Time-Optimal Control of Systems with Fractional Dynamics

We introduce a formulation for the time-optimal control problems of systems displaying fractional dynamics in the sense of the Riemann-Liouville fractional derivatives operator. To propose a solution to the general time-optimal problem, a rational approximation based on the Hankel data matrix of the impulse response is considered to emulate the behavior of the fractional differentiation operator. The original problem is then reformulated according to the new model which can be solved by traditional optimal control problem solvers. The time-optimal problem is extensively investigated for a double fractional integrator and its solution is obtained using either numerical optimization or time-domain analysis.