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H. Soner (1986)
Optimal control with state-space constraint ISiam Journal on Control and Optimization, 24
(2010)
Su di un problema di visita ottima
A. Ilchmann, H. Logemann, E. Ryan (2010)
Tracking with Prescribed Transient Performance for Hysteretic SystemsSIAM J. Control. Optim., 48
P.L. Lions (1985)
Neumann type boundary conditions for Hamilton–Jacobi equationsDuke Math. J., 52
Fabio Bagagiolo (2002)
Dynamic programming for some optimal control problems with hysteresisNonlinear Differential Equations and Applications NoDEA, 9
M. Bardi, I. Capuzzo Dolcetta (1997)
Optimal Control and Viscosity Solution of Hamilton–Jacobi–Bellman Equation
M. Day (2006)
Neumann-Type Boundary Conditions for Hamilton-Jacobi Equations in Smooth DomainsApplied Mathematics and Optimization, 53
H. Ishii (1989)
A boundary value problem of the Dirichlet type for Hamilton-Jacobi equationsAnnali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 16
Anastasia Gudovich, M. Quincampoix (2011)
Optimal Control with Hysteresis Nonlinearity and Multidimensional Play OperatorSIAM J. Control. Optim., 49
M. Crandall, L. Evans, P. Lions (1984)
Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations.Transactions of the American Mathematical Society, 282
R. Bellman (1962)
Dynamic Programming Treatment of the Travelling Salesman ProblemJ. ACM, 9
A. Visintin (1994)
Differential Models of Hysteresis
Fabio Bagagiolo (2004)
VISCOSITY SOLUTIONS FOR AN OPTIMAL CONTROL PROBLEM WITH PREISACH HYSTERESIS NONLINEARITIESESAIM: Control, Optimisation and Calculus of Variations, 10
S. Zagatti (2008)
On viscosity solutions of Hamilton-Jacobi equationsTransactions of the American Mathematical Society, 361
In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous “Traveling Salesman Problem” and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton–Jacobi equation. We introduce some “external” variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton–Jacobi equation turns out to be discontinuous
Applied Mathematics and Optimization – Springer Journals
Published: Feb 1, 2012
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