In this paper we develop a new method to approximate the solution to the Hamilton-JacobiBellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial di erential equations. These equations are then approximated ...

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies high-dimensional problems often rely on specific, restrictive problem structures, or valid only locally around some nominal trajectory. In this paper, we propose a data-driven method t...

This note is concerned with nonlinear stochastic minimax dynamic games which are subject to noisy measurements. The minimizing players are control inputs while the maximizing players are square-integrable stochastic processes. The minimax dynamic game is formulated using an information state, which depends on the paths of the observed processes. The information state satisfies a partial differe...

Abstract. In this paper, we value hydroelectric power plant cash flows under a stochastic control framework, taking into consideration the implication of operational constraints such as ramping and minimum flow rate constraints for the purpose of environmental protection. The power plant valuation problem under a ramping constraint is characterized as a bounded stochastic control problem, resul...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

In this paper, the piecewise homotopy perturbation method (PHPM) is employed to solve the Hamilton– Jacobi–Bellman (HJB) equation arising in the optimal control problems. The method is a simple modification of the standard homotopy perturbation method (HPM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the...

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...