Rw. Beard et al., APPROXIMATE SOLUTIONS TO THE TIME-INVARIANT HAMILTON-JACOBI-BELLMAN EQUATION, Journal of optimization theory and applications, 96(3), 1998, pp. 589-626
Citations number
71
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science
In this paper, we develop a new method to approximate the solution to
the Hamilton-Jacobi-Bellman (HJB) equation which arises in optimal con
trol when the plant is modeled by nonlinear dynamics. The approximatio
n is comprised of two steps. First, successive approximation is used t
o reduce the HJB equation to a sequence of linear partial differential
equations. These equations are then approximated via the Galerkin spe
ctral method. The resulting algorithm has several important advantages
over previously reported methods. Namely, the resulting control is in
feedback form and its associated region of attraction is well defined
. In addition, all computations are performed off-line and the control
can be made arbitrarily close to optimal. Accordingly, this paper pre
sents a new tool for designing nonlinear control systems that adhere t
o a prescribed integral performance criterion.