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

Integrated fault estimation and accommodation design for discrete-time Takagi-Sugeno fuzzy systems with actuator faults

This paper addresses the problem of integrated robust fault estimation (FE) and accommodation for discrete-time Takagi–Sugeno (T–S) fuzzy systems. First, a multiconstrained reduced-order FE observer (RFEO) is proposed to achieve FE for discrete-time T–S fuzzy models with actuator faults. Based on the RFEO, a new fault estimator is constructed. Then, using the information of online FE, a new approach for fault accommodation based on fuzzy-dynamic output feedback is designed to compensate for the effect of faults by stabilizing the closed-loop systems. Moreover, the RFEO and the dynamic output feedback fault-tolerant controller are designed separately, such that their design parameters can be calculated readily. Simulation results are presented to illustrate our contributions

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Starting with the baseline controller design, this paper proposes an integrated approach of active fault tolerant control based on proportional derivative extended state observer (PDESO) for linear parameter varying descriptor systems. The PDESO can simultaneously provide the estimates of the system states, sensor faults, and actuator faults. The L₂ robust performance of the closed-loop system to bounded exogenous disturbance and bounded uncertainty is achieved by a two-step design procedure adapted from the traditional observer-based controller design. Furthermore, an LMI pole-placement region and the L₂ robustness performance are combined into a multiobjective formulation by suitably combing the appropriate LMI descriptions. A parameter-varying system example is given to illustrate the design procedure and the validity of the proposed integrated design approach

Actuator and sensor fault estimation based on a proportional-integral quasi-LPV observer with inexact scheduling parameters

© 2019. ElsevierThis paper presents a method for actuator and sensor fault estimation based on a proportional-integral observer (PIO) for a class of nonlinear system described by a polytopic quasi-linear parameter varying (qLPV) mathematical model. Contrarily to the traditional approach, which considers measurable or unmeasurable scheduling parameters, this work proposes a methodology that considers inexact scheduling parameters. This condition is present in many physical systems where the scheduling parameters can be affected by noise, offsets, calibration errors, and other factors that have a negative impact on the measurements. A H8 performance criterion is considered in the design in order to guarantee robustness against sensor noise, disturbance, and inexact scheduling parameters. Then, a set of linear matrix inequalities (LMIs) is derived by the use of a quadratic Lyapunov function. The solution of the LMI guarantees asymptotic stability of the PIO. Finally, the performance and applicability of the proposed method are illustrated through a numerical experiment in a nonlinear system.Peer ReviewedPostprint (author's final draft

Finite-horizon estimation of randomly occurring faults for a class of nonlinear time-varying systems

This paper is concerned with the finite-horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time-varying. The faults are assumed to occur in a random way governed by two sets of Bernoulli distributed white sequences. The stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well-studied nonlinearities. The aim of the problem is to estimate the random faults, over a finite horizon, such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an H∞-norm in the mean square sense. By using the completing squares method and stochastic analysis techniques, necessary and sufficient conditions are established for the existence of the desired finite-horizon H∞ fault estimator whose parameters are then obtained by solving coupled backward recursive Riccati difference equations (RDEs). A simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method

Integrated fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems

This paper proposes an integrated fault estimation and fault-tolerant control (FTC) design for Lipschitz non-linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non-linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H∞ optimization with a single-step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single-link manipulator example is given to illustrate the effectiveness of the proposed approach