Present article provides a set-based fault tolerant control strategy for multi-sensor systems, where sensors are communicating with a controller via a shared network. Possible faults, such as abrupt sensor outages and network-induced delays, are identified as degradation modes which might affect the information provided by each sensor. Measurements that are transmitted from a sensor to the controller are characterized by a residual signal which is sensitive to the sensor's abrupt faults and network-induced delays. In order to avoid control based on information which is provided by a faulty sensor, we designed a fault detection and isolation mechanism that is implemented through a set membership evaluation. This evaluation differentiates between ``healthy'', ``faulty'' and ``delayed'' data transmission. Unequivocal fault detection and isolation are assured if the corresponding sets are disjoint. Since in general this is not the case, sets separation is enforced by a reference governor. Fault detection and isolation mechanism is design in order to transmit only measurements from sensors which are fully operational, even if potentially affected by delays. If there is a delayed information that reaches the controller, then control action is reconfigured in order to govern the plant as close as possible to the reference signal. Such control action is provided by a model-based controller with compensation block. Sufficient condition that guarantees the existence of the compensation signal is presented as well.
In this paper, we consider a multi-sensor networked control configuration with linear plant which is affected by a bounded additive disturbance. Shared network is used for the communication between sensors and controller. It is assumed that the sensors are prone to abrupt faults, while the controller’s input may be updated with a varying time-delay. In order to identify and isolate the sensor(s) providing faulty information, we
equip the controller with a set-based detection and isolation routine. Furthermore, in the case when the network induces time-delays, control is performed based on the knowledge we have on the mathematical model
of the plant. In the presence of model inaccuracies or disturbance, such a control action may not guarantee satisfying performance of the system. Therefore, a stabilising controller with delay compensation has
been designed. The functioning of the proposed control algorithm has been illustrated through an example.
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.
In this paper, an improved algorithm for actuator-fault detection and isolation (FDI) using a bank of interval observers is presented, where each interval observer matches
one considered system mode. In this approach, interval observers and invariant sets are simultaneously used for FDI. Under a collection of improved FDI conditions, this new algorithm can detect and isolate the considered actuator faults. At the end of this paper, a circuit example is used to illustrate the eectiveness of the proposed strategy.
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.
In this paper, an actuator-fault detection and isolation (FDI) approach is proposed. The FDI approach is based on a bank of interval observers, each of which is designed to match a healthy or faulty system mode. To ensure reliable FDI for all considered actuator faults, a collection of invariant set-based FDI conditions are established for the proposed technique. Under these guaranteed FDI conditions, all the considered faults can be detected and isolated during the transition induced by fault occurrences. Comparing with the existing set-based FDI approaches, the advantage of the proposed technique consists in that it combines the advantages of interval observers in the transient-state functioning and the advantages of invariant sets in the steady-state functioning. This paper is completed with the study of a continuous stirred-tank reactor (CSTR), which illustrates the effectiveness of the proposed method.
This paper addresses the coverage problem for a collection of agents and fixed obstacles (e.g., the “gallery” and the “patrolling” problems). A collection of sufficient conditions over the positions of the agents are provided such that whenever these are verified there is no “blind” region in the feasible space. These conditions are expressed by making use of hyperplane
arrangements which lead to a mixed-integer formulation. Practical applications regarding the coverage problem inside an augmented space with obstacles validate these concepts and
provide an efficient implementation (in terms of computing power).
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.
This chapter proposes a distributed approach for the resolution of a multiagent problem under collision and obstacle avoidance conditions. Using hyperplane arrangements and mixed integer programming, we provide an efficient description of the feasible region verifying the avoidance constraints. We exploit geometric properties of hyperplane arrangements and adapt this description to the distributed scheme in order to provide an efficient Model Predictive Control (MPC) solution. Furthermore,we prove constraint validation for a hierarchical ordering of the agents.
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.
In the present paper we provide a robust approach for fault tolerant control (FTC) schemes using the methodology detailed in Seron et al. , Olaru et al. . We guarantee the detection and isolation of a fault through a set-separation condition (FDI mechanism) and use this condition further in the reconfiguration control (RC) mechanism in order to stabilize the closed-loop system and respect performance criteria.
