Value iteration algorithm for continuous-time linear quadratic stochastic optimal control problems

In this study, we investigate a continuous-time infinite-horizon linear quadratic stochastic optimal control problem with multiplicative noise in control and state variables. Using the techniques of stochastic stability, exact observability, and stochastic approximation, a value iteration algorithm is developed to solve the corresponding generalized algebraic Riccati equation. Unlike the existing policy iteration algorithm, this algorithm does not rely on an initial stabilizing control. Further, this algorithm can also be used to compute policy evaluation steps that arise in the policy iteration algorithm. Herein, a simulation example is provided to validate the obtained results.