Applications of the Generalized Bellman-Kalaba Solution Formula on Liénard′s Equation

Generalized solution of Sine-Gordon equation

In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.

Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation

In this paper we study the convergence of the Galerkin approximation method applied to the Generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control. The GHJB equation can also be used to successively approximate the Hamilton-Jacobi-Bellman ...

Evolutionary Programming as a Solution Technique for the Bellman Equation

Evolutionary programming is a stochastic optimization procedure which has proved useful in optimizing difficult functions. It is shown that evolutionary programing can be used to solve the Bellman equation problem with a high degree of accuracy and substantially less CPU time than Bellman equation iteration. Future applications will focus on sometimes binding constraints – a class of problem fo...

On Implicit Approximation of the Bellman Equation ?

In this article, an efficient algorithm for an optimal decision strategy approximation is introduced. It approximates the Bellman equation without omitting the principal uncertainty stemming from incomplete knowledge. Thus, the approximated optimal strategy retains the ability to constantly verify the current knowledge. An integral part of the proposed solution is a reduction in memory demands ...

On the solution of the generalized airfoil equation