Solution of fractional order optimal control problems using SVD-based rational approximations

This paper introduces a new direction to approximately solving fractional order optimal control problems (FOCPs). A general methodology is described that can potentially solve any type of FOCPs (linear/nonlinear, time-invariant/time-variant, SISO/MIMO, state/input constrained, free terminal conditions etc.). The method uses a rational approximation of the fractional derivative operator obtained from the singular value decomposition of the Hankel data matrix of the impulse response. The FOCP is then reformulated to be solved by RIOTS_95, a general-purpose optimal control problem (OCP) solver in the form of a MATLAB toolbox. Illustrative examples from the literature are reproduced to demonstrate the effectiveness of the propose methodology and a free final time OCP is also demonstrated.