Robust Probabilistic Control for Linear Stochastic Systems with Functional Uncertainty

This paper proposes a cautious randomised controller that is derived such that it minimises the discrepancy between the joint distribution of the system dynamics and a predefined ideal joint probability density function (pdf). This distance is known as the Kullback-Leibler divergence. The developed methodology is demonstrated on a class of uncertain stochastic systems that can be characterised by Gaussian density functions. The density function of the dynamics of the system is assumed to be unknown, therefore estimated using the generalised linear neural network models. The analytic solution of the randomised cautious controller is obtained by evaluating the multi-integrals in the Kulback-Leibler divergence cost function. The derived cautious controller minimises to high accuracy the expected value of the Kullback-Leibler divergence taking into consideration the covariance of the dynamics estimated probability density functions.