Adaptive Linear Quadratic Control for Stochastic Discrete-Time Linear Systems With Unmeasurable Multiplicative and Additive Noises

This note investigates the adaptive linear quadratic control problem (ALQCP) for stochastic discrete-time (DT) linear systems with unmeasurable multiplicative and additive noises. A data-driven value iteration algorithm is developed to solve the stochastic algebraic Riccati equation (SARE) that results from the concerned problem and to simultaneously obtain the optimal feedback policy. The proposed algorithm directly uses online data to solve the ALQCP based on an unbiased estimator and an initial stabilizing controller with unknown system dynamics and unmeasurable multiplicative and additive noises. It is shown that the proposed algorithm under a finite length of online data converges to a neighborhood of the solution to the SARE with a probability and the input-to-state stability, and the neighborhood can be arbitrarily small while the probability can be arbitrarily close to one as the length of online data increases. The simulation results demonstrate the efficacy of the proposed algorithm.