The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to action up second order. We specialize our results case of traceless and transverse fluctuations, we discuss how intrinsic properties matter stress tensor can affect (and modify) process gravity wave propagation even most co...

This paper focuses on zero-sum stochastic differential games in the framework of forward-backward equations a finite time horizon with both players adopting impulse controls. By means BSDE methods, particular that notion from Peng’s backward semigroups, authors prove dynamic programming principle for upper and lower value functions game. The are then shown to be unique viscosity solutions Hamil...

One of recent achievements in the field of nonlinear H∞ optimal control theories for Euler-Lagrange systems is the analytic solution to the Hamilton-JacobiIsaccs (HJI) equation associated to the so-called nonlinear H∞ inverse-optimal control [1]. In this paper, we address the problem of nonlinear H∞ optimal control design for an Euler-Lagrange system, rather than the inverse-optimal problem. By...

We generalize the analysis of Ball, Day and Kachroo [2] to a fluid model of a single server re-entrant queue. The approach is to solve the Hamilton-Jacobi-Isaacs equation associated with optimal robust control of the system. The method of “staged” characteristics is generalized from [2] to construct the solution explicitly. Formulas are developed allowing explicit calculations for the Skorokhod...

We show that input-to-state stabilizability (as defined by Sontag) is both necessary and sufficient for the solvability of a Hamilton–Jacobi–Isaacs equation associated with a meaningful differential game problem similar to, but more general than, the “nonlinear H1” problem. The significance of the result stems from the fact that constructive solutions to the input-tostate stabilization problem ...

We present new thirdand fifth-order Godunov-type central schemes for approximating solutions of the Hamilton–Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme ...

to the Nonlinear Benchmark Problem Panagiotis Tsiotras Dept. of Mechanical, Aerospace and Nuclear Engineering University of Virginia Charlottesville, VA 22903-2442 Martin Corless and Mario A. Rotea School of Aeronautics and Astronautics Purdue University West Lafayette, IN 47907-1282 Abstract In this paper, we use the theory of L2 disturbance attenuation for linear (H1) and nonlinear systems to...

This paper studies the optimum stochastic control problem with piecewise deterministic dynamics. The controls enter through the system dynamics as well as the transitions for the underlying Markov chain process, and are allowed to depend on both the continuous state and the current state of the Markov chain. The paper shows that the feedback optimal control relies on the viscosity solutions of ...

Abstract. In this paper, we consider a numerical scheme to solve first order Hamilton-Jacobi (HJ) equations posed on a junction. The main mathematical properties of the scheme are first recalled and then we give a traffic flow interpretation of the key elements. The scheme formulation is also adapted to compute the vehicles densities on a junction. The equivalent scheme for densities recovers t...

The goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi-domains. We consider an optimal control problem in which the controlled system contains a fast and a slow variables. This problem is reformulated as an Hamilton-JacobiBellman (HJB) equation. The main difficulty comes from the fact that the fast variable lives in a multi-domain. The ge...