Stability, positive invariance and design of constrained regulators for networked control systems

Driven by recent telecommunication demand, shared communication channels are more abundant today than ever before. These shared wired/wireless networks for communication are being exploited more and more in control systems to connect sensors, controllers and actuators resulting in so-called networked control systems (NCSs). NCSs replace the more traditional control systems where dedicated point-to-point (wired) connections are being used. The advantages of using NCS technology are inexpensive and easily modifiable communication links which allow control algorithms to be easily implemented in situations where dedicated connections are not possible (either economically or physically). However, the drawback is that the control system is susceptible to undesirable (possibly destabilizing) side-effects such as time-varying transmission intervals, time-varying delays, packet dropouts, quantization and a shared communication medium. These network-induced effects undermine fundamental assumptions on which traditional control theory is built and, therefore, it is essential to develop new techniques and tools that can be used to analyze and/or design control systems which communicate via a shared network. This thesis advances NCS analysis and design methodologies by contributing new theoretical developments, new software tools and new experimental validation results. The first new theoretical development is in the area of analyzing robust stability properties with respect to network-induced effects. A sum of squares (SOS) approach for a class of nonlinear NCSs incorporating bounded time-varying delays, bounded time-varying transmission intervals and a shared communication medium is developed. Mathematical models that describe these nonlinear NCSs are cast into suitable hybrid system formulations. Based on these hybrid system formulations, (families of) Lyapunov functions are constructed using SOS techniques. Amongst other benefits, it is shown that this technique improves the guaranteed robustness margins compared to existing work. The second new theoretical development concerns the design of networkaware decentralized controllers guaranteeing robust stability properties with respect to network-induced effects. We develop one of the first approaches based on semidefinite programming techniques to synthesize stabilizing decentralized observer-based output-feedback controllers for linear plants where the controllers, sensors and actuators are connected via a shared communication network subject to time-varying transmission intervals and delays. To effectively deal with the shared communication medium, a switched observer structure is adopted that switches based on the transmitted measured outputs and a switched controller structure is also adopted that switches based on the transmitted control inputs at each transmission time. By taking a discrete-time switched linear system perspective on modeling these decentralized NCSs, we are able to derive a general model that captures all these networked and decentralized control aspects. We provide linear matrix inequality (LMI)-based synthesis conditions which, if satisfied, provide stabilizing observer-based controllers that are both decentralized and robust to network effects. Regarding new software tools, the first prototype of a toolbox is developed to automate (robust) stability analysis (and controller design) for NCSs. Specifically, it is shown that the toolbox can be employed to efficiently verify if a linear time-invariant (LTI) plant and an LTI controller interconnected with a shared network are robust to certain network imperfections. The main intention of the toolbox is to make the available theory readily accessible to and applicable for the general control community. Additionally, the chosen software structure enables the incorporation of custom models or custom stability/performance analysis conditions in an easy manner, thereby allowing the control community to contribute and to further develop the toolbox. Finally, an experimental case study involving a wirelessly controlled inverted pendulum/cart system is investigated. In particular, the communication network itself is analyzed such that the network-induced effects can be characterized in terms of bounds on the transmission intervals and transmission delays. Based on these bounds, the prototype toolbox is applied to analyze the robustness regions for different performance specifications, which aid in tuning the controller to achieve more closed-loop robustness with respect to the network-induced effects. This leads to a validation of the developed theory in an experimental setting. In addition to the validation of the developed theory, many new insights into the network behavior are obtained and explained, thereby raising new interesting questions for future research on NCSs.

The paper presents stabilization of a Networked Control System (NCS) with uncertain, time-varying delays using two stabilization approaches namely, Parameter Dependant Lyapunov Function (PDLF) and Quadratic Lyapunov Function (QLF). The PDLF approach depends upon the time varying delay parameters. Thus, for larger delays the system's stability is ensured. In NCS, the uncertainties arising out from the variations in time-delay is modeled using polytopic approach and the stability region of the system is presented in terms of controller gain and maximum tolerable delay. The overall NCS is represented in discrete domain. The proposed PDLF stabilization results have been compared with that of the QLF approach. Lyapunov-based stability criterion is presented in Linear Matrix inequalities (LMIs). The stabilized state feedback controller is designed using LMIs and considering the bounded time-varying delays. The proposed approach is illustrated by two numerical examples. From the results obtained, it is observed that the PDLF approach improves the stability region of the system.

Design, Analysis and Real-time Implementation of Networked Predictive Control Systems

By multi-rate networked control systems (NCS), we mean the sampling periods of the sensor, the controller and the actuator in networked control systems are not the same, that is to say there are more than one sampling rate in networked control systems. When the sensor, the controller and the actuator are all clock driven, multi-rate NCS with both short time delay and packet dropout is modeled as a switched system model. Based on the approaches of switched system and Lyapunov functions, the necessary conditions for asymptotical stability for multi-rate NCS with both short time delay and packet dropout are given. A numerical example is given to verify the theories results in this paper.

In this paper, stability and disturbance attenuation issues for a class of networked control systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H/sup /spl infin// disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such networked control system as a discrete-time switched system. Then the NCSs' stability and performance problems can be reduced to corresponding problems for the switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based in the discrete-time switched systems and piecewise Lyapunov functions.

Connecting a complex control system with various sensors, actuators, and controllers as a networked control system by a shared data network can effectively reduce complicated wiring connections. This system is also easy to install and maintain. The trend is to use networked control systems for time-sensitive applications, such as remote DC motor actuation control. The performance of a networked control system can be improved if the network can guarantee quality-of-service (QoS). Due to time-varying network traffic demands and disturbances, QoS requirements provided by a network may change. In this case, a network has to reallocate its resources and may not be able to provide QoS requirements to a networked control application as needed. Therefore, the application may have to gracefully degrade its performance and perform the task as best as possible with the provided network QoS. This paper proposes a novel approach for networked DC motor control systems using controller gain adaptation to compensate for the changes in QoS requirements. Numerical and experimental simulations, and prototyping, are presented to demonstrate the feasibility of the proposed adaptation scheme to handle network QoS variation in a control loop. The effective results show the promising future of the use of gain adaptation in networked control applications.

In the paper, we study the stability of the discrete-time networked control systems. If the network link is with a limited communication capacity, the network-induced delay is unavoidable. Considering the network-induced delay, the closed-loop networked control systems are usually subject to the delayed state. The traditional method for the study of the networked control systems is mainly to construct a Lyapunov function and derive the stability criterion. Generally, the derived stability condition is only sufficient. The selection of the Lyapunov function is attracting increasing attention as a better Lyapunov function may lead to less conservative results. In this work, we use an alternate way to get the less conservative results. A time-domain Smith predictor is employed to predict the non-delayed state. Then, the control law is the feedback of the delayed measurements and the non-delayed prediction. Simulation results are given to show that the proposed control law can expand the upper bounds with the existing relative conservative stability criterion.

This chapter presents a new stability and L 2-gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced in [13] and [12] in the framework of impulsive system representation. Most of the existing works on the stability of NCS (in the framework of time delay approach) are reduced to some Lyapunov-based analysis of systems with uncertain and bounded time-varying delays. This analysis via time-independent Lyapunov functionals does not take advantage of the sawtooth evolution of the delays induced by sample-and-hold. The latter drawback was removed in [4], where time-dependent Lyapunov functionals for sampled-data systems were introduced. This led to essentially less conservative results. The objective of the present chapter is to extend the time-dependent Lyapunov functional approach to NCS, where variable sampling intervals, data packet dropouts and variable network-induced delays are taken into account. The new analysis is applied to a novel network-based static output-feedback H ∞ control problem. Numerical examples show that the novel discontinuous terms in Lyapunov functionals essentially improve the results.

Networked control systems (NCS) consist of sensors, actuators and controllers the operations of which may be distributed over geographically disparate locations and co-ordinated by the exchange of information passed over a communication network. The communication network may be physically wired or not. The widespread applications of the Internet have been a major driving force for research and development of NCS. NCS have advantages in terms of cost reduction, system diagnosis and flexibility, minimizing wiring and making the addition and replacement of individual elements relatively simple; efficient data sharing makes taking globally intelligent control decisions easier with an NCS. The applications of NCS are very wide, from the large scale of factory automation and plant monitoring to the smaller but complicated networks of computers in modern cars, places and autonomous robots. Networked Control Systems presents the most recent results in stability and robustness analysis as well as new developments related to networked fuzzy and optimal control. Many of the chapters contain details of case-studies, experimental, simulation and/or other application-related work showing how the theories put forward can be implemented in real systems. The state-of-the art research reported in this volume by an international team of contributors will make Networked Control Systems an essential reference for researchers and postgraduate students in control, electrical, computer and mechanical engineering and computer science.

In this paper, we develop a systematic Lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration. The only assumptions we make about the system are well-posedness of the algebraic loop and local stability. Problems to be considered include the estimation of the domain of attraction, the reachable set under a class of bounded energy disturbances and the nonlinear L2 gain. The regional analysis is established through an effective treatment of the algebraic loop and the saturation/deadzone function. This treatment yields two forms of differential inclusions, a polytopic differential inclusion (PDI) and a norm-bounded differential inclusion (NDI) that contain the original system. Adjustable parameters are incorporated into the differential inclusions to reflect the regional property. The main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain Lyapunov function where the PDI or the NDI is valid. With quadratic Lyapunov functions, conditions for stability and performances are derived as linear matrix inequalities (LMIs). To obtain less conservative conditions, we use a pair of conjugate non-quadratic Lyapunov functions, the convex hull quadratic function and the max quadratic function. These functions yield bilinear matrix inequalities (BMIs) as conditions for stability and guaranteed performance level. The BMI conditions cover the corresponding LMI conditions as special cases, hence the BMI results are guaranteed to be as good as the LMI results. In most examples, the BMI results are significantly better than the LMI results

Networked Control Systems is a control system in which control loop is closed via shared communication network. Due to advantages of NCS, the relevant literature has been growing rapidly to discuss the modeling approach, stability analysis, controller synthesis and so forth and to implement it into the real application. This paper describes output feedback controller design for dissipative networked control systems via markovian jump system approach. Dissipativity refers to an existence of supply rate dealing with the systems such that the closed loop system has a dissipative property. Main result of this paper is a solvability condition in the form of LMI terms for achieving dissipativity of output feedback problem in networked control systems via markovian jump system approach.

This paper explores stability properties of networked control systems with time-varying, but bounded delays that are introduced by network and/or consecutive packet dropouts. By using network predictive control, the networked control system can be converted into a switched system with stable and unstable subsystems. Then based on average dwell time technique, the stability of networked predictive control system can be guaranteed under some mild conditions.

In this paper, the robust H∞ control problem is developed for a class of linear time-varying networked control system (NCS) with uncertainties and external disturbance. In network, the network-induced delay and packet dropouts are simultaneously considered. Firstly, a discrete-time switched system model is established based on the signals transmission delay in network. Then, a time-varying H∞ controller is designed. Such the controller can vary according to delay in network. Furthermore, by constructing delay-dependent Lyapunov-Krasovskii functional, a sufficient condition is given to guarantee that the closed-loop system is stochastically stable with an H∞ disturbance attenuation level in terms of nonlinear matrix inequalities. In order to solve the controller gain, the cone complementarity linearization (CCL) algorithm is employed. Finally, a networked DC motor control system is analyzed to illustrate the effectiveness of the proposed method.

l∞-based stability criteria and its applications on FLC systems

Networked control systems (NCS) are in existence for quite some time. The network-induced delays and packet drops; and their effect on control system's performance has been a burning topic for last one decade. Dependability in context of NCS has not got much attention. While it is an important aspect of NCS intended to be used in critical application. The paper reviews the present state of developments in NCS and presents open problems pertaining to dependability of NCS. Solutions to these problems may increase the presence of NCS by many folds and in many fields.