The Maximal Positively Invariant Set: Polynomial Setting

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating that the related preimage map preserves basic semialgebraic structure. In fact, this property propagates to underlying set--dynamics induced by the associated restricted preimage map in general and to its maximal trajectory in particular. The finite time convergence of the corresponding maximal trajectory to the maximal positively invariant set is verified under reasonably mild conditions. The analysis is complemented with a discussion of computational aspects and a prototype implementation based on existing toolboxes for polynomial optimization

Sensor-fault tolerance using robust MPC with set-based state estimation and active fault isolation

In this paper, a sensor fault-tolerant control (FTC) scheme using robust model predictive control (MPC) and set theoretic fault detection and isolation (FDI) is proposed. The MPC controller is used to both robustly control the plant and actively guarantee fault isolation (FI). In this scheme, fault detection (FD) is passive by interval observers, while fault isolation (FI) is active by MPC. The advantage of the proposed approach consists in using MPC to actively decouple the effect of sensor faults on the outputs such that one output component only corresponds to one sensor fault in terms of FI, which can utilize the feature of sensor faults for FI. A numerical example is used to illustrate the effectiveness of the proposed scheme.Postprint (author’s final draft

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

In this paper, an actuator fault-tolerant control (FTC) scheme is proposed, which is based on tube-based model predictive control (MPC) and set-theoretic fault detection and isolation (FDI). As a robust MPC technique, tube-based MPC, can effectively deal with system constraints and uncertainties with relatively low computational complexity. Set-based FDI can robustly detect and isolate actuator faults. Here, fault detection (FD) is passive by invariant sets, while fault isolation (FI) is active by tubes. Using the constraint-handling ability of MPC controllers, an active FI approach is implemented. A numerical example illustrates the effectiveness of the proposed approach.Postprint (author’s final draft

Robust Fault Diagnosis by Optimal Input Design for Self-sensing Systems

This paper presents a methodology for model based robust fault diagnosis and a methodology for input design to obtain optimal diagnosis of faults. The proposed algorithm is suitable for real time implementation. Issues of robustness are addressed for the input design and fault diagnosis methodologies. The proposed technique allows robust fault diagnosis under suitable conditions on the system uncertainty. The designed input and fault diagnosis techniques are illustrated by numerical simulation.Comment: Accepted in IFAC World Congress 201

Distributed zonotopic set-membership state estimation based on optimization methods with partial projection

A distributed set-membership approach is proposed for the state estimation of large-scale systems. The uncertain system states are bounded in a sequence of the distributed set-membership estimators considering unknown-but-bounded system disturbances and measurement noise. In the framework of the set-membership approach, the measurement consistency test is implemented by nding parameterized intersection zonotopes. The size of the intersection zonotope is minimized by solving an optimization problem including a sequence of linear/bilinear matrix inequalities based on the weighted 2-norm criterion of the generator matrix. Meanwhile, for the distributed set-membership estimators, the partial projection method is considered to correct the estimation of the neighbor state. On the other hand, an on-line method is also provided. Finally, the proposed distributed set-membership approach is veried in a case study based on a urban drainage network.Postprint (author's final draft

A Novel RPI Set Computation Method for Discrete-time LPV Systems with Bounded Uncertainties

Set invariance plays a fundamental role in the analysis and design of linear systems. This paper proposes a novel method for constructing robust positively invariant (RPI) sets for discrete-time linear parameter varying (LPV) systems. Starting from the stability assumption in the absence of disturbances, we aim to construct the RPI sets for parametric uncertain system. The existence condition of a common quadratic Lyapunov function for all vertices of the polytopic system is relaxed in the present study. Thus the proposed method enlarges the application field of RPI sets to LPV systems. A family of approximations of minimal robust positively invariant(mRPI) sets are obtained by using a shrinking procedure. Finally, the effect of scheduling variables on the size of the mRPI set is analyzed to obtain more accurate set characterization of the uncertain LPV system. A numerical example is used to illustrate the effectiveness of the proposed method

Mixed active/passive robust fault detection and isolation using set-theoretic unknown input observers

2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIEEE This paper proposes a robust fault detection and isolation (FDI) approach that combines active and passive robust FDI approaches. Standard active FDI approaches obtain robustness by using the unknown input observer (UIO) to decouple unknown inputs from residuals. Differently, standard passive FDI approaches achieve robustness by using the set theory to bound the effect of uncertain factors (disturbances and noises). In this paper, we combine the UIO-based and the set-based approaches to produce a mixed robust FDI, which can mitigate the disadvantages and exert the advantages of the two robust FDI approaches. In order to emphasize the role of set theory, the UIO design based on the set theory is named as the set-theoretic UIO (SUIO). A quadrotor subsystem is used to illustrate the effectiveness of the proposed FDI approach.Peer ReviewedPostprint (author's final draft

Set-valued observer-based active fault-tolerant model predictive control

This paper proposes an integrated actuator and sensor active fault-tolerant model predictive control scheme. In this scheme, fault detection is implemented by using a set-valued observer, fault isolation (FI) is performed by set manipulations, and fault-tolerant control is carried out through the design of a robust model predictive control law. In this paper, a set-valued observer is used to passively complete the fault detection task, while FI is actively performed by making use of the constraint-handling capability of robust model predictive control. The set-valued observer is chosen to implement fault detection and isolation (FDI) because of its simple mathematical structure that is not affected by the type of faults such as sensor, actuator, and system-structural faults. This means that only one set-valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the fault detection and isolation task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust model predictive control is that it can effectively deal with system constraints, disturbances, and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well-known two-tank system is used to illustrate the effectiveness of the proposed fault-tolerant model predictive control scheme.Peer ReviewedPostprint (author's final draft

Positive invariant sets for fault tolerant multisensor control schemes

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 ε-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