Multi-objective Minimum Entropy Controller Design for Stochastic Processes

Minimum variance control is an established method in control of systems corrupted by noise. In these cases, as it is not possible to directly control the actual value of the system variables, one aims to reduce the variations instead. However, when the system noises are non-Gaussian, this approach fails because non-Gaussian noise cannot be characterised by simple measures such as variance. In these cases, the Entropy is proposed as a generalisation of the variance measure and the control objective becomes that of minimising the Entropy. Previously a limited form of this problem has been solved using first order Newtonian methods. In this paper, the control objective is first expanded to also include an error term related to the closed loop tracking performance, and the combined problem is then solved using a fast global optimisation search algorithm. The effectiveness of the approach is demonstrated through a case study based on a first principle model of a nonlinear heat exchanger.