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

A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Copyright [2004] 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.Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked

Fuzzy-model-based robust fault detection with stochastic mixed time-delays and successive packet dropouts

This is the Post-Print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEThis paper is concerned with the network-based robust fault detection problem for a class of uncertain discrete-time Takagi–Sugeno fuzzy systems with stochastic mixed time delays and successive packet dropouts. The mixed time delays comprise both the multiple discrete time delays and the infinite distributed delays. A sequence of stochastic variables is introduced to govern the random occurrences of the discrete time delays, distributed time delays, and successive packet dropouts, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fuzzy fault detection filter such that 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 fuzzy fault detection filters, and then, the corresponding solvability conditions for the desired filter gains are established. In addition, the optimal performance index for the addressed robust fuzzy fault detection problem is obtained by solving an auxiliary convex optimization problem. An illustrative example is provided to show the usefulness and effectiveness of the proposed design method.This work was supported in part by the National Natural Science Foundation of China under Grant 61028008, 60825303, 61004067, National 973 Project under Grant 2009CB320600, the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University), Ministry of Education, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the University of Hong Kong under Grant HKU/CRCG/200907176129 and the Alexander von Humboldt Foundation of Germany

A State Observer Design for Simultaneous Estimation of Charge State and Crossover in Self-Discharging Disproportionation Redox Flow Batteries

This paper presents an augmented state observer design for the simultaneous estimation of charge state and crossover flux in disproportionation redox flow batteries, which exhibits exponential estimation error convergence to a bounded residual set. The crossover flux of vanadium through the porous separator is considered as an unknown function of the battery states, model-approximated as the output of a persistently excited linear system. This parametric model and the simple isothermal lumped parameter model of the battery are combined to form an augmented space state representation suitable for the observer design, which is carried out via Lyapunov stability theory including the error-uncertainty involved in the approximation of the crossover flux. The observer gain is calculated by solving a polytopic linear matrix inequality problem via convex optimization. The performance of this design is evaluated with a laboratory flow battery prototype undergoing self-discharge.Comment: arXiv admin note: text overlap with arXiv:1903.0407

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper, the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput (MIMO) nonlinear systems in the presence of system uncertainties, unknown non-symmetric input saturation and external disturbances. Fuzzy logic systems (FLS) are used to approximate the system uncertainty of MIMO nonlinear systems. Then, the compound disturbance containing the approximation error and the time-varying external disturbance that cannot be directly measured are estimated via a disturbance observer. By appropriately choosing the gain matrix, the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set. This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications, in particular unknown non-symmetric input saturation and control singularity. Within this setting, the disturbance observer technique is combined with the FLS approximation technique to compensate for the effects of unknown input saturation and control singularity. Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques. Numerical simulation results are presented to illustrate the effectiveness of the proposed tracking control schemes