6 citations · 20 across the 7 of their papers we have counts for
7 papers
Stable representations of Hamilton-Jacobi-Bellman equations with infinite horizon
Arkadiusz Misztela, Sławomir Plaskacz
In this paper, for the Hamilton-Jacobi-Bellman equation with an infinite horizon and state constraints, we construct a suitably regular representation. This allows us to reduce the…
Reduction of lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations
Arkadiusz Misztela
This article is devoted to the study of lower semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians in a gradient variable. Such Hamiltonians appear in the…
An initial condition reconstruction in Hamilton-Jacobi equations
Arkadiusz Misztela, Sławomir Plaskacz
We describe the family of initial conditions for Hamilton-Jacobi equations (HJE) corresponding to optimal control problems that can be retrieved by solving HJE backward in time.
Representation of Hamilton-Jacobi equation in optimal control theory with unbounded control set
Arkadiusz Misztela
In this paper we study the existence of sufficiently regular representations of Hamilton-Jacobi equations in the optimal control theory with unbounded control set. We use a new met…
Representation of Hamilton-Jacobi equation in optimal control theory with compact control set
Arkadiusz Misztela
In this paper we study the existence of sufficiently regular representations of Hamilton-Jacobi equations in optimal control theory with the compact control set. We introduce a new…
Representation of convex Hamilton-Jacobi equations in optimal control theory
Arkadiusz Misztela
In the paper we study the following problem: given a Hamilton-Jacobi equation where the Hamiltonian is convex with respect to the last variable, are there any optimal control probl…
On nouniqueness of solutions of Hamilton-Jacobi-Bellman equations
Arkadiusz Misztela
An example of a nonunique solution of the Cauchy problem of Hamilton-Jacobi-Bellman (HJB) equation with surprisingly regular Hamiltonian is presented. The Hamiltonian H(t,x,p) is l…