In this paper, a fault detection and isolation (FDI) approach using a bank of interval observers is developed. From the methodological point of view, a bank of interval
observers is designed according to different dynamical models of the system under different modes (healthy or faulty). Each interval observer matches one system mode while all the interval observers monitor the system simultaneously. In order to guarantee FDI, a set of FDI conditions based on invariant set notions are established. These conditions ensure that the considered faults can be accurately isolated after a period of monitoring time. Finally, simulation results are used to present the effectiveness of the approach.
The current paper addresses the problem of minimizing the computational complexity of optimization problems with non-convex and possibly non-connected feasible region of polyhedral type. Using hyperplane arrangements and Mixed-Integer Programming we provide an efficient description of the feasible region in the solution space. Moreover, we exploit the geometric properties of the hyperplane arrangements and adapt this description in order to provide an efficient solution of the mixed-integer optimization problem. Furthermore, a zonotopic representation of the sets appearing in the problem is considered. The advantages of this representation are highlighted and exploited through proof of concepts illustrations as well as simulation results.
In this paper we provide a RPI over-approximation of the mRPI set associated for linear dynamics with zonotopic disturbances.We prove that the RPI construction converges toward the mRPI set and its conservatism diminishes monotonically with respect to the complexity of the representation (a “tightness” coefficient is calculated a priori). The results are tested in illustrative examples.
In this paper, an actuator-fault detection and isolation (FDI) approach using interval observers is proposed. An interval observer designed according to the healthy model of the supervised system is used to monitor the system. When the system is under different modes, state or output interval vectors predicted by the interval observer manifest different dynamical behaviors, which is the basis for FDI. To guarantee FDI, a group of set-based sufficient conditions based on invariant sets are established. Under these conditions, actuator faults can be accurately detected and isolated during the transition between different system modes. Finally, a numerical example is used to present the effectiveness of the proposed approach.
In this paper, the relationship between two set-based fault detection (FD) approaches, the interval observer-based and the invariant set-based approaches, is investigated. In FD, an interval observer has been shown to be suitable to generate adaptive thresholds for residuals, which can monitor the system behavior in real time. Invariant sets focus more on the steady state behavior of the system rather than on the transient behavior. This paper discusses these two approaches, presents a relationship between them and compares them in the FD task. At the end, simulation examples are used to compare and discuss these two approaches.
This paper proposes an interval observer-based sensor fault detection and isolation (FDI) approach for closed-loop systems. In the proposed approach, residuals are defined in such a way that their components are independent of each other at the time instant after fault occurrence, namely kf +1, where kf denotes the fault occurrence time instant. In this way, it is guaranteed that at kf +1 the changes in each component of the residuals are only related to the fault in the corresponding sensor. By detecting the threshold violation of the corresponding residual interval components, the proposed approach can detect and isolate sensor faults at the same time instant. At the end of this paper, a numerical example is used to present the effectiveness of the proposed approach.
In this paper we analyze the advantages of describing the constraint set of a constrained optimization problem by an (inner-approximating) zonotope. We compare this with the usual polytopic description and note that by using the generator description characterizing zonotopes we can exploit their special structure in order to obtain a simpler
formulation of the optimization problem. We test the results on a typical MPC setting and observe the improvements.
This paper deals with robust invariant sets construction for discrete-time linear timeinvariant dynamics. The case of a zonotopic disturbance set is analysed in detail by exploiting the properties of these geometrical structures. A constructive method is provided for diminishing the conservatism of ultimate bound invariant sets. It is shown that the resulting zonotopic set is related to the minimal robust positively invariant set in the sense that their boundaries have common points.