Multiple-Segment Fourier-based Approach for Linear Quadratic Optimal Control

Document Type

Conference Proceeding



Publication Date



Institute of Electrical and Electronic Engineers (IEEE)

Source Publication

Proceedings. ICCON IEEE International Conference on Control and Applications


A Fourier-based state parameterization approach for determining the neur optimal trajectories of linear time-invariant dynamic systems with quadratic performance indices has been developed. The necessary condition of optimally is derived as a system of linear algebraic equations in terms of free boundary values and Fourier coefficients. In contrast to earlier work in which the state trajectory was represented by a single segment Fourier-type approximation, here the use of multiple segment approximations is developed. Simulation results show that the single segment Fourier-based approach' is faster than standard transition-matrix and Riccati-based approaches. The multiple segment Fourier-based approach is numerically more robust than the transition-matrix approach and computationally more efficient than Riccati-based approaches in solving linear quadratic optimal control problems. Furthermore, compared to the single segment Fourier-based approach, the multiple segment implementation improves the accuracy of the near optimal solution for highly responsive dynamic systems.


Published as a part of Proceedings. ICCON IEEE International Conference on Control and Applications (April 3-6, 1989). DOI.

Mark L. Nagurka was affiliated with Carnegie Mellon University at the time of publication.