Hamilton–Jacobi–Bellman Equation for Control Systems With Friction
- 25 November 2020
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 66 (12), 5651-5664
- https://doi.org/10.1109/tac.2020.3040726
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-Jacobi-Bellman equation for the related free time optimal control problem and to characterise the value function as the unique, locally Lipschitz continuous viscosity solutionKeywords
This publication has 38 references indexed in Scilit:
- Extensions of Clarke's proximal characterization for reachable mappings of differential inclusionsJournal of Mathematical Analysis and Applications, 2008
- Strong invariance and one-sided Lipschitz multifunctionsNonlinear Analysis, 2005
- Sweeping process with regular and nonregular setsJournal of Differential Equations, 2003
- Parametrized Integral of Multifunctions in Banach SpacesJournal of Mathematical Analysis and Applications, 1999
- Numerical aspects of the sweeping processComputer Methods in Applied Mechanics and Engineering, 1999
- Hamilton–Jacobi theory for a generalized optimal stopping time problemNonlinear Analysis, 1998
- Measurable Viability Theorems and the Hamilton-Jacobi-Bellman EquationJournal of Differential Equations, 1995
- Parametrized Integration of Multifunctions with Applications to Control and OptimizationSIAM Journal on Control and Optimization, 1989
- Evolution problem associated with a moving convex set in a Hilbert spaceJournal of Differential Equations, 1977
- Integrals of set-valued functionsJournal of Mathematical Analysis and Applications, 1965