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arXiv · 1909.08380

Hamilton-Jacobi-Bellman Equation for Control Systems with Friction

Fabio Tedone·Michele Palladino
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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.

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Fabio Tedone, Michele Palladino. 2019-09-18. Hamilton-Jacobi-Bellman Equation for Control Systems with Friction. https://doi.org/10.1109/tac.2020.3040726

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