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## Über dieses Buch

"Robust Control for Uncertain Networked Control Systems with Random Delays" addresses the problem of analysis and design of networked control systems when the communication delays are varying in a random fashion. The random nature of the time delays is typical for commercially used networks, such as a DeviceNet (which is a controller area network) and Ethernet network.

The main technique used in this book is based on the Lyapunov-Razumikhin method, which results in delay-dependent controllers. The existence of such controllers and fault estimators are given in terms of the solvability of bilinear matrix inequalities. Iterative algorithms are proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. Finally, to demonstrate the effectiveness and advantages of the proposed design method in the book, numerical examples are given in each designed control system.

## Inhaltsverzeichnis

### Introduction

The point-to-point architecture is the traditional communication architecture for control systems, that is, sensors and/or actuators are connected to controllers via wires. In recent years, due to the expansion of physical setups and functionality, a traditional point-to-point architecture is no longer able to meet new requirements, such as modularity, integrated diagnostics, quick and easy maintenance, and low cost. Such requirements are particularly demanding in the control of complex control systems [1, 2, 12] and remote control systems [3, 4, 10, 13].
Dan Huang, Sing Kiong Nguang

### Modeling of Networked Control Systems

In this chapter, the modeling procedure of NCSs will be presented. Before proceeding to the modeling procedure, the following assumptions will be used throughout this book:
• The sensor is time-driven: the states of the plant are sampled periodically.
• The controller is event-driven: the control signal is calculated as soon as a new sensor data arrives at the controller.
• The actuator is event-driven: the control signal is applied to the plant as soon as a new controller data arrives at the actuator.
Dan Huang, Sing Kiong Nguang

### State Feedback Control of Uncertain Networked Control Systems

The Markovian jump linear system (MJLS), which was introduced by Krasovskii and Lidskii [66], is an important class of stochastic dynamic systems that is popular in modeling abrupt changes in the system structure. This is due to the fact that dynamic systems are very often inherently vulnerable to component failures or repairs, sudden environmental disturbances, changing subsystem interconnection and abrupt variations of the operating point of a nonlinear plant etc. This class of systems is normally used to model stochastic processeswhich change from one mode to another randomly or according to some probabilities. Controllability, stabilizability, observability, and optimal control, as well as some important applications of such systems, can be found in [67, 68, 69, 70, 71, 72, 73, 74] and references therein.
Dan Huang, Sing Kiong Nguang

### Dynamic Output Feedback Control for Uncertain Networked Control Systems

This chapter investigates the stabilization problem for a class of uncertain NCSs with random communication network-induced delays. The synthesis design procedure of a robust dynamic output feedback controller for linear NCSs is presented in this chapter. The sampling effects and the resulting system delays are incorporated into the design procedure. A system transformation approach is applied to convert the hybrid system which consists of both continuous and discrete signals into a system in the continuous realm. Based on the Lyapunov–Razumikhin method, the existence of such a controller is given in terms of the solvability of BMIs. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. An illustrative example is given along with the theoretical presentation.
Dan Huang, Sing Kiong Nguang

### Robust Disturbance Attenuation for Uncertain Networked Control Systems

For time-delay problems encountered in engineering, two approaches are employed. One is to obtain information on the time-delay and subsequently to use this information to solve the problem. The other is to attenuate the effects caused by delay disturbances when the delays cannot be effectively used or obtained. Furthermore, the problem of performance controlwith disturbance attenuation for time-delay systems has gathered much attention in recent years [73, 80, 81].
Dan Huang, Sing Kiong Nguang

### Robust Filter Design for Uncertain Networked Control Systems

Knowing the system state is necessary to solve many control theory problems. In most practical cases, however, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. In this sense, a filter is a system that estimates the values of internal systems variables that are not measured from the available outputs [86, 115]. More precisely, the aim of a filter design is that the induced operator norm of the mapping from the noise to the filter error is kept within a prescribed bound.
Dan Huang, Sing Kiong Nguang

### Robust Fault Estimator Design for Uncertain Networked Control Systems

In order to avoid production deteriorations or damages, system faults have to be identified and decisions that stop the propagation of their effects have to be made. This gives the rise to the research on fault detection and isolation (FDI) and in recent years, the problem has attracted lots of attention from researchers. Among them, the model-based approach is the common approach, see survey papers [88, 89, 90]. The prime importance [116, 117] in designing a model-based fault-detection system is the increasing robustness of residual to unknown inputs and modeling errors and enhancing the sensitivity to faults. Two approaches are mainly applied in FDI to address these two issues. One is to use the $$\mathcal H_\infty$$ norm of transfer function matrix from fault to residual signal as a measure to estimate the sensitivity to the faults [119, 120]. Another method is to adopt the $$\mathcal H_\infty$$ filtering formulation to make the the error between residual and fault as small as possible [118, 121]. Furthermore, the existence of time-delays is commonly encountered in dynamic systems and has to be dealt with in the realm of FDI. Some results have been obtained to address this issue, see [91]-[95]. However, these results are mostly obtained for systems with state delays.
Dan Huang, Sing Kiong Nguang

