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This paper presents a novel extended modal series method for solving the infinite horizon optimal control problem of nonlinear interconnected largescale dynamic systems. In this method, the infinite horizon nonlinear largescale two-point boundary value problem (TPBVP), derived from Pontryagin's maximum principle, is transformed into a sequence of linear time-invariant TPBVPs. Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of a uniformly convergent series. Moreover, in special cases, the proposed procedure facilitates the application of parallel processing, which improves its computational efficiency. In this study, an iterative algorithm is also presented, which has a low computational complexity and a fast convergence rate. Just a few iterations are required to obtain a suboptimal trajectory-control pair. Finally, effectiveness of the proposed approach is verified by solving the optimal attitude control problem.

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In this work, the variational iteration method (VIM) is used to solve a class of fractional optimal control problems (FOCPs). New Lagrange multipliers are determined and some new iterative formulas are presented. The fractional derivative (FD) in these problems is in the Caputo sense. The necessary optimality conditions are achieved for FOCPs in terms of associated Euler–Lagrange equations and then the VIM is used to solve the resulting fractional differential equations. This technique rapidly provides the convergent successive approximations of the exact solution and the solutions approach the classical solutions of the problem as the order of the FDs approaches 1. To achieve the solution of the FOCPs using VIM, four illustrative examples are included to demonstrate the validity and applicability of the proposed method.

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