Characterizing Sliding Surfaces of Cyber-Physical Systems

Abstract

When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution function of the closed-loop system is not anymore piecewise continuous along the trajectory, mainly due to if statements inside the control algorithm. As a consequence, an unwanted chattering effect may occur. This behavior is often difficult to observe even in simulation. We propose here a set-membership method based on interval analysis to detect different types of discontinuities. One of them is the sliding surface where the state trajectory jumps indefinitely between two distinct behaviors. As an application, we consider the validation of a sailboat controller. We show that our approach is able to detect and explain some unwanted sliding effects that may be observed in rare and specific situations on our actual sailboat robots.

Interval centred form for proving stability of non-linear discrete-time systems

“…Among those properties, stability is often wanted for a dynamical system : achieving stability around a given setpoint in the state space of the latter is one of the aims of control theory. Proving stability of a dynamical system can be done rigorously [11], which is of major importance when applied to real-life systems. Indeed, a stable system is considered safe, since its behaviour is predictable.…”