Adaptive Control for Stochastic Systems with Unknown Parameters and Input Delay

The adaptive dual control problem of a single-in single-out (SISO) stochastic system with unknown parameters and input delay is studied in this paper. The unknown parameters are assumed to be constant but belong to a known finite set. For each group of possible model parameters, a Kalman filter is used to estimate the system state online and the posterior probability of this model can also be calculated accordingly. The optimal control of each model is designed, based on an M steps ahead loss function. The final dual controller is obtained by a weighted sum of all possible optimal control outputs considering the posterior probabilities of each model. Numerical simulations were performed to verify the effectiveness of the proposed controller.