Nonconvex Integro-Differential Sweeping Process with Applications
Abderrahim Bouach, Tahar Haddad, Lionel Thibault · SIAM Journal on Control and Optimization · 2022
In this paper, we analyze and discuss the well-posedness of a new variant of the so-called sweeping process. In this variant, the prox-regular moving set $C(t)$ is supposed to have an absolutely continuous variation and is perturbed by an integral forcing term. The integrand of the forcing term depends on two time-variables; that is, we study a general integro-differential sweeping process of Volterra type. The results are applied to nonregular electrical circuits containing time-varying capacitors and nonsmooth electronic devices like diodes. A circuit with transmission line, diode, and inductor is also analyzed. All these applications represent an additional novelty of our paper.