Fault detection and isolation using viability theory and interval observers

Abstract

This paper proposes the use of interval observers and viability theory in fault detection and isolation (FDI). Viability theory develops mathematical and algorithmic methods for investigating the viability constraints characterisation of dynamic evolutions of complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behaviour by using simple sets that approximate the exact set of possible behaviour (in the parameter or state space). In this paper, FDI is based on checking for an inconsistency between the measured and predicted behaviours using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approach.

Actuator fault tolerance evaluation approach of nonlinear model predictive control systems using viability theory

“…[21]. As discussed in the introduction, the FDI could also be implemented using viability theory as presented in [9].…”

“…The use of viability theory to fault diagnosis has already been explored by the authors [9] following similar ideas [10] but using set-invariance theory. Finding the viability theory concepts that can be used in fault tolerance evaluation is a major contribution of this paper.…”

Determining the Viability of an Unbounded Polyhedron for a Switched System

“…Te research on viability focuses on continuous evolution of a dynamic system within a constraint region, aiming to maintain the system state within the constraint region by describing the possible trajectories and trying to select appropriate control, which provides essential guarantee for the safe and continuous evolution of the system, making the study of viability theory of great importance. Viability theory has brought a new research approach to the safe evolution of dynamic systems, and it has now been applied to fshery ecosystems [2], renewable energy systems [3,4], robot control [5,6], and system fault detection [7].…”