Value-added Simulation of Hybrid Systems

Analytical investigations of real-world, hybrid dynamical systems are technically challenging. Consequently, simulation plays a vital role in their analysis. Simulation typically addresses forward problems though, offering limited insights into parametric influences. The paper addresses this issue, presenting computationally efficient algorithms that extend the capabilities of simulation. The starting point is a model that captures the intricacies of hybrid systems, yet is suited to numerical integration. It will be shown that trajectory sensitivities are well defined for hybrid systems, and can be computed efficiently. These sensitivities allow the mapping of parameter uncertainty into approximate error bounds on nominal (piecewise smooth) trajectories. Furthermore, they provide gradient information that facilitates the solution of inverse problems. A range of problems will be considered, including shooting methods for locating (possibly non-smooth) limit cycles and grazing phenomena, and optimization algorithms for parameter estimation and controller tuning. Keywords— Hybrid dynamical systems, inverse problems, parameter uncertainty, shooting methods, trajectory sensitivities.