Error estimates for numerical approximation of Hamilton-Jacobi equations related to hybrid control systems

Roberto Ferretti, Achille Sassi and Hasnaa Zidani
submitted
Publication type:
Paper in peer-reviewed journals
Keywords :
Semi-Lagrangian schemes; Error estimates; Dynamic Programming; Hybrid control;
Abstract:
Hybrid control systems are dynamical systems that can be controlled by a combination of both continuous and discrete actions. In this paper we study the approximation of optimal control problems associated to this kind of systems, and in particular of the Quasi-Variational Inequality which characterizes the value function. Our main result features the error estimates between the value function of the problem and its approximation. We also focus on the hypotheses describing the mathematical model and the properties defining the class of numerical scheme for which the result holds true.
BibTeX:
@article{Fer-Sas-Zid-2200,
    author={Roberto Ferretti and Achille Sassi and Hasnaa Zidani },
    title={Error estimates for numerical approximation of Hamilton-Jacobi 
           equations related to hybrid control systems },
    year={submitted },
}