Second-order sliding mode approaches to control and estimation for fractional order dynamics

This chapter outlines some results concerning the application of second-order sliding-mode techniques in the framework of control and estimation problems for some classes of fractional-order systems (FOS). Concerning the control problems, a second-order sliding mode control approach is developed to stabilize a class of linear uncertain multivariable fractional-order dynamics. Concerning estimation and observation problems, two main results are illustrated. A method for reconstructing in finite time an external disturbance acting on a known FOS is presented, and, as a second instance, a method for estimating the discrete state of a switched FOS is discussed. Both the schemes make use of second-order sliding mode observers. The method for discrete state reconstruction in switched FOS find useful application in the framework of fault detection, as shown in the experimental section part. Key point of all the approaches herein presented is the use of fractional-order sliding manifolds. Simple controller/observer tuning formulas are constructively developed along the paper by Lyapunov analysis. Simulation and experimental results confirm the expected performance.