Time-Optimal Control of Systems with Fractional Dynamics

We introduce a formulation for the time-optimal controlproblems of systems displaying fractional dynamics in the sense of theRiemann-Liouville fractional derivatives operator. To propose a solutionto the general time-optimal problem, a rational approximation based onthe Hankel data matrix of the impulse response is considered to emulatethe behavior of the fractional differentiation operator. The original problem is then reformulated according to the new model which can be solvedby traditional optimal control problem solvers. The time-optimal problem is extensively investigated for a double fractional integrator and itssolution is obtained using either numerical optimization time-domainanalysis