HamiltonJacobiBellman Equation for Control Systems with Friction
Abstract
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness of the solution for each given input function $u(t)$. Under general hypotheses, we are able to derive the HamiltonJacobiBellman equation for the related free time optimal control problem and to characterise the value function as the unique, locally Lipschitz continuous viscosity solution.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.08380
 Bibcode:
 2019arXiv190908380T
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  Dynamical Systems