Control for Itô Stochastic Systems With Input Delay

Ist Teil von

• IEEE transactions on automatic control, 2017-01, Vol.62 (1), p.350-365

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2017

Quelle

IEEE Xplore

Beschreibungen/Notizen

• This paper examines the long-standing problem of linear quadratic regulation and stabilization for Itô stochastic systems with input delay. This problem remains a primary challenge because the separation principle does not hold for Itô stochastic systems. This paper presents a complete solution to the problem: 1) The (sufficient and necessary) solvability condition of the optimal control and the analytical controller are given based on the modified Riccati differential equation defined herein. 2) The sufficient and necessary stabilization condition in mean square sense is explored. We show that the Itô stochastic system with input delay is stabilized if and only if the modified algebraic Riccati equation developed in this paper has a unique positive-definite solution. The essential obstacle encountered in this paper concerns a Delayed Forward-Backward Stochastic Differential Equation (D-FBSDE), which is mathematical challenging.