Enclosing the Sliding Surfaces of a Controlled Swing
This work addresses a specific issue in hybrid system verification, offering an incremental improvement for control systems in domains like robotics or automation.
The paper tackles the problem of unwanted chattering effects in cyber-physical systems with non-continuous controllers by proposing an interval approach to characterize sliding surfaces, demonstrating efficient outer approximation using thick sets to account for uncertainties.
When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. This may lead to some unwanted chattering effects than may damage the system. This behavior is difficult to observe even in simulation. In this paper, we propose an interval approach to characterize the sliding surface which corresponds to the set of all states such that the state trajectory may jump indefinitely between two distinct behaviors. We show that the recent notion of thick sets will allows us to compute efficiently an outer approximation of the sliding surface of a given class of hybrid system taking into account all set-membership uncertainties. An application to the verification of the controller of a child swing is considered to illustrate the principle of the approach.