Optimal Control of Nonlinear Dynamical Systems Based on a New Parallel Eigenvalue Decomposition Approach

Abstract

This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two-point boundary value problems is solved iteratively instead of solving the coupled nonlinear two-point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower-order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.