The present paper deals with the interplay between healthy and faulty sensor functioning in a multisensor scheme based on a switching control strategy. Fault tolerance guarantees have been recently obtained in this framework based upon the characterisation of invariant sets for state estimations in healthy and faulty functioning. A source of conservativeness of this approach is related to the issue of sensor recovery. A common working hypothesis has been to assume that once a sensor switches to faulty functioning it can no longer be used by the control mechanism even if at an ulterior moment it switches back to healthy functioning. In the current paper, we present necessary and sufficient conditions for the acknowledgement of sensor recovery and we propose and compare different techniques for the reintegration of sensors in the closed-loop decision-making mechanism.

The present paper proposes a switching control scheme for a plant with multiple sensor–estimator/control–actuator pairs. The scheme is shown to handle the specific stability problems originated by the switching between the different feedback loops and accommodate to faults in the measurement (sensors) channels. The main contribution is a fault tolerant switching scheme with stability guarantees assured by a pre-imposed dwell time. The detection and the fault tolerance capabilities are achieved through the separation of sets associated with suitable residual signals corresponding to healthy and faulty functioning. Another contribution of the paper resides in a recovery technique for the post-fault reintegration of the biased estimations. This technique makes use of a virtual sensor whose associated estimation, based on an optimization procedure, minimizes the recovery time.

Fault-tolerant control theory is a well-studied topic but the use of the sets in detection, isolation and/or reconfiguration is rather tangential. The authors of this book propose a systematic analysis of the set-theoretic elements and devise approaches which exploit advanced elements within the field. The main idea is to translate fault detection and isolation conditions into those conditions involving sets. Furthermore, these are to be computed efficiently using positive invariance and reachability notions. Constraints imposed by exact fault control are used to define feasible references (which impose persistent excitation and, thus, non-convex feasible sets). Particular attention is given to the reciprocal influences between fault detection and isolation on the one hand, and control reconfiguration on the other.

The scope of the thesis is the analysis and design of fault tolerant control (FTC) schemes through the use of set-theoretic methods. In the framework of multisensor schemes, the faults appearance and the modalities to accurately detect them are investigated as well as the design of control laws which assure the closed-loop stability. By using invariant/contractive sets to describe the residual signals, a fault detection and isolation (FDI) mechanism with reduced computational demands is implemented based on set-separation. A dual mechanism, implemented by a recovery block, which certificates previously fault-affected sensors is also studied. From a broader theoretical perspective, we point to the conditions which allow the inclusion of FDI objectives in the control law design. This leads to static feedback gains synthesis by means of numerically attractive optimization problems. Depending on the parameters selected for tuning, is shown that the FTC design can be completed by a reference governor or a predictive control scheme which adapts the state trajectory and the feedback control action in order to assure FDI. When necessary, the specific issues originated by the use of set-theoretic methods are detailed and various improvements are proposed towards: invariant set construction, mixed integer programming (MIP), stability for switched systems (dwell-time notions).

The present paper deals with a fault tolerant control scheme for a multisensor plant based on set theoretic methods under the assumption of bounded exogenous signals. Robust guarantees for the global stability of the system and the separability and identification of abrupt faults occurring in the sensor outputs are provided. The methodology is exemplified on a positioning system showing improved detection and isolation capabilities even for reference signals passing with oscillations around the position corresponding to faulty functioning of the sensors.

This paper deals with a multisensor scheme based on set theoretic principles, whereby different invariant sets that characterize healthy and faulty functioning of system components are computed offline. Such sets allow to partition the ensemble of sensors into ‘healthy’, ‘faulty’ and ‘under recovery’ subclasses. Fault detection and isolation consists of online setmembership verifications with low computational complexity. Sensors that are deemed healthy are utilized in the computation of the feedback control law, while sensors that are deemed ‘faulty’ or ‘under recovery’ are prevented from participating in the feedback control action. The main focus of this paper is on the reintegration of ‘under recovery’ sensors, that is to say, the transition of sensors from the ‘under recovery’ to the ‘healthy’ sensor subclass. This transition, in contrast to all other possible transitions, is particularly difficult to evaluate since it involves set membership conditions based on unmeasurable quantities. This difficulty is circumvented by resorting to necessary and sufficient conditions for the recognition of recovery, which are based exclusively upon measurable quantities. The interplay between the necessary conditions and the sufficient conditions, together with the particular system structure and fault detection mechanism, allows to obtain further important improvements in the recovery procedure in terms of transient times and sensitivity to the topology of the invariant sets.

The present paper deals with a switching control scheme for a plant with multiple estimator-controller-actuator pairs. The scheme has to deal with specific problems originated by the switching between the different feedback loops and accommodate to faults in the observation channels (sensors outputs). The main contribution is a fault tolerant switching scheme with stability guarantees assured by a pre-imposed dwell-time. The detection and the fault tolerance capabilities are assured through set separation for the residual signals corresponding to healthy and faulty functioning. Another contribution of the paper resides in a recovery technique for faulty sensors which makes use of a virtual sensor whose estimation, based on an optimization procedure, minimizes recovery time.

This article deals with fault tolerant multisensor control schemes for systems with linear dynamics. Positive invariance is a common analysis and control design tool for systems affected by bounded constraints and disturbances. This article revisits the construction of \epsilon-approximations of minimal robust positive invariant sets for linear systems upon contractive set-iterations. The cases of switching between different sets of disturbances and the inclusion of a predefined region of the state space are treated in detail. All these results are used in multisensor control schemes which have to deal with specific problems originated by the switching between different estimators and by the presence of faults in some of the sensors. The construction of positive invariant sets for different operating regimes provides, in this context, effective fault detection information. Within the same framework, global stability of the switching strategies can be assured if the invariant sets topology allows the exclusive selection of estimates obtained from healthy sensors.

The present paper deals with a multisensor scheme based on a switching control strategy. Fault tolerance guarantees were obtained in this framework lately upon the characterization of invariant sets for state estimations in healthy and faulty functioning. A source of conservativeness of this approach is related to the issue of sensor recovery. Thus, in the previous work, it was supposed that the sensors are functioning under healthy dynamics for a long enough time, in order to enter the respective invariant sets, before being considered for feedback. In the current paper we present necessary and sufficient conditions for the acknowledgement of sensor recovery and the reintegration of sensors in the closed-loop decision making mechanism.

The present paper deals with a fault tolerant control scheme for a multisensor plant under the assumption of bounded noises. A practical example, concerning a positioning system is detailed. Robust guarantees for the global stability of the system and the separability and identification of abrupt faults occurring in the sensor outputs are provided.