Generalised Probabilistic Control Design for Uncertain Stochastic Control Systems

In this paper a novel generalised fully probabilistic controller design for the minimisation of the Kullback‐Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented for a linear Gaussian uncertain class of stochastic systems. A single layer neural network is used to approximate the probability density function of the system dynamics. The generalised probabilistic control law is obtained by solving the recurrence equation of dynamic programming to the fully probabilistic design control problem while taking into consideration the dependency of the parameters of the estimated probability density function of the system dynamics on the input values. It is shown to be of the class of cautious type controllers which accurately minimises the value of the Kullback‐Leibler divergence without disregarding the variance of the model prediction as an element to be minimised. Comparison of theoretical and numerical results obtained from the F‐16 fighter aircraft application with existing state‐of‐the‐art demonstrates the effectiveness of the proposed method.