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This article focuses on the design of online optimal input sequence for robust active fault diagnosis of discrete-time linear parameter-varying systems using set-theoretic methods. Instead of the traditional set-separation constraint conditions leading to the design of offline input sequence, the proposed approach focuses on online (re)shaping of the input sequence based on the real-time information of the output to discriminate system modes at each time instant such that the diagnosability of system has potential to be further improved. The criterion on the design of optimal input is characterized based on a nonconvex fractional programming problem at each time instant, which is shown to be efficiently solved within a convex optimization framework. In addition to this main contribution, by exploiting Lagrange duality, the optimal input is explicitly obtained by solving a characteristic equation. At the end, a physical circuit model is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel fault tolerant multi-sensor switching control framework for linear parameter-varying systems considering multiplicative and additive sensor faults simultaneously. We show that the closed-loop stability is preserved under sensor fault situation if established guaranteed fault detection conditions based on invariant sets are fulfilled. At each time instant, the switching control strategy selects the sensor group that provides the optimal closed-loop performance, which is characterized by a quadratic performance objective function. Furthermore, faults on each channel of all group of sensors can be also pre-guaranteed to be isolated under the fulfillment of established fault isolation conditions, which ensures a more precise determination of the location of fault occurrence. At the end, a practical vehicle model is provided to illustrate the effectiveness of the proposed method.

This paper proposes a mixed active/passive robust fault detection and isolation (FDI) method for discrete-time linear paramter varying (LPV) systems based on set-theoretic unknown input observers (SUIO) and invariant sets. The robustness against system uncertainties in FDI of LPV systems can be guaranteed by actively decoupling or passively bounding their effect on residual signal. Furthermore, the quadratic H∞stability condition of the LPV-form state-estimation-error dynamics is established based on a group of linear matrix inequalities (LMIs). Under the precondition of stability, a family of residual sets are constructed to establish set-separation guaranteed fault isolation (FI) conditions using invariant sets off-line. As long as the occurred faults satisfy the guaranteed FI conditions, they can be isolated from each other. At the end, a numerical example is used to illustrate the effectiveness of the proposed method.

This paper proposes a generalized minimum detectable fault(MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discrete-time linear parameter varying(LPV) systems with bounded inputs and uncertainties. First, we equivalently transform the multiple multiplicative actuator faults into the form of multiple additive actuator faults, which is beneficial to simplify the problem. Then, by considering the 1-norm of the fault vector, we define the generalized MDF in the case of multiple additive actuator faults, which can be computed via solving a simple linear programming(LP) problem. Moreover, an analysis of the effect of the input vector on the magnitude of the generalized MDF is made. Since the proposed generalized MDF computation method is robust by considering the bounds of inputs and uncertainties, robust fault detection(FD) can be guaranteed whenever the sum of the magnitudes of all occurred faults is larger than the magnitude of the generalized MDF. At the end of this paper, a numerical example is used to illustrate the effectiveness of the proposed method.

This paper proposes a novel robust fault detection (FD) approach and designs a set-theoretic unknown input observer (SUIO) for linear parameter-varying (LPV) systems with both state and output equations scheduled by inexact scheduling variables. First, for such LPV systems, we propose a novel robust FD method by combing the set theory with the unknown input observer, which considers the bounds of measurement errors of scheduling variables to generate FD-oriented sets. In general, as long as sensors with sufficiently high precision are equipped to measure the scheduling variables, the bounds of measurement errors of scheduling variables can be less conservative than those direct bounds of scheduling variables, which can reduce robust FD conservatism in this way. Second, we give the unknown input decoupling condition of SUIO for such LPV systems and propose an SUIO design method under this condition for robust state estimation (SE). Besides, stability conditions for the proposed methods are established via matrix inequalities. At the end of this paper, a case study is used to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel tube-based robust fault estimation (FE) method for dynamic systems by decoupling unknown inputs and using set-membership approach. FE problems are considered in a novel prospective in this paper. Instead of estimating a specific fault value like most of FE methods, in order to guarantee the FE robustness, we compute a fault tube to contain the real fault at each time instant under an assumption that the system uncertainties (i.e., modeling errors, process disturbances and measurement noises) are bounded. Theoretically, any trajectory in the fault tube can be used as an estimation of the real fault. The size of the tube indicates the performance of FE. That is, the smaller the tube is, the better the obtained FE results are. At the end of this paper, a numerical example is used to show the effectiveness of the proposed robust FE approach.

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