Solution of infinite horizon nonlinear optimal control problems by piecewise adomian decomposition method

Abstract

In this paper, a Piecewise Adomian Decomposition Method (PADM) is used to obtain the analytical approximate solution for a class of infinite horizon nonlinear optimal control problems (OCPs). The method is a new modification of the standard ADM, in which it is treated as an algorithm in a sequence of small intervals (i.e. with small time step) for finding accurate approximate solutions to the corresponding OCPs. Applying the PADM, the nonlinear two-point boundary value problem (TPBVP), derived from the application of Pontryagin's maximum principle (PMP), is transformed into a sequence of linear time-invariant TPBVP's. Through the finite iterations of algorithm, a suboptimal control law is obtained for the nonlinear optimal control problem. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. It is remarkable accuracy properties are finally demonstrated by two examples.

Keywords

• Adomian decomposition method
• optimal control problems
• boundary value problems
• initial value problems
• Pontryagin's maximum principle
• Hamiltonian system