Robust Control Lyapunov Functions for Fractional Order Uncertain Lagrangian and Hamiltonian Systems.

In this presentation are shown the mathematical fundamentals to obtain robust control Lyapunov functions for fractional order uncertain Lagrangian and Hamiltonian systems. As it is known, Lagrangian and Hamiltonian mathematical representations are important to model different types of physical systems such as mechanical, electrical, chemical, biological. It is important to consider the types of uncertainties in this kind of systems, but in this case this presentation is focused in multiplicative and additive uncertainties. It is important that a complete topological analysis is performed for both kinds of uncertainties. These uncertainties are studied in the case of Lagrangian and Hamiltonian systems. Then the implementation of the design methods to obtain robust control Lyapunov functions are evinced in this presentation. The robust control Lyapunov functions are designed considering the fractional order representation of the Lagrangian and Hamiltonian systems. These study finish with two case of study, one the modeling of a fractional order electrical machine and a fractional order mechanical system, in order to obtain appropriate fractional order robust control Lyapunov functions for robust control law design. In this presentation is evinced how the modeling of different types of physical systems are modeled, so the advantages of implementing the fractional order approach has advantages over the integer order one.