Solving the Hamilton–Jacobi–Bellman equation using Adomian decomposition method

Abstract

The aim of this research is to solve the Hamilton–Jacobi–Bellman equation (HJB) arising in nonlinear optimal problem using Adomian decomposition method. First Riccati equation with matrix variable coefficients, arising in linear optimal and robust control approach, is considered. By using the Adomian method, we consider an analytical approximation of the solution of nonlinear differential Riccati equation. An application in optimal control is presented. The solution in different order of approximations and different methods of approximation will be compared with respect to accuracy. Then the HJB equation, obtained in nonlinear optimal approach, is considered and an analytical approximation of the solution of it, using Adomian method, is presented.

Keywords:

• Adomian decomposition method
• ADM
• Riccati differential equation
• optimal control
• Hamilton–Jacobi–Bellman equation
• HJB

2000 AMS Subject Classification :

• 49J15