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.