The present paper deals with fault tolerant control for linear dynamics with additive disturbances. The control action is generated based on information collected from a redundant, multi-sensors network. Delays that may appear during plant measurements transmission through real communication channels are considered as faults. Depending on presence of delay in feedback loop, dierent invariant sets can be computed. We show that fault tolerant control can be achieved through invariant sets separation with respect to dierent delay values. Sets separation is accomplished for specic values of the reference signal. Therefore, we introduce in the loop a reference governor which is designed by a receding horizon technique. Thus, we provide reference signals which practically guarantee fault detection and identication in real time.
In this study, set theoretic methods are used to design a fault-tolerant scheme for a multisensor control application. The basic principle is the separation of the invariant sets for the estimations of the state and tracking error under healthy and faulty functioning. The fault scenario assumes abrupt changes of the observation equations. The main contribution of this paper is the introduction of controlled invariant sets in the fault detection mechanism. The control action is chosen in order to guarantee the closed-loop positive invariance of a candidate region when the exogenous signals (additive disturbances, noise and reference/set-points) are bounded.
This paper is concerned with improvements in constraints handling for mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly not connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a typical control application, the control of multiagent systems using receding horizon optimization techniques, is considered.
The present paper deals with the reference tracking problem for processes with linear dynamics and multisensor information subject to abrupt sensor faults. A key point for fault tolerance will be the separation between healthy and faulty closed-loop behavior upon a set-characterization approach. This is achieved through set theoretic operations involving the healthy/faulty behavior of residual signals related to the system dynamics. As a main contribution, a reference governor scheme is designed using a receding horizon technique. It is shown that fault detection guarantees can be achieved by appropriate adjusting of the governor's delay/prediction window under mild assumptions on the fault scenario.
This paper is concerned with the improved constraints handling in mixed-integer optimization problems. The novel element is the reduction of the number of binary variables
used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly non-connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a practical implementation, the problem of obstacle avoidance using receding horizon optimization techniques is considered.
This paper addresses the problem of computing maximal robustly positively invariant sets for discrete-time linear time-invariant systems with disturbance inputs. It is assumed that the disturbance is unknown, additive, but bounded. The main contribution is the determination of bound of the number of steps in the iterative construction of the maximal invariant sets.
The last decade has seen the emergence of set-theoretic methods in fault detection and identification mechanisms. These techniques are seen as restrictive and mathematically challenging due to the strict conditions (e.g. signal boundedness) imposed for reactivity to faults by means of set separation. The present paper aims at implementing such methods to a practical application proposed by a wind turbine benchmark setup. It is shown that strict boundedness conditions can be adjusted in order to obtain robust fault detection.
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.
The current paper addresses the problem of optimizing a cost function over a non-convex and possibly non-connected feasible region. A classical approach for solving this type of optimization problem is based on Mixed integer technique. The exponential complexity as a function of the number of binary variables used in the problem formulation highlights the importance of reducing them. Previous work which minimize the number of binary variables is revisited and enhanced. Practical limitations of the procedure are discussed and a typical control application, the control of Multi-Agent Systems is exemplified.
The paper discusses the problem of lane departure avoidance for a vehicle. A corrective mechanism imposes its control action whenever the vehicle is no longer inside a nominal region centered along the middle of the lane. Set theoretic methods are used in order to design this control action and to guarantee global stability. Additionally, for the same lane departure avoidance system, a fault tolerant control mechanism is proposed in order to discard faulty sensors in a redundant measurement setting, thus guaranteeing stability even in the presence of faults.
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.
The present paper uses set theoretic methods for the design of a fault tolerant control scheme in the case of a multisensor application. The basic principle is the separation
of invariant sets for the estimations of the state and tracking error under healthy and faulty functioning. The fault scenario is based on abrupt changes of the observation equations. The main contribution is the introduction of controlled invariant sets in the fault detection mechanism. The control action is chosen so that the closed loop invariance is assured for a candidate region which accounts for the bounds on the exogenous signals (additive disturbances, noise and reference/set-points).
This paper presents a fault tolerant multisensor strategy for feedback control of a class of nonlinear systems upon a geometrical approach. A key point to ensure fault tolerance is the separation between healthy and faulty closed-loop behavior. Here we achieve this through set theoretic operations upon sets describing the healthy/faulty behavior of the system. The results rely both on an appropriate choice for the exogenous signals and on fixed point conditions for a nonlinear mapping which describes the gap between the nonlinear system and a linearized model in the functioning interval. A reference governor is employed such that, under a receding horizon technique, only feasible exogenous signals are provided to the system.
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.