Stochastic LQR optimal control with white and colored noise: Dynamic programming technique

This work deals with LQR optimal control problems where the randomness of the dynamic systems evolves according to: (a) multiplicative and additive white noise, (b) mixture white noise and (c) white noise and colored noise. Total cost quadratic and discounted cost quadratic are studied. The white noise is represented by the Wiener process whereas the colored noise is represented by the solution of the Ornstein-Uhlenbeck’s stochastic dierential equation, whit initial condition is constant or normally distributed. In order to find the value functions and optimal policies, as well as algebraic and stochastic Riccati equations the dynamic programming technique was used. The theoretical results are illustrated by two applications. Numerical simulations are carried out using Matlab.

Keywords: Brownian motion, Correlation time, Itô ’s calculus, Markov processes, stochastic Ricatti equation.