Optimal Set-Point Regulation of Fractional Systems

This paper deals with the input-output system inversion of fractional order minimum-phase scalar linear systems. Given an arbitrarily smooth τ-parameterized output function, the corresponding τ-parameterized input is computed explicitly in order to obtain a smooth transition of the system from a steady state value to a new one in a time interval τ. The minimum time constrained transition problem is addressed. Given the predefined output function and set of constraints on the input signal and its derivatives, the existence of an optimal feasible input is proven under very mild conditions. An illustrative example shows the effectiveness of the proposed solution.