An Algorithm to Generate Solutions to Hybrid Dynamical Systems with Inputs
Pauline Bernard, Ricardo G. Sanfelice · 2019
In this paper, we define solutions for hybrid systems with pre-specified hybrid inputs. Unlike previous work where solutions and inputs are assumed to be defined on the same domain a priori, we consider the case where intervals of flow and jump times of the input are not necessarily synchronized with those of the state trajectory. The proposed approach relies on reparametrizing the jumps of the input in order to write it on a common domain. The solutions then consist of a pair made of the state trajectory and the reparametrized input. Our definition generalizes the notions of solutions of continuous and discrete systems with inputs. We provide an algorithm that automatically performs the construction of solutions for a given hybrid input. Examples illustrate the notions and algorithm.