Second order conditions for periodic optimal control problems
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 trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory.
Solution of Bellman's equation by means of a system of nonlinear singular integral equations.
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...
State estimation of linear dynamic system with unknown input and uncertain observation using dynamic programming
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.
Sufficient conditions for Lagrange, Mayer, and Bolza optimization problems.
Systèmes dynamiques et fibrations. Concept d'opt-automate