Hamilton-Jacobi-Bellman 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 Hamilton-Jacobi-Bellman 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 e-prints
- Pub Date:
- September 2019
- DOI:
- 10.48550/arXiv.1909.08380
- arXiv:
- arXiv:1909.08380
- Bibcode:
- 2019arXiv190908380T
- Keywords:
-
- Mathematics - Optimization and Control;
- Mathematics - Dynamical Systems
- E-Print:
- doi:10.1109/TAC.2020.3040726