Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

New advances in H∞ control and filtering for nonlinear systems

The main objective of this special issue is to summarise recent advances in H∞ control and filtering for nonlinear systems, including time-delay, hybrid and stochastic systems. The published papers provide new ideas and approaches, clearly indicating the advances made in problem statements, methodologies or applications with respect to the existing results. The special issue also includes papers focusing on advanced and non-traditional methods and presenting considerable novelties in theoretical background or experimental setup. Some papers present applications to newly emerging fields, such as network-based control and estimation

Measurements, Models, Systems and Design

531 s.

A semidefinite relaxation procedure for fault-tolerant observer design

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design

Kernel-based fault diagnosis of inertial sensors using analytical redundancy

Kernel methods are able to exploit high-dimensional spaces for representational advantage, while only operating implicitly in such spaces, thus incurring none of the computational cost of doing so. They appear to have the potential to advance the state of the art in control and signal processing applications and are increasingly seeing adoption across these domains. Applications of kernel methods to fault detection and isolation (FDI) have been reported, but few in aerospace research, though they offer a promising way to perform or enhance fault detection. It is mostly in process monitoring, in the chemical processing industry for example, that these techniques have found broader application. This research work explores the use of kernel-based solutions in model-based fault diagnosis for aerospace systems. Specifically, it investigates the application of these techniques to the detection and isolation of IMU/INS sensor faults – a canonical open problem in the aerospace field. Kernel PCA, a kernelised non-linear extension of the well-known principal component analysis (PCA) algorithm, is implemented to tackle IMU fault monitoring. An isolation scheme is extrapolated based on the strong duality known to exist between probably the most widely practiced method of FDI in the aerospace domain – the parity space technique – and linear principal component analysis. The algorithm, termed partial kernel PCA, benefits from the isolation properties of the parity space method as well as the non-linear approximation ability of kernel PCA. Further, a number of unscented non-linear filters for FDI are implemented, equipped with data-driven transition models based on Gaussian processes - a non-parametric Bayesian kernel method. A distributed estimation architecture is proposed, which besides fault diagnosis can contemporaneously perform sensor fusion. It also allows for decoupling faulty sensors from the navigation solution

Model based fault diagnosis and prognosis of nonlinear systems

Rapid technological advances have led to more and more complex industrial systems with significantly higher risk of failures. Therefore, in this dissertation, a model-based fault diagnosis and prognosis framework has been developed for fast and reliable detection of faults and prediction of failures in nonlinear systems. In the first paper, a unified model-based fault diagnosis scheme capable of detecting both additive system faults and multiplicative actuator faults, as well as approximating the fault dynamics, performing fault type determination and time-to-failure determination, is designed. Stability of the observer and online approximator is guaranteed via an adaptive update law. Since outliers can degrade the performance of fault diagnostics, the second paper introduces an online neural network (NN) based outlier identification and removal scheme which is then combined with a fault detection scheme to enhance its performance. Outliers are detected based on the estimation error and a novel tuning law prevents the NN weights from being affected by outliers. In the third paper, in contrast to papers I and II, fault diagnosis of large-scale interconnected systems is investigated. A decentralized fault prognosis scheme is developed for such systems by using a network of local fault detectors (LFD) where each LFD only requires the local measurements. The online approximators in each LFD learn the unknown interconnection functions and the fault dynamics. Derivation of robust detection thresholds and detectability conditions are also included. The fourth paper extends the decentralized fault detection from paper III and develops an accommodation scheme for nonlinear continuous-time systems. By using both detection and accommodation online approximators, the control inputs are adjusted in order to minimize the fault effects. Finally in the fifth paper, the model-based fault diagnosis of distributed parameter systems (DPS) with parabolic PDE representation in continuous-time is discussed where a PDE-based observer is designed to perform fault detection as well as estimating the unavailable system states. An adaptive online approximator is incorporated in the observer to identify unknown fault parameters. Adaptive update law guarantees the convergence of estimations and allows determination of remaining useful life --Abstract, page iv

Decentralized sliding mode control and estimation for large-scale systems

This thesis concerns the development of an approach of decentralised robust control and estimation for large scale systems (LSSs) using robust sliding mode control (SMC) and sliding mode observers (SMO) theory based on a linear matrix inequality (LMI) approach. A complete theory of decentralized first order sliding mode theory is developed. The main developments proposed in this thesis are: The novel development of an LMI approach to decentralized state feedback SMC. The proposed strategy has good ability in combination with other robust methods to fulfill specific performance and robustness requirements. The development of output based SMC for large scale systems (LSSs). Three types of novel decentralized output feedback SMC methods have been developed using LMI design tools. In contrast to more conventional approaches to SMC design the use of some complicated transformations have been obviated. A decentralized approach to SMO theory has been developed focused on the Walcott-Żak SMO combined with LMI tools. A derivation for bounds applicable to the estimation error for decentralized systems has been given that involves unknown subsystem interactions and modeling uncertainty. Strategies for both actuator and sensor fault estimation using decentralized SMO are discussed.The thesis also provides a case study of the SMC and SMO concepts applied to a non-linear annealing furnace system modelderived from a distributed parameter (partial differential equation) thermal system. The study commences with a lumped system decentralised representation of the furnace derived from the partial differential equations. The SMO and SMC methods derived in the thesis are applied to this lumped parameter furnace model. Results are given demonstrating the validity of the methods proposed and showing a good potential for a valuable practical implementation of fault tolerant control based on furnace temperature sensor faults

Model based fault diagnosis and prognosis of class of linear and nonlinear distributed parameter systems modeled by partial differential equations

With the rapid development of modern control systems, a significant number of industrial systems may suffer from component failures. An accurate yet faster fault prognosis and resilience can improve system availability and reduce unscheduled downtime. Therefore, in this dissertation, model-based prognosis and resilience control schemes have been developed for online prediction and accommodation of faults for distributed parameter systems (DPS). First, a novel fault detection, estimation and prediction framework is introduced utilizing a novel observer for a class of linear DPS with bounded disturbance by modeling the DPS as a set of partial differential equations. To relax the state measurability in DPS, filters are introduced to redesign the detection observer. Upon detecting a fault, an adaptive term is activated to estimate the multiplicative fault and a tuning law is derived to tune the fault parameter magnitude. Then based on this estimated fault parameter together with its failure limit, time-to-failure (TTF) is derived for prognosis. A novel fault accommodation scheme is developed to handle actuator and sensor faults with boundary measurements. Next, a fault isolation scheme is presented to differentiate actuator, sensor and state faults with a limited number of measurements for a class of linear and nonlinear DPS. Subsequently, actuator and sensor fault detection and prediction for a class of nonlinear DPS are considered with bounded disturbance by using a Luenberger observer. Finally, a novel resilient control scheme is proposed for nonlinear DPS once an actuator fault is detected by using an additional boundary measurement. In all the above methods, Lyapunov analysis is utilized to show the boundedness of the closed-loop signals during fault detection, prediction and resilience under mild assumptions --Abstract, page iv