Sliding Mode Control: theoretical developments and applications to uncertain mechanical systems.

The control of dynamical systems in presence of uncertainties and disturbances is a common problem to deal with when considering real plants. The effect of these uncertainties on the system dynamics should be carefully taken into account in the controller design phase since they can worsen the performance or even cause system instability. For this reason, during recent years, the problem of controlling dynamical systems in presence of heavy uncertainty conditions has become an important subject of research. As a result, considerable progresses have been attained in robust control techniques, such as nonlinear adaptive control, model predictive control, backstepping, sliding model control and others.
These techniques are capable of guaranteeing the attainment of the control objectives in spite of modelling errors and/or parameter uncertainties affecting the controlled plant.
Among the existing methodologies, the Sliding Mode Control (SMC) technique turns out to be characterized by high simplicity and robustness.
Essentially, SMC utilizes discontinuous control laws to drive the system state trajectory onto a specied surface in the state space, the socalled sliding or switching surface, and to keep the system state on this manifold for all the subsequent times.
In order to achieve the control objective, the control input must be designed with an authority sucient to overcome the uncertainties and the disturbances acting on the system. The main advantages of this approach are two: rst, while the system is on the sliding manifold it behaves as a reduced order system with respect to the original plant; and, second, the dynamic of the system while in sliding mode is insensitive to model uncertainties and disturbances.
However, in spite of the claimed robustness properties, the reallife implementation of SMC techniques presents a major drawback: the socalled chattering eect, i.e., dangerous highfrequency vibrations of the controlled system. This phenomenon is due to the fact that, in reallife applications, it is not reasonable to assume that the control signal can switch at innite frequency. On the contrary, it is more realistic, due to the inertias of the actuators and sensors and to the presence of noise and/or exogenous disturbances, to assume that it switches at a very high (but nite) frequency.
Chattering and the need for discontinuous control constitute two of the main criticisms to sliding modes control techniques, and these drawbacks are much more evident when dealing with mechanical systems, since rapidly changing control actions induce stress and wear in mechanical parts and the system could be damaged in a short time.
This work analyzes a quite recent development of sliding mode control, namely the second order sliding mode approach, which is encountering a growing attention in the control research community. Second order sliding mode techniques produce continuous control laws while keeping the same advantages of the original approach, and provide for even higher accuracy in realization.
The objective of this thesis is to survey the theoretical background of sliding mode control, in particular higher order sliding mode control, to show that the second order sliding mode approach is an eective solution to the abovecited drawbacks and to develop some original contribution to the theory and application of sliding mode control. Moreover, some important control problems involving uncertain mechanical systems are addressed and solved by means of the sliding mode control methodology in this thesis. In particular, the sliding mode control methodology will be applied to three different context: Automotive control; Control of nonholonomic systems; Multiagent systems. Apart from the robustness features against dierent kind of uncertainties and disturbances, the proposed control schemes have the advantage of producing low complexity control laws compared to other robust control approaches (H1, LMI, adaptive control, etc.) which appears particularly suitable in the considered contexts.