Extension of multiunit global optimisation to three‐input systems

Finding the global optimum of an objective function has been of interest in many disciplines. Recently, a global optimisation technique based on multiunit extremum seeking has been proposed for scalar and two‐input systems. The idea of multiunit extremum‐seeking is to control the gradient evaluated using finite difference between two identical units operating with an offset. For scalar systems, it was shown that the global optimum could be obtained by reducing the offset to zero. For two‐input systems, the univariate global optimisation is performed on the circumference of a circle of reducing radius. In this study, the concept is extended to three‐input systems where the circle of varying radius sits on a shrinking sphere. The key contribution lies in formulating the rotation required to keep the best point found in the search domain. The theoretical concepts are illustrated on the global optimisation of several examples. Comparison results with other competitive methods show that the proposed technique performs well in terms of number of function evaluations and accuracy. © 2011 Canadian Society for Chemical Engineering