In this paper we consider a semi-Lagrangian scheme for minimum time problems with L-penalization. The minimum time function of the penalized control problem can be characterized as the solution of a Hamilton-Jacobi Bellman (HJB) equation. Furthermore, the minimum time converges with respect to the penalization parameter to the minimum time of the non-penalized problem. To solve the control prob...

We introduce a new formulation of the minimum time problem in which we employ the signed minimum time function positive outside of the target, negative in its interior and zero on its boundary. Under some standard assumptions, we prove the so called Bridge Dynamic Programming Principle (BDPP) which is a relation between the value functions defined on the complement of the target and in its inte...

We consider an Hamilton-Jacobi equation of the form H(x,Du) = 0 x ∈ Ω ⊂ R , (1) where H(x, p) is assumed Borel measurable and quasi-convex in p. The notion of Monge solution, introduced by Newcomb and Su, is adapted to this setting making use of suitable metric devices. We establish the comparison principle for Monge sub and supersolution, existence and uniqueness for equation (1) coupled with ...

In this article, a theoretical justification of one type of skew-symmetric optimal translational motion (moving in the minimal acceptable time) of a flexible object carried by a robot from its initial to its final position of absolute quiescence with the exception of the oscillations at the end of the motion is presented. The Hamilton-Ostrogradsky principle is used as a criterion for searching ...

A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with the quantum variables with the result that the value of the quasiclassical variables depends on the quantum state. This provides a formalism to...

ESPITE extensive studies on spontaneously hypertensive rats, there have been no studies on the cardiac output except a preliminary work by Albrecht et al,4) which reported a decreasing tendency of cardiac output with age. These authors employed the Stewart-Hamilton principle for the measurement of cardiac output. An attempt was made in this study to measure cardiac output in SHR by applying an ...

In this paper, we construct second-order central schemes for multidimensional Hamilton–Jacobi equations and we show that they are nonoscillatory in the sense of satisfying the maximum principle. Thus, these schemes provide the first examples of nonoscillatory second-order Godunov-type schemes based on global projection operators. Numerical experiments are performed; L1/L∞-errors and convergence...

Stochastic variational integrators for constrained, stochastic mechanical systems are developed in this paper. The main results of the paper are twofold: an equivalence is established between a stochastic Hamilton-Pontryagin (HP) principle in generalized coordinates and constrained coordinates via Lagrange multipliers, and variational partitioned Runge-Kutta (VPRK) integrators are extended to t...

The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniqu...

This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classical Routh reduction, which we show is naturally posed in this fibered setting. ...