Minimising entropy and mean tracking control for affine nonlinear and non-Gaussian dynamic stochastic systems

The entropy concept in stochastic systems is used to formulate a control algorithm which minimises the closed-loop randomness for a class of nonlinear dynamic stochastic systems and places the output mean value as close as possible to a given value. Since the entropy measures the randomness of stochastic systems in a more general sense than that of the variance measure for Gaussian random variables, the use of entropy here can produce control algorithms which minimise uncertainties for the closed-loop stochastic systems subjected to any bounded random inputs (generally non-Gaussian). The output probability density function of the system is approximated by the recently developed linear B-spline decoupling model, and the dynamic part of the system links the coefficients of the B-spline expansion with a deterministic control input by a nonlinear affine model. To minimise the randomness of the closed-loop system, the entropy of the output probability density function is included in the proposed performance function. By minimising this performance function, a controller is obtained through a first-order approximation of the ´logarithm´ function involved in the output entropy calculations. An illustrative example is used to show the use of the control algorithm, and encouraging results have been obtained.