# Elements of Sliding Mode Control Theory

Monday, September 14, 2015 - 11:00am - 12:00pm

Lind 305

Antonella Ferrara (Università di Pavia)

Sliding Mode Control is a nonlinear control method based on the use of a discontinuous control input which forces the controlled system to switch from one continuous structure to another, i.e. to evolve as a variable structure system. This structure variation makes the system state reach in a finite time a pre-specified subspace of the system state space, where the desired dynamical properties are assigned to the controlled system.

In the past years, an extensive literature has been devoted to the developments of Sliding Mode Control theory. This kind of methodology offers a number of benefits, the major of which is its robustness versus a significant class of uncertainties and disturbances. Yet, it presents a crucial drawback, the so-called chattering phenomenon, due to the high frequency switching of the control signal, which may disrupt or damage actuators, thus limiting its actual applicability. This drawback has been circumvented by recent theoretical developments oriented to increase the so-called order of the sliding mode, giving rise to Second Order and Higher Order Sliding Mode Control algorithms.

The three lectures based short course on Sliding Mode Control will cover the major theoretical aspects. It will start from the basic concepts (i.e. the definition and existence of a sliding mode, the solution in Filippov’s sense of the associated discontinuous differential equation, the invariance property versus matched uncertainties of the system in sliding mode), arriving to illustrate recent Higher Order Sliding Mode Control algorithms capable of solving, in a robust way, classical optimal control problems, such as the Fuller’s Problem.

In the past years, an extensive literature has been devoted to the developments of Sliding Mode Control theory. This kind of methodology offers a number of benefits, the major of which is its robustness versus a significant class of uncertainties and disturbances. Yet, it presents a crucial drawback, the so-called chattering phenomenon, due to the high frequency switching of the control signal, which may disrupt or damage actuators, thus limiting its actual applicability. This drawback has been circumvented by recent theoretical developments oriented to increase the so-called order of the sliding mode, giving rise to Second Order and Higher Order Sliding Mode Control algorithms.

The three lectures based short course on Sliding Mode Control will cover the major theoretical aspects. It will start from the basic concepts (i.e. the definition and existence of a sliding mode, the solution in Filippov’s sense of the associated discontinuous differential equation, the invariance property versus matched uncertainties of the system in sliding mode), arriving to illustrate recent Higher Order Sliding Mode Control algorithms capable of solving, in a robust way, classical optimal control problems, such as the Fuller’s Problem.

MSC Code:

93C10

Keywords: