Active Fault Isolation: A Duality-Based Approach via Convex Programming

Abstract

Abstract. This paper presents the mathematical conditions and the associated design methodology of an active fault diagnosis technique for continuous-time linear systems. Given a set of faults known a priori, the system is modeled by a finite family of linear time-invariant systems, accounting for one healthy and several faulty configurations. By assuming bounded disturbances and using a residual generator, an invariant set and its projection in the residual space (i.e., its limit set) are computed for each system configuration. Each limit set, related to a single system configuration, is parameterized with respect to the system input. Thanks to this design, active fault isolation can be guaranteed by the computation of a test input, either constant or periodic, such that the limit sets associated with different system configurations are separated, and the residual converges towards one limit set only. In order to alleviate the complexity of the explicit computation of the limit set, an implicit dual representation is adopted, leading to efficient procedures, based on quadratic programming, for computing the test input. The developed methodology offers a competent continuous-time solution to the optimization-based computation of the test input via Hahn-Banach duality. Simulation examples illustrate the application of the proposed active fault diagnosis methods and its efficiency in providing a solution, even in relatively large state-dimensional problems.

Fault Isolation for Large Scale Discrete-Time Systems Based on Implicit Set Representation

“…To distinguish multiple fault pairs, we can seek a signal that concurrently separates all the limit sets, or we can first inject a signal that separates the first pair, then switch to a different signal. As a further extension, we could consider the discrete-time counterpart of the periodic excitation signals discussed in [4]. Our approach allows us to decide off-line which are the best signals to adopt, while the on-line decision is simply made by checking if the residual is to the left or to the right of the separating hyperplanes (which requires a negligible computational effort).…”

“…Given a set of pre-defined fault scenarios, the scalability advantages of the procedure make it suitable for large-scale dynamical systems (such as networked systems with a large number of components). Results for continuous-time FDI design [4] have recently shown that the fault isolation problem can be solved for continuous-time linear systems based on the Hahn-Banach theorem and a duality approach; the present results, conversely, specifically deal with discrete-time systems.…”

Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems

“…In this section, we propose two solutions to the problems of mode detection for a causal and a switched non-causal descriptor systems based on the characterization of RPI sets. In many critical infrastructures and cyber-physical systems, a fault can be interpreted as a change in the mode of operation [13]. Therefore, active mode detection can be seen an important step towards fault-tolerant control.…”

Set-invariance characterizations of discrete-time descriptor systems with application to active mode detection

“…control strategies, such as fault detection and isolation (Blanchini, Casagrande, Giordano, Miani, Olaru, & Reppa, 2017;Xu, Puig, Ocampo-Martinez, Stoican, & Olaru, 2014), fault-tolerant control (Olaru et al, 2010;Seron, De Doná, & Olaru, 2012;Stoican & Olaru, 2013) and robust model predictive control (Mayne, Seron, & Raković, 2005). A remarkable application of RI sets is on mode detection of systems subject to multiple modes of operation.…”