A Modified Iterative Method for Solving the Hamilton-Jacobi-Bellman Equation Hartono
Department of Mathematics, Sanata Dharma University
Kampus III Paingan, Maguwoharjo, Depok, Sleman, Yogyakarta
yghartono[at]usd.ac.id
Abstract
In the field of optimal control, the Hamilton-Jacobi-Bellman equation specifies both the necessary and sufficient condition for finding optimal control with respect to the intended objective function. The equation is a nonlinear partial differential equation which is generally intractable to be solved analytically. Hence, in order to obtain the solution of some optimal control problem formulated in the Hamilton-Jacobi-Bellman equation, it is necessary to develop some reliable and efficient numerical method.
In this article, we propose a modified version of our iterative method, previously published in a journal, to solve the state- constrained Hamilton-Jacobi-Bellman equation. The modification is made on the way to update the value function of the objective function. In this new scheme, instead of updating the value function on each point on the domain, we select only some points neighboring a nominee of the optimal path making up the solution of the optimal control problem. Therefore, comparing to the old scheme, the computation results not only a reliable solution but it is also much faster and efficient.
Keywords: optimal control problem, Hamilton-Jacobi-Bellman equation, iterative method
