in this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. this controller is derived based on the closed form solution of the hamilton-jacobi-bellman (hjb) equation associated with the cheap control problem. this methodology employs an algebraic equation with parametric coefficients for the systems with s...

The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A formal perturbative solution of th...

We propose a Hamilton-Jacobi equation approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton-Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins’ and Reeds-Shepp’s cars, and gives further generalizations. We show that the value function of the control problem so...

We develop Hamilton–Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a geometric account of the Hamiltonization, identify necessary and sufficient conditions for Hamiltonization, and apply the conventional Hamilton–Jacobi theor...

We consider the single-leg airline revenue management problem in continuous time with Poisson arrivals. Earlier work on this problem generally uses the Hamilton-Jacobi-Bellman equation to find an optimal policy whenever the value function is differentiable and is a solution to this equation. In this paper, we employ a different probabilistic approach, which do not rely on the smoothness of the ...

A canonical problem in real option pricing, as described in the classic text of Dixit and Pindyck [2], is to determine the optimal time to invest at a fixed cost, to receive in return a stochastic cashflow. In this paper we are interested in this problem in an incomplete market where the cashflow is not spanned by the traded assets. We follow the formulation in Miao and Wang [21]; our contribut...

This document is a brief overview of the Hamilton-Jacobi theory of Chaplygin systems based on [1]. In this paper, after reducing Chaplygin systems, Ohsawa et al. use a technique that they call Chaplygin Hamiltonization to turn the reduced Chaplygin systems into Hamiltonian systems. This method was first introduced in a paper by Chaplygin in 1911 where he reduced some nonholonomic systems by the...

This paper treats the problem of consumption and portfolio choice in continuous time, with stochastic income that cannot be replicated by trading the available securities. The optimal controls and value functions are characterized in terms of the viscosity solution of the associated Hamilton-JacobiBellman equation, which is shown to exist and is characterized. The optimal policy is then given f...

In general, the value function associated with an exit time problem is a discontin-uous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton-Jacobi equation involving the proximal subdiierentials (superdiierentials) with subdiierential type (superdiierential type) mixed boundary condition. We also show that if t...

In general, the value function associated with an exit time problem is a discontinuous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton–Jacobi equation involving the proximal subdifferentials (superdifferentials) with subdifferential-type (superdifferential-type) mixed boundary condition. We also show that i...