A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete-time stochastic complex networks with randomly occurred nonlinearities (RONs) and time delays. The discrete-time complex networks under consideration are subject to: (1) stochastic nonlinearities that occur according to the Bernoulli distributed white noise sequences; (2) stochastic disturbances that enter the coupling term, the delayed coupling term as well as the overall network; and (3) time delays that include both the discrete and distributed ones. Note that the newly introduced RONs and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment (e.g., Internet-based control systems). By constructing a novel Lyapunov-like matrix functional, the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem. By employing a combination of the linear matrix inequality (LMI) techniques, the free-weighting matrix method and stochastic analysis theories, several delay-dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete-time stochastic complex networks with time delays. The criteria derived are characterized in terms of LMIs whose solution can be solved by utilizing the standard numerical software. A simulation example is presented to show the effectiveness and applicability of the proposed results

Robust predictive tracking control for a class of nonlinear systems

A robust predictive tracking control (RPTC) approach is developed in this paper to deal with a class of nonlinear SISO systems. To improve the control performance, the RPTC architecture mainly consists of a robust fuzzy PID (RFPID)-based control module and a robust PI grey model (RPIGM)-based prediction module. The RFPID functions as the main control unit to drive the system to desired goals. The control gains are online optimized by neural network-based fuzzy tuners. Meanwhile using grey and neural network theories, the RPIGM is designed with two tasks: to forecast the future system output which is fed to the RFPID to optimize the controller parameters ahead of time; and to estimate the impacts of noises and disturbances on the system performance in order to create properly a compensating control signal. Furthermore, a fuzzy grey cognitive map (FGCM)-based decision tool is built to regulate the RPIGM prediction step size to maximize the control efforts. Convergences of both the predictor and controller are theoretically guaranteed by Lyapunov stability conditions. The effectiveness of the proposed RPTC approach has been proved through real-time experiments on a nonlinear SISO system

Event-triggered proportional-derivative control for nonlinear network systems with a novel event-triggering scheme: Differential of triggered state consideration

This article proposes event-triggered proportional-derivative control for a class of nonlinear network control systems. For derivative action of the proposed proportional-derivative control, a novel event-triggering scheme is devised together with the control that considers a differential of a triggered state. The class of the nonlinear network systems is represented as a Lur'e system to consider various nonlinear cases. Time varying transmission delay is considered which can be defined by lower and upper delay bounds. The proposed proportional-derivative control is designed by Lyapunov-Krasovskii stability analysis, and the design condition is presented by linear matrix inequalities. The proposed event-triggered proportional-derivative control and event-triggering condition are verified with numerical simulation. ? 2017 The Author(s).111Ysciescopu

Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Dynamics analysis and integrated design of real-time control systems

Real-time control systems are widely deployed in many applications. Theory and practice for the design and deployment of real-time control systems have evolved significantly. From the design perspective, control strategy development has been the focus of the research in the control community. In order to develop good control strategies, process modelling and analysis have been investigated for decades, and stability analysis and model-based control have been heavily studied in the literature. From the implementation perspective, real-time control systems require timeliness and predictable timing behaviour in addition to logical correctness, and a real-time control system may behave very differently with different software implementations of the control strategies on a digital controller, which typically has limited computing resources. Most current research activities on software implementations concentrate on various scheduling methodologies to ensure the schedulability of multiple control tasks in constrained environments. Recently, more and more real-time control systems are implemented over data networks, leading to increasing interest worldwide in the design and implementation of networked control systems (NCS). Major research activities in NCS include control-oriented and scheduling-oriented investigations. In spite of significant progress in the research and development of real-time control systems, major difficulties exist in the state of the art. A key issue is the lack of integrated design for control development and its software implementation. For control design, the model-based control technique, the current focus of control research, does not work when a good process model is not available or is too complicated for control design. For control implementation on digital controllers running multiple tasks, the system schedulability is essential but is not enough; the ultimate objective of satisfactory quality-of-control (QoC) performance has not been addressed directly. For networked control, the majority of the control-oriented investigations are based on two unrealistic assumptions about the network induced delay. The scheduling-oriented research focuses on schedulability and does not directly link to the overall QoC of the system. General solutions with direct QoC consideration from the network perspective to the challenging problems of network delay and packet dropout in NCS have not been found in the literature. This thesis addresses the design and implementation of real-time control systems with regard to dynamics analysis and integrated design. Three related areas have been investigated, namely control development for controllers, control implementation and scheduling on controllers, and real-time control in networked environments. Seven research problems are identified from these areas for investigation in this thesis, and accordingly seven major contributions have been claimed. Timing behaviour, quality of control, and integrated design for real-time control systems are highlighted throughout this thesis. In control design, a model-free control technique, pattern predictive control, is developed for complex reactive distillation processes. Alleviating the requirement of accurate process models, the developed control technique integrates pattern recognition, fuzzy logic, non-linear transformation, and predictive control into a unified framework to solve complex problems. Characterising the QoC indirectly with control latency and jitter, scheduling strategies for multiple control tasks are proposed to minimise the latency and/or jitter. Also, a hierarchical, QoC driven, and event-triggering feedback scheduling architecture is developed with plug-ins of either the earliest-deadline-first or fixed priority scheduling. Linking to the QoC directly, the architecture minimises the use of computing resources without sacrifice of the system QoC. It considers the control requirements, but does not rely on the control design. For real-time NCS, the dynamics of the network delay are analysed first, and the nonuniform distribution and multi-fractal nature of the delay are revealed. These results do not support two fundamental assumptions used in existing NCS literature. Then, considering the control requirements, solutions are provided to the challenging NCS problems from the network perspective. To compensate for the network delay, a real-time queuing protocol is developed to smooth out the time-varying delay and thus to achieve more predictable behaviour of packet transmissions. For control packet dropout, simple yet effective compensators are proposed. Finally, combining the queuing protocol, the packet loss compensation, the configuration of the worst-case communication delay, and the control design, an integrated design framework is developed for real-time NCS. With this framework, the network delay is limited to within a single control period, leading to simplified system analysis and improved QoC