Reinforcement learning for linear exponential quadratic Gaussian problem

This paper addresses the infinite -horizon linear exponential quadratic Gaussian problem for a class of stochastic systems with additive noise. A model -free generalized policy iteration reinforcement learning algorithm is proposed to estimate the kernel matrices and update the control gains using the data along system trajectories. The estimation errors of the kernel matrices are proven to be bounded and the control gains generated by the algorithm are proven to be admissible under mild conditions. A numerical example is given to illustrate the obtained results.