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## Über dieses Buch

This book presents theoretical and practical findings on the state estimation, diagnosis and control of complex systems, especially in the mathematical form of descriptor systems. The research is fully motivated by real-world applications (i.e., Barcelona’s water distribution network), which require control systems capable of taking into account their specific features and the limits of operations in the presence of uncertainties stemming from modeling errors and component malfunctions. Accordingly, the book first introduces a complete set-based framework for explicitly describing the effects of uncertainties in the descriptor systems discussed. In turn, this set-based framework is used for state estimation and diagnosis. The book also presents a number of application results on economic model predictive control from actual water distribution networks and smart grids. Moreover, the book introduces a fault-tolerant control strategy based on virtual actuators and sensors for such systems in the descriptor form.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
In modern societies, reliable and sustainable operation of certain infrastructures plays a fundamental role in the quality of individual life, economic development and security of nations. Large-scale critical infrastructure systems, especially those located in urban areas, such as water distribution networks (WDNs) and smart grids (SGs), are a subject of increasing concern. Therefore, it is of vital importance to develop management systems that guarantee a reliable and sustainable operation of these infrastructures. On the other hand, for the management of these infrastructures, it is also significant that their operation must use efficiently the resources that they can deliver, e.g., water and electricity, and also be efficient from an economic point of view and guarantee future supply.
Ye Wang

### Chapter 2. Set-Based State Estimation Approaches for Descriptor Systems

Abstract
This chapter proposes a general set-based framework for robust state estimation of discrete-time descriptor systems, which builds a bridge to fault diagnosis and control design problems. Specifically, a set-membership state estimator and a zonotopic Kalman observer are investigated. The considered LTI descriptor systems are affected by three types of system uncertainties: unknown inputs and unknown-but-bounded system disturbances and measurement noise. One limitation for the use of zonotopic approaches in real applications is that some system disturbances are unknown and it may not be possible to bound them in a predefined zonotope as a priori. To overcome this problem, two classes of unknown system disturbances are considered: (i) bounded disturbances in a zonotope; (ii) unbounded disturbances, which are considered to be unknown inputs and can be decoupled in the observer design. As shown in Fig. 2.1, two set-based approaches with different criteria are studied and therefore the relationship between both approaches is also established. In particular, it is proved that the zonotopic observer in the current estimation type is equivalent to the set-membership approach. Besides, the set-membership approach is extended for discrete-time LPV descriptor systems, where a new zonotope minimization criterion based on the $$\mathcal {L}_{\infty }$$ norm is defined.
Ye Wang

### Chapter 3. Distributed Set-Membership Approach Based on Zonotopes

Abstract
As society develops, an increasing number of large-scale systems, such as cyber-physical systems  [1] and critical infrastructures (i.e. water distribution networks  [2, 3] and smart grids  [4]), are becoming more automatized. Such kind of systems have a large amount of states, inputs and outputs. Considering their complexity and dimension, these large- scale systems can be formulated as interconnected systems with coupled states. In the frameworks of diagnosis and optimal control of large-scale systems, a suitable distributed state estimation approach plays a significant role in the development of model-based fault diagnosis strategies  [5] and the design of controllers  [6, 7]. Revising the literature, different approaches have been investigated for distributed state estimation problems, as e.g. the distributed moving horizon approaches in [8, 9].
Ye Wang

### Chapter 4. Set-Based Fault Detection and Isolation for Descriptor Systems

Abstract
This chapter presents set-based FDI strategies for discrete-time descriptor systems. In this chapter, as shown in Fig. 4.1, we apply the set-based framework proposed in Chap. 2 into FDI  [1, 2] for discrete-time descriptor systems. In particular, fault sensitivity should be taken into account for implementing an FD strategy  [3, 4]. In this chapter, we will show two different criteria for achieving fault sensitivity: (i) the one based on a $$\mathcal {H}_{-}$$ index and therefore the condition is transformed as an LMI; (ii) the other based on a new defined criterion and algebraic solution is explicitly presented. In the first method, the effects of occurred faults are propagated in the center of state bounding zonotopes while in the second method, those effects are bounded and propagated in the segment matrix of state bounding zonotopes. Besides, the FI strategy is implemented by adopting a bank of zonotopic UIOs.
Ye Wang

### Chapter 5. Set-Based Fault Estimation for Descriptor Systems

Abstract
Fault estimation, as a significant stage of fault diagnosis, aims to estimate the magnitude of occurred faults in a system. The problem of fault estimation has been studied using a large amount of approaches during the past decades  [14]. A suitable fault estimation with robust performance against system uncertainties is very useful for implementing an active fault-tolerant control system  [5]. Based on the robust control techniques, robust fault estimations are implemented in a variety of systems, such as  [68], where the effects of uncertainties are bounded, and as a result, fault estimation results are obtained with the minimum estimation error.
Ye Wang

### Chapter 6. Set-Invariance Characterizations and Active Mode Detection for Descriptor Systems

Abstract
This chapter presents a general framework of set-invariance characterizations for discrete-time descriptor systems, and its application to active mode detection  [1, 2] following the research line shown in Fig. 6.1. Among alternative techniques for the computation of invariant sets  [39], we use ultimate boundedness of trajectories to obtain set-invariance characterizations for the systems subject to unknown-but-bounded disturbances  [10].
Ye Wang

### Chapter 7. Economic Model Predictive Control Strategies Based on a Periodicity Constraint

Abstract
Periodic behavior appears in some specific systems, such as WDNs  [13] and electrical networks  [4]. One specific example stems from the periodic behavior of customer demands in WDNs. A WDN generally consists of a large number of hydraulic elements, such as storage tanks, pressurized pipelines, pumping stations (including several parallel pumps) and valves. EMPC is suitable for optimizing the economic performance of operations in WDNs, as shown in  [57], but these methods do not take specific advantage of the periodic nature of the consumer demands and energy costs. Taking into account the daily water demand patterns and periodic electricity prices, periodic operations can also be considered in the EMPC design.
Ye Wang

### Chapter 8. Applications of Economic Model Predictive Control Strategies for Complex Systems

Abstract
This chapter presents three application results of EMPC strategies for realistic water distribution networks and power systems. The control-oriented model of all these systems is built in a descriptor form. The importance of this chapter is to demonstrate the proposed EMPC strategies in real case studies. Meanwhile, some additional difficulties encountered from these applications appear. To address these, a two-layer control strategy and a nonlinear constraint relaxation approach are presented.
Ye Wang

### Chapter 9. Fault-Tolerant Control of Discrete-Time Descriptor Systems Using Virtual Actuator and Virtual Sensor

Abstract
Due to the increasing complexity of modern control systems, the possibility of actuator and sensor faults has increased dramatically. These faults may degrade the performance, leading to unsatisfactory behavior, or in the worst cases to instability, thus bearing catastrophic consequences for the system itself and for the safety of living beings around them. Motivated by the increasing need for safety and reliability, FTC techniques have attracted a lot of interest in the control community, since they allow to maintain the system performance close to the desired one while preserving stability in spite of the faults [1, 2].
Ye Wang

### Chapter 10. Concluding Remarks

Abstract
In this thesis, several theoretical contributions and application results on robust state estimation, set-based fault diagnosis, EMPC and FTC strategies for complex systems have been presented.
Ye Wang

### Backmatter

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