Fourier-based state parameterization for linear quadratic optimal control

This paper considers the optimal control of linear time-invariant dynamical systems with quadratic performance indices. The proposed approach approximates each state variable of a state-space model by the sum of a third order polynomial and a finite term Fourier-type series. In contrast to standard linear optimal control approaches which typically require the solution of Riccati equations, the method adopted is a near optimal approach in which the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. These equations can be solved directly by a method such as Gaussian elimination, making the approach computationally efficient.