A Chebyshev-Based State Representation for Linear Quadratic Optimal Control
American Society for Mechanical Engineers
Journal of Dynamic Systems, Measurement, and Control
A computationally attractive method for determining the optimal control of unconstrained linear dynamic systems with quadratic performance indices is presented. In the proposed method, the difference between each state variable and its initial condition is represented by a finite-term shifted Chebyshev series. The representation leads to a system of linear algebraic equations as the necessary condition of optimality. Simulation studies demonstrate computational advantages relative to a standard Riccati-based method, a transition matrix method, and a previous Fourier-based method.
Nagurka, Mark L. and Wang, S.-K., "A Chebyshev-Based State Representation for Linear Quadratic Optimal Control" (1993). Mechanical Engineering Faculty Research and Publications. 134.