Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed methodPeer ReviewedPostprint (author's final draft

Distributed Set-Based Observers Using Diffusion Strategy

Distributed estimation is more robust against single points of failure and requires less communication overhead compared to the centralized version. Among distributed estimation techniques, set-based estimation has gained much attention as it provides estimation guarantees for safety-critical applications and copes with unknown but bounded uncertainties. We propose two distributed set-based observers using interval-based and set-membership approaches for a linear discrete-time dynamical system with bounded modeling and measurement uncertainties. Both algorithms utilize a new over-approximating zonotopes intersection step named the set-based diffusion step. We use the term diffusion since our intersection of zonotopes formula resembles the traditional diffusion step in the stochastic Kalman filter. Our new zonotopes intersection takes linear time. Our set-based diffusion step decreases the estimation errors and the size of estimated sets and can be seen as a lightweight approach to achieve partial consensus between the distributed estimated sets. Every node shares its measurement with its neighbor in the measurement update step. The neighbors intersect their estimated sets constituting our proposed set-based diffusion step. We represent sets as zonotopes since they compactly represent high-dimensional sets, and they are closed under linear mapping and Minkowski addition. The applicability of our algorithms is demonstrated by a localization example. All used data and code to recreate our findings are publicly availabl

Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper proposes a set-membership state estimator and a zonotopic Kalman observer for discrete-time descriptor systems. Both approaches are developed in a set-based context considering system disturbances, measurement noise, and unknown inputs. This set-membership state estimation approach determines the set of consistent states with the model and measurements by constructing a parameterized intersection zonotope. Two methods to minimize the size of this intersection zonotope are provided: one inspired by Kalman filtering and the other based on solving an optimization problem involving a series of linear matrix inequalities. Additionally, we propose a zonotopic Kalman observer for discrete-time descriptor systems. Moreover, the relationship between both approaches is discussed. In particular, it is proved that the zonotopic Kalman observer in the current estimation type is equivalent to the set-membership approach. Finally, a numerical example is used to illustrate and compare the effectiveness of the proposed approaches.Peer ReviewedPostprint (author's final draft

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Distributed estimation techniques forcyber-physical systems

Nowadays, with the increasing use of wireless networks, embedded devices and agents with processing and sensing capabilities, the development of distributed estimation techniques has become vital to monitor important variables of the system that are not directly available. Numerous distributed estimation techniques have been proposed in the literature according to the model of the system, noises and disturbances. One of the main objectives of this thesis is to search all those works that deal with distributed estimation techniques applied to cyber-physical systems, system of systems and heterogeneous systems, through using systematic review methodology. Even though systematic reviews are not the common way to survey a topic in the control community, they provide a rigorous, robust and objective formula that should not be ignored. The presented systematic review incorporates and adapts the guidelines recommended in other disciplines to the field of automation and control and presents a brief description of the different phases that constitute a systematic review. Undertaking the systematic review many gaps were discovered: it deserves to be remarked that some estimators are not applied to cyber-physical systems, such as sliding mode observers or set-membership observers. Subsequently, one of these particular techniques was chosen, set-membership estimator, to develop new applications for cyber-physical systems. This introduces the other objectives of the thesis, i.e. to present two novel formulations of distributed set-membership estimators. Both estimators use a multi-hop decomposition, so the dynamics of the system is rewritten to present a cascaded implementation of the distributed set-membership observer, decoupling the influence of the non-observable modes to the observable ones. So each agent must find a different set for each sub-space, instead of a unique set for all the states. Two different approaches have been used to address the same problem, that is, to design a guaranteed distributed estimation method for linear full-coupled systems affected by bounded disturbances, to be implemented in a set of distributed agents that need to communicate and collaborate to achieve this goal

Estimation of Liquid Level in a Harsh Environment Using Chaotic Observer

The increased demand for liquid level measurement has been a key factor in designing accurate and reliable control systems. Here, a study was carried out to calculate the liquid level in a tank using a pressure sensor for changes in inlet liquid parameters like temperature, density and velocity. Prediction of their variables for the long term is essential due to the randomness present in the input and measurement. Hence, observer design for state estimation of a non-linear dynamic system with uncertainties in the measurement and process becomes important. This work provides a feedback observer solution for a system with multiple inputs and single measurable output. A full state observer model is developed to estimate a system’s states with a sensor placed at a definite position from the pipe’s input point through which the liquid flows at different densities and temperatures. Using the observability properties, Luenberger full state observer is designed by various methods, verified using MATLAB and SIMULINK for the system state estimation. To incorporate process noise and measurement noise, the Kalman estimator is integrated with the system. Chaotic systems are susceptible to initial conditions, variations in parameters and are complex dynamic systems. However, providing consistently precise measurements through particular meters necessitates time-consuming computations that can be reduced by employing machine learning approaches that make use of optimizers. The results obtained are compared with the prediction models obtained using Artificial Neural Networks and are validated through the readings obtained from the experimental setup

Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.Comment: This paper was accepted and presented in the 1st IFAC Virtual World Congress, 202

A detectability criterion and data assimilation for non-linear differential equations

In this paper we propose a new sequential data assimilation method for non-linear ordinary differential equations with compact state space. The method is designed so that the Lyapunov exponents of the corresponding estimation error dynamics are negative, i.e. the estimation error decays exponentially fast. The latter is shown to be the case for generic regular flow maps if and only if the observation matrix H satisfies detectability conditions: the rank of H must be at least as great as the number of nonnegative Lyapunov exponents of the underlying attractor. Numerical experiments illustrate the exponential convergence of the method and the sharpness of the theory for the case of Lorenz96 and Burgers equations with incomplete and noisy observations