Second order conditions for periodic optimal control problems
Second order unbounded parabolic equations in separated form
We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of first order...
Second-order elliptic integro-differential equations : viscosity solutions' theory revisited
Semigeodesics and the minimal time function
We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.
Semigeodesics and the minimal time function
We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.
Shape optimization of control problems described by wave equations
Singular dynamics for semiconcave functions
Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory.
Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations.
Solution of Bellman's equation by means of a system of nonlinear singular integral equations.
Solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications
Solutions de viscosité des equations de Hamilton-Jacobi en dimension infinie. Cas stationnaire.
We show the uniqueness and the existence of viscosity solutions of Hamilton-Jacobi equations on a smooth Banach space. The tool used is the variational principle of Deville, Godefroy and Zizler. The existence is given by Perron’s method. So we give a comparison assertion for semicontinuous solutions.
Solutions d'équations d'Hamilton-Jacobi et géométrie symplectique
Solutions of semi-Markov control models with recursive discount rates and approximation by -optimal policies
This paper studies a class of discrete-time discounted semi-Markov control model on Borel spaces. We assume possibly unbounded costs and a non-stationary exponential form in the discount factor which depends of on a rate, called the discount rate. Given an initial discount rate the evolution in next steps depends on both the previous discount rate and the sojourn time of the system at the current state. The new results provided here are the existence and the approximation of optimal policies for...
Soluzioni di viscosità
This is the expanded text of a lecture about viscosity solutions of degenerate elliptic equations delivered at the XVI Congresso UMI. The aim of the paper is to review some fundamental results of the theory as developed in the last twenty years and to point out some of its recent developments and applications.
Some results for an optimal control problem with a semilinear state equation
We consider a quadratic control problem with a semilinear state equation depending on a small parameter . We show that the optimal control is a regular function of such parameter.
State estimation of linear dynamic system with unknown input and uncertain observation using dynamic programming
State space synthesis of discrete linear systems
Stochastic differential games involving impulse controls
A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.
Stochastic differential games involving impulse controls*
A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.