### Takagi–Sugeno Fuzzy Control System

A nonlinear dynamic system can usually be represented by a set of nonlinear differential equations of the form
$$\dot{x}=f(x,u), (8.1)$$
where f( ∙ ) is a nonlinear vector function, x is the state vector, and u is the control input.
In the rest parts of the book, we approximate the nonlinear plant (8.1) by a T-S fuzzy model [62]. This fuzzy modeling is simple and natural. The system dynamics are captured by a set of fuzzy implications which characterize local relations in the state space. The main feature of a T-S fuzzy model is to express the local dynamics of each fuzzy implication (rule) by a linear system model. The overall fuzzy model of the system is achieved by fuzzy “blending” of the linear system models.
Dan Huang, Sing Kiong Nguang

### State Feedback Control for Uncertain Nonlinear Networked Control Systems

In this chapter, our concern is to consider a class of nonlinear uncertain NCSs with sensors and actuators connected to a controller via two communication networks in the continuous-time domain. Linear feedback control techniques can be utilized as in the case of feedback stabilization. The design procedure is stated as follows. First the nonlinear plant is represented by a T-S fuzzy model. In this type of fuzzy model, local dynamics in different state space regions are represented by linear models. The overall model of the system is achieved by “blending” of these linear models. Then for each local linear model, a linear feedback controller is to be designed. The resulting overall controller, which is nonlinear in general, is again a fuzzy blending of each individual linear controller.
Dan Huang, Sing Kiong Nguang

### Dynamic Output Feedback Control for Uncertain Nonlinear Networked Control Systems

In this chapter, a fuzzy dynamic output feedback controller is designed for a class of uncertain nonlinear NCSs. The design procedure is inherited from the previous chapter. The results are given in terms of the solvability of BMIs.
Dan Huang, Sing Kiong Nguang

### Robust Disturbance Attenuation for Uncertain Nonlinear Networked Control Systems

In this chapter, we consider the problem of robust fuzzy disturbance attenuation for a class of uncertain nonlinear NCSs. The Lyapunov–Razumikhin method has been employed to derive such a controller for this class of systems such that it is stochastically stabilizable with a disturbance attenuation level γ . Sufficient conditions for the existence of such a controller for this class of NCSs are derived in terms of the solvability of BMIs.
Dan Huang, Sing Kiong Nguang

### Robust Fuzzy Filter Design for Uncertain Nonlinear Networked Control Systems

This chapter investigates the problem of robust fuzzy filter design for a class of nonlinear NCSs, which is a development of the results obtained in Chapter 6. The nonlinear plant is firstly represented by a set of local linear models based on the T-S fuzzy modeling technique presented in Chapter 7. We then proceed to the design of robust fuzzy filters for the system. By applying Lyapunov–Razumikhin method, the existence of a delay-dependent filter is given in terms of the solvability of BMIs. It should be noted that the overall designed fuzzy filter is also a blending of local linear filters according to a given fuzzy rules. The viability of the results is verified by a real world example.
Dan Huang, Sing Kiong Nguang

### Fault Estimation for Uncertain Nonlinear Networked Control Systems

This chapter proposes a robust fuzzy fault estimator for a class of nonlinear uncertain NCSs that ensures the fault estimation error is less than prescribed $$\mathcal{H}_\infty$$ performance level, irrespective of the uncertainties and network-induced effects. Sufficient conditions for the existence of such a fault estimator for this class of NCSs are derived in terms of the solvability of BMIs.
Dan Huang, Sing Kiong Nguang

### Conclusions

This book proposes novel methodologies for stability analysis, disturbance attenuation, and fault estimation for a class of linear/nonlinear uncertain NCSs with random communication network-induced delays and data packet dropouts in both sensor-to-controller and controller-to-actuator channels. Models for such network-induced effects are first developed by using Markov processes. Based on the Lyapunov–Razumikhin method, the existence of the designed controllers and fault estimators are given in terms of the solvability of BMIs. Iterative algorithms are proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. The effectiveness and advantages of the proposed design methodologies are verified by numerical examples in each chapter. The simulation results show that the proposed design methodologies can achieve the prescribed performance requirement.
Dan Huang, Sing Kiong Nguang

### Backmatter

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