This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists of 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-JacobiBellman equation for the related free time optimal control problem and to characterise the value function as the unique, locally Lipschitz continuous viscosity solution.

Hamilton-Jacobi-Bellman Equation for Control Systems with Friction

Tedone, Fabio;Palladino, Michele
2021

Abstract

This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists of 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-JacobiBellman 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/176075
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