Title

Towards Optimal Control of Systems with Backlash

Abstract

The focus is on systems with backlash. These are systems described by second order differential equations coupled with unilateral state constraints modeling inelastic shocks. From the mathematical view point, these systems have been studied by Jean Jacques Moreau, Michelle Schatzman and Laetitia Paoli, among others. To deal with discontinuities of the velocity when the systems impacts with the boundary of the constraints, Michelle Schatzman proposed a mathematical model where both the velocities and the reaction force due to impact are considered to be measures. Noteworthy, the mathematical model for such systems lacks uniqueness of solution to the Cauchy problem.

Here, we introduce approximation systems where the forces during the impact are taken into account. Such approximations are relevant for two reasons. Firstly, we define a set of solutions as limits of the solutions to the approximation systems. This set may be smaller than the set of of the solutions usually considered in the literature. Secondly, such approximations are adequate to derive necessary condition to the time optimal control of interest. To the best of our knowledge, this is the first attempt to derive necessary conditions of optimality for optimal control problems involving systems with backlash.

This is a joint work with M. Margarida A. Ferreira from Universidade do Porto and Georgi Smirnov from Universidade do Minho.

Bio

Maria do Rosário de Pinho is an Associate Professor at the Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto (FEUP), and a researcher at Systec, Associated Laboratory Arise, and ISR-Porto. Her main research interests lie in the theory of optimal control problems. The main focus is on development of optimality conditions for constrained optimal control problems, with an emphasis on mixed constrained optimal control problems and on problems that lack classical properties of continuity as those involving sweeping systems. She also keeps a strong focus on applied optimal control problems, spanning from biomath, agriculture and robotics, and on the development of numerical methods for optimal control problems. She received a BSc in Mathematics and a MSc in Engineering from the University of Porto and PhD in Control Theory from Imperial College.