An information geometric algorithm for multi-input and multi-output stochastic distribution control systems with output feedback vector

An information geometric algorithm is proposed to control the shape of the conditional output probability density function for stochastic distribution control systems. The considered system is of multi-input and multi-output with stochastic noises and a output feedback vector. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function using the probability theories, whose shape can be considered to be determined by the control input vector and the output feedback vector. The set of the conditional output probability density function forms a manifold(M), and the control input and the output feedback can be considered as the coordinate system from the viewpoint of information geometry. The Kullback-Leibler divergence acts as the distance between the conditional output probability density function and the target probability density function, and can be considered as an error function. For the output feedback vector is known, our propose is to design the control input vector to make the conditional output probability density function as close as possible to the given one. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Finally, an illustrative example is utilized to demonstrate the effectiveness of the algorithm.