Nonlinear Periodic Optimal Control: A Pseudospectral Fourier Approach

Abstract A pseudospectral method for generating optimal trajectories of the class of periodic optimal control problems is proposed. The method consists of representing the solution of the periodic optimal control problem by an mth degree trigonometric interpolating polynomial, using Fourier nodes as grid points, and then discretizing the problem using the trapezoidal rule as the quadrature formula for smoothly differentiable periodic functions. The periodic optimal control problem is thereby transformed into an algebraic nonlinear programming problem. Due to its dynamic nature, the pseudospectral Fourier approach avoids many of the numerical difficulties typically encountered in solving standard periodic optimal control problems. An illustrative example is provided to demonstrate the applicability of the proposed method.

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