Backstepping Controller Retuning using ε Subdifferential Optimization

This paper presents a general optimization approach in automatic´s field. It discusses the design and retuning of controllers as well as the validation of the general manufacturer specifications, which will be expressed by a frequency and/or temporal templates in order to be solved by a general optimization problem. This is a very complex and particular problem. It will be shown that it involves nondifferentiable functions and criteria. The resolution of this kind of problems can be difficult or impossible via gradient and all classical descent algorithms. In this study, we propose an ε subdifferential algorithm, very efficient for nonsmooth optimization. This algorithm, mixing with an exact computation of gradient based on parametric sensitivity functions, appears to be well suited to problems with nonsmooth costs and constraints. As illustration, this method will be used to retune backstepping controller for a magnetic suspension system. Simulations and comparison results are given to demonstrate the effectiveness of the proposed approach.