Groupe d’études et de recherche en analyse des décisions

Local and Global Optimization of Dynamic Systems by Controlling the Gradient obtained from Multiple Units

Balasubrahmanyan Srinivasan Professeur agrégé, Département de génie chimique, Polytechnique Montréal, Canada

Real-time optimization addresses the problem of tracking a changing optimal solution online. One of the techniques therein reformulates optimization as a gradient control problem. Traditionally, the gradient is estimated using correlation methods with the input being subject to a a temporal perturbation. In this work, a new gradient-estimation method is proposed where multiple identical copies of the system is assumed to be present. The various units are operated with a prefixed offset between their inputs and the difference between their outputs is used to compute the gradient by finite difference. First, it is shown that the multi-unit algorithm would lead to much faster convergence than the traditional methods. Secondly, it is shown that by reducing the offset to zero, this algorithm would indeed lead to the global optimum, even though it is just a gradient control method.