his paper addresses the trajectory tracking problem for a quadcopter system under nominal and fault-affected scenarios, the latter case considers stuck actuator(s)). Differential flatness is employed for trajectory generation and control design. The particularity resides in that a full parametrization of the states and inputs is given without any assumptions or simplifications on the quadcopter dynamics. Furthermore, using the properties of flatness and a combination between computed torque control and feedback linearization, a two layer control design is proposed. The tracking performances and stability gurantees are analyzed for nominal and faulty functioning under extensive simulations.
This paper deals with the problem of fault detection and isolation in water networks.We consider classification strategies for sensor placement and subsequent dictionary learning and classification for accurate fault detection and isolation. Various sensor placement strategies are proposed and it is shown that faults with varying magnitudes are correctly identified in a detailed emulation benchmark.
The paper presents a method for patch classification and remoteimage segmentation based on correlated color information. During the trainingphase, a supervised learning algorithm is considered. In the testing phase, weused the classifier built a priori to predict which class an input image samplebelongs to. The tests showed that the most relevant features are contrast, energyand homogeneity extracted from the co-occurrence matrix between H and Scomponents. Compared to gray-level, the chromatic matrices improve the processof texture classification. For experimental results, the images were acquiredby the aid of an unmanned aerial vehicle and represent various types of terrain.Two case studies have shown that the proposed method is more effective thanconsidering separate color channels: flooded area and road segmentation. Also it is shown that the new algorithm provides a faster execution time than the similar one proposed.
The sparse representations field presents a wide set of algorithms for learning overcomplete dictionaries. During the learning process many of the dictionary columns remain unused by the resulting representations. In this paper we present a few replacement strategies and their direct impact on a set of popular algorithms such as K-SVD. Experiments show significant reductions in the representation error and also evidentiate clear differences between the strategies.
This paper addresses a novel combination between mixed-integer representations and potential field constructions for typical multi-agent marine control problems. First, we prove that for any kind of repulsive functions applied over a function which we denote as sum function, the feasible domain is piece-wise affine (PWA). Next, concepts like hyperplane arrangements together with potential field approaches are used for providing an efficient description of the feasible non-convex domain. This combination offers an original and beneficent computation of control laws under non-convex constraints. Simulation results over a common application of obstacle avoidance, which can be extended for unmanned surface vehicles, prove the effectiveness of the proposed approach.
This paper considers the collision avoidance problem in a multi-agent multi-obstacle framework. The originality in solving this intensively studied problem resides in the proposed geometrical view combined with differential flatness for trajectory generation and B-splines for the flat output parametrization. Using some important properties of these theoretical tools we show that the constraints can be validated at all times. Exact and sub-optimal constructions of the collision avoidance optimization problem are provided. The results are validated through extensive simulations over standard autonomous aerial vehicle dynamics.
This paper discusses a practical implementation for photogrammetry missions in an UAV setting. Further advances, which exploit geometrical properties of the problem are considered. In particular, a bi-level optimization procedure which minimizes the total path-length is discussed. Various constraints and limitations are taken into account.
One challenging and not extensively studied issue in obstacle avoidance is the corner cutting problem. Avoidance constraints are usually imposed at the sampling time without regards to the intra-sample behavior of the dynamics. This paper improves upon state of the art by describing a multi-obstacle environment via a hyperplane arrangement, provides a piecewise description of the forbidden regions and represents them into a combined mixed integer and predictive control formulation. Furthermore, over-approximation constraints which reduce to strictly binary conditions are discussed in detail. Illustrative proofs of concept, comparisons
with the state of the art and simulation results over a classical multi-obstacle avoidance problem validate the benets of the proposed approach.
This paper addresses the microgrid energy management problem within a coherent framework of control tools based on Mixed-Integer Linear Programming (MILP) and constrained Model Predictive Control (MPC). These help characterize the microgrid components’ dynamics and the overall system control architecture. A fault tolerant strategy is considered in order to ensure the proper amount of energy in the storage devices such that (together with the utility grid) the essential consumer demand is reliably covered. Simulation results on a particular microgrid architecture validate the proposed approach.
This paper addresses some alternatives to classical trajectory generation for an autonomous vehicle which needs to pass through a priori given way-points. Using differential flatness for trajectory generation and B-splines for the flat output parametrization, the current study concentrates on constraint relaxations and on obstacle avoidance conditions. The results are validated through simulations over standard UAV dynamics.
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.
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, 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.
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 we revisit the explicit MPC representation and related notions. We point to the special structure of the constraint matrices and exploit it in order to provide novel results. We give an upper bound for the collection of admissible active sets with use in the mixed integer representation of the KKT problem and a partial recursive description of the explicit partitioning of the MPC problem. The results are tested over illustrative examples.
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 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.
A formulation of Persistently Exciting Model Predictive Control (PE-MPC) for Single-Input Single-Output (SISO) systems is presented. PE-MPC is an extension of a conventional model predictive control where a Persistence of Excitation Condition (PEC) is included as inequality constraint, to allow for adaptive implementation and on-line tuning of the model. The PEC makes the PE-MPC feasible region non-convex. For SISO systems the non-convex region can be represented as the union of two convex regions. Therefore an ad-hoc solution of the PE-MPC optimization problem can be eciently computed. This is done by exploiting the particular structure of the PEC constraint. Finally a numerical example of SISO sytem is given and several scenarios are simulated to analyze the PE-MPC properties.
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.
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 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.
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.
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.
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 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.
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 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 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 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.
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.