摘要：AbstractLinear quadratic regulation (LQR) is very fundamental in modern control theory. The theory has been developing for several decades. However, the LQR problem for stochastic systems with input delays still remains outstanding. The paper focuses on the LQR problem for Ito stochastic systems with two control channels and a delay, which will pave a way to approach the correspondingH∞control problem. In contrast with the single channel problem, this problem is more typical and involved since the two channels problem actually encounters interaction between channels besides the delay. The paper focuses on providing a necessary and sufficient solvability condition and optimal control. The sufficiency is proved by finding a suitable value functional and completing the square. The necessary condition is obtained by the variant of the calculus of variations. What’s more important, due to that the result is given based on coupling ordinary and partial differential equations, we present the analytic solution to these equations. The idea is also suitable for handling the LQR problem for Ito stochastic systems with multiple control channels and multiple delays.
关键词：KeywordsLQRstochastic systemsinput delayoptimal controlIto stochastic systems
