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 adaptation to viability constraints of evolutions governed by complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behavior by using simple sets that approximate the exact set of possible behavior (in the parameter or state space). In this paper, fault detection is based on checking for an inconsistency between the measured and predicted behaviors using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approach.
Highlights
Conventional feedback control systems are vulnerable to malfunctions in sensors, actuators or other system components
The main contribution of this paper is to propose the combined use of interval observers and viability theory in Fault detection and isolation (FDI)
By computing kernels in different modes of system operation and showing their separability in offline computations, it can be guaranteed that the faults can be detected and isolated in online implementation. Another contribution of this study is to provide algorithms to find viability sets for non-linear systems that can be expressed in linear parameter varying (LPV) form
Summary
Conventional feedback control systems are vulnerable to malfunctions in sensors, actuators or other system components. Another set-theoretic FDI approach is to consider invariant sets that can overcome difficulties with interval observer approach In this approach, for each mode (healthy or faulty), an invariant set for the residual can be obtained (Olaru, De Doná, Seron, & Stoican, 2010). By computing kernels in different modes of system operation (one healthy and at least one faulty mode) and showing their separability in offline computations, it can be guaranteed that the faults can be detected and isolated in online implementation. Another contribution of this study is to provide algorithms to find viability sets for non-linear systems that can be expressed in linear parameter varying (LPV) form.
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