A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This work presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes´ theorem. Using Bayes´ rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems.