Comparative analysis of stabilization techniques for a Networked Control System with time-varying delays

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.

This paper is concerned with stability criteria of networked control systems (NCSs) with both the time-varying network-induced delay and data packet dropout taken into account. A continuous time model of NCSs with time-varying and uncertainties is proposed. Based on the dividing of the time-varying delay, a new Lyapunov functional is constructed, and a delay-dependent stability criterion is derived to guarantee the globally asymptotic stability of the networked control systems (NCSs). Expressed in terms of linear matrix inequalities (LMIs), the stability condition can be checked using the numerically efficient Matlab LMI Control Toolbox. Compared with some report methods, no slack matrix variable is introduced and the proposed methods gave a much less conservative maximum allowable delay bound (MADB). A numerical example is provided to demonstrate the effectiveness of the proposed method.

This paper concerns the problem of the model, stability and controller design for networked control system (NCS) with time-varying delay and dropped out packet. For the NCS with time-varying delay and data packet dropout, four new control methods of dynamical state feedback control, dynamical state feedback proportional-integral (PI) control, state feedback proportional-derivative (PD) control and dynamical state feedback PD control are presented. The NCS with time-varying delay and data packet dropout based on the four control methods is modeled as an asynchronous dynamical system (ADS) constrained by event rates. Furthermore, based on the ADS theory, principle of Lyapunov stability and method of linear matrix inequality, both the semi-negative definite matrix conditions of exponential stability and the controller design for NCS are given. Finally, numerical example illustrates the feasibility of the results.

Dynamic output-feedback-based [formula omitted] design for networked control systems with multipath packet dropouts

The use of avionics networks for flight control system has reduced aircraft weight, system installation, integration and maintenance costs as well as introduced time delays and structured uncertainties. This paper studies the robust stability and stabilisation problem of uncertain networked flight control system with random time delays. Some new sufficient criteria with simple mathematical forms for robust stability and stabilisation of networked flight control system are derived by a free weighting matrix approach. A memoryless state feedback robust controller and the maximum bound of time delay are obtained based on the solution of linear matrix inequalities (LMIs) which are established by the Lyapunov-Krasovskii stability theory. Numerical examples are given to illustrate the effectiveness of design procedure.

The problem of stabilization of networked control systems (NCSs) with time-varying transmission delays is investigated. The time-varying delays lie in any two adjoining sampling instants of the plant. A technique is proposed for designing stabilizing controllers by converting NCSs with time-varying transmission delays into parameter uncertain systems with constant input delay, then the theory of robust stabilization of delay systems can be applied to solving this problem. Sufficient condition on stabilization of such NCSs is developed in terms of linear matrix inequality.

Delay-independent dual-rate PID controller for a packet-based networked control system

The article proposes a novel approach to robust stability analysis of linear parameter-varying systems, of which the system matrix is polynomial-dependent on a time-varying parameter with degree L. The robust asymptotically stability of the system is transformed into feasibility test of a pair of linear matrix inequalities (LMIs) that include the parameter, its varying-rate bound and given coefficient matrices. The result presented in this article is less conservative comparing with the previous results that are based on either quadratic Lyapunov function, or a parameter-dependent Lyapunov function, respectively. A numerical example shows the validity of the result.

This paper addresses the stability analysis and dynamic output feedback control for a class of T–S fuzzy networked control systems with mixed time-varying delays and interval distributed time-varying delays. Firstly, the T–S fuzzy model is employed to approximate the networked control system based on the system model. Secondly, the dynamic output feedback controller with hybrid intermittent feedback control law is designed for the T–S fuzzy networked control system. Thirdly, the delay-dependent stability conditions are derived by introducing the Lyapunov functional with Leibniz–Newton formula. Compared with previous works, both the mixed time-varying delays and interval distributed time-varying delays are considered in the T–S fuzzy networked control system. The control design conditions are relaxed because of the proposed controller. By introducing the Lyapunov functional with Leibniz–Newton formula, the linear matrix inequalities are solved effectively by the standard convex optimization algorithm. Finally, the simulation examples and some computing results are given to show the effectiveness and advantage of the proposed method, respectively.

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

The problem of stabilization of networked control systems (NCSs) with data packet dropout is studied. Sufficient conditions are presented on the stability and stabilization of the NCSs with packet dropout. The novelty of this work lies in that NCSs with arbitrary but finite data packet dropout are modelled as switched linear systems, and this enables us to apply the result of switched systems to the analysis and synthesis of such NCSs. The admissible upper bound of the dropped packets can be determined by a set of linear matrix inequalities (LMIs) which guarantee the stability of the NCSs. Stabilizing controllers (via state feedback and static output feedback) can be constructed by solving a set of LMIs. Also, for an NCS with a convergence rate constraint, similar results are obtained. Examples are worked out to illustrate the effectiveness of the proposed method

A nonlinear networked control system in which the system information is transmitted over the network through multiple communication channels is considered. Each channel is modeled by a time-varying delay element. Stability of the control system is studied using the Lyapunov-Krasovskii method for continuous-time delayed systems. The sufficient condition for stability of the networked control system is presented in the form of a compact LMI. The results are applied to a robot arm networked control system to show the capabilities of the proposed method for nonlinear networked control applications.

This paper investigates the stability of networked control systems under hybrid attacks. Two types of attacks are considered: Denial of Service (DoS) attacks and deception attacks. The analysis combines the dynamic event‐triggered mechanism with Linear Matrix Inequality (LMI) to examine the stability of the closed‐loop system. Additionally, by evaluating the maximum attack probability and the maximum attack intensity of deception attacks, a Lyapunov function equation is constructed to prove the system's stability. Finally, simulations are conducted to demonstrate the feasibility of the conclusions.

In this article, the stability analysis, the positive invariance of polyhedral sets and the design of state-feedback regulators for networked control systems (NCS) with bounded transmission delays, constant and unknown or time-varying, are investigated. The dynamics of the NCS is described by autoregressive-moving-average (ARMA) models. Contrary to former approaches based on quadratic Lyapunov functions, in this article polyhedral Lyapunov functions are used for both stability and positive invariance analysis and state-feedback synthesis. Then, based on the property that the exponential of a matrix can be expressed as a weighted sum of its constituent matrices, it is proven that the problems of determination of stability margins or the design of stabilising controllers can be reduced to linear programming optimisation problems. The use of ARMA models allows the development of methods for the design of state-feedback controllers satisfying state constraints or convergence rate specifications defined on the NCS state space and not on the state of an augmented state space representation.

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model