A Predictor-like Controller for Linear Ito Stochastic Systems with Input Delays

Linear quadratic regulation (LQR) is very fundamental in modern control theory. The theory has been developing for several decades. However, a more general problem, the LQR problem for stochastic systems with multiple control channels and delays still remains outstanding. To better understand our idea, the paper focuses on dealing with the problem with two control channels and a delay, which is more difficult than the one with a single delayed control channel since the former actually encounters interaction of control channels besides the delay. A new value function is proposed, which is key for finding the predictor-like controller. The idea is also suitable for handling the LQR problem for Ito stochastic systems with multi-control-channel and multi-delay.

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