Multidimensional global extremum seeking via the DIRECT method

This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants - DIRECT is a sampling type global optimisation method for Lipschitz-continuous functions defined over compact multidimensional domains. Finite-time semi-global practical convergence is established based on a deadbeat sampled-data control law, whose sampling period is a parameter which determines the region and accuracy of convergence. A crucial part of the development is dedicated to a robustness analysis of the DIRECT method against bounded additive perturbations on the objective function. A numerical example of global extremum seeking in the presence of local extrema based on DIRECT is presented at the end.