A generalised integral polynomial Lyapunov function for nonlinear systems

[EN] This work generalises the line-integral Lyapunov function in (Rhee and Won, 2006) for stability analysis of continuous-time nonlinear models expressed as fuzzy systems. The referred result applied only to Takagi¿Sugeno representations, and required memberships to be a tensor-product of functions of a single state; these are generalised here so that membership arguments can be arbitrary polynomials of the state variables; in this way, systems for which earlier results cannot be applied are now covered. Both the modelling and the integral terms appearing in the Lyapunov functions are generalised to a fuzzy polynomial case. Illustrative examples show the advantage of the proposed method against previous literature, even in the TS case.The authors gratefully to the financial support of Spanish ministry of Economy and European Union, grant DPI2016-81002-R (AEI/FEDER, UE), the CONACyT/COECyT Sonora scholarship 383252, and Project ITSON-PROFAPI-CA 2017-0088.Gonzalez-German, IT.; Sala, A.; Bernal Reza, MÁ. (2019). A generalised integral polynomial Lyapunov function for nonlinear systems. Fuzzy Sets and Systems. 356:77-91. https://doi.org/10.1016/j.fss.2018.02.005S779135

非線形システムに対する制御系設計と外乱抑制のための積分型リアプノフ関数アプローチ

電気通信大学202

Performance Guarantee of a Class of Continuous LPV System with Restricted-Model-Based Control

This paper considers the problem of the robust stabilisation of a class of continuous Linear Parameter Varying (LPV) systems under specifications. In order to guarantee the stabilisation of the plant with very large parameter uncertainties or variations, an output derivative estimation controller is considered. The design of such controller that guarantee desired  induced gain performance is examined. Furthermore, a simple procedure for achieving the  norm performance is proved for any all-poles single-input/single-output second order plant. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. Finally, the effectiveness of the proposed method is verified via a numerical example

Stabilization and local stability analysis of continuous-time nonlinear systems represented by Takagi-Sugeno fuzzy models

Orientadores: Pedro Luis Dias Peres, Ricardo Coração de Leão Fontoura de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Esta dissertação aborda os problemas de análise de estabilidade local, estimativa de região de atração e estabilização local por realimentação de estados para sistemas não lineares contínuos no tempo representados por modelos nebulosos Takagi-Sugeno (T¿S). Para certificar a estabilidade local e projetar o controlador, condições suficientes, expressas em termos de desigualdade matriciais lineares (do inglês, Linear Matrix Inequalities ¿ LMIs) dependentes de parâmetros são fornecidas, tendo como base matrizes de Lyapunov e variáveis de folga polinomiais homogêneas de grau arbitrário. Utilizando-se uma representação politópica para a derivada das funções de pertinência do modelo T¿S, evita-se a necessidade do estabelecimento de limitantes para a taxa de variação. Como contribuição adicional, propõe-se que termos não lineares da matriz Jacobiana associada ao modelo T¿S sejam substituídos, sempre que possível, pela correspondente série de Taylor truncada em uma ordem pré-determinada, evitando a definição de um novo conjunto de parâmetros incertos, o que aumentaria a complexidade da representação. Exemplos emprestados da literatura T¿S são utilizados para ilustrar que os métodos propostos fornecem melhores resultados que outras abordagens, em termos de maiores estimativas para as regiões de atração, tanto no caso de análise de estabilidade, quanto na síntese de controle estabilizante por realimentação de estados.Nesta dissertação também foi feito um estudo sobre o uso de programação linear, como alternativa aos resolvedores especializados em LMIs, para a análise de estabilidade de sistemas lineares incertosAbstract: This dissertation addresses the problems of local stability analysis, estimation of domains of attraction, and local state-feedback stabilization for continuous time nonlinear systems represented by Takagi-Sugeno (T¿S) fuzzy models. Sufficient conditions, expressed in terms of parameter-dependent Linear Matrix Inequalities (LMIs), are given to certify the local stability and for control design, based on homogenous polynomial Lyapunov matrices and slack variables of arbitrary degree. By using a polytopic representation for the time-derivative of the membership functions of the T-S model, upper bounds for the variation rates are not required. As an additional contribution, nonlinear terms of the Jacobian matrix associated with the T¿S model are replaced, whenever possible, by the corresponding Taylor series, truncated at a predetermined order, avoiding the definition of a new set of uncertain parameters, which would increase the complexity of the representation. Examples borrowed from the T¿S literature are used to illustrate that the proposed methods provide better results than other approaches in terms of larger estimates for the regions of attraction, both in the case of stability analysis and in the synthesis of state-feedback stabilizing controllers. A study about the use of linear programming, as an alternative to specialized LMI solvers, for stability analysis of uncertain linear systems is also included in the dissertationMestradoAutomaçãoMestra em Engenharia Elétrica132807/2018-12017/18785-5CNPQFAPES

Proposed Fuzzy Real-Time HaPticS Protocol Carrying Haptic Data and Multisensory Streams

Sensory and haptic data transfers to critical real-time applications over the Internet require better than best effort transport, strict timely and reliable ordered deliveries. Multi-sensory applications usually include video and audio streams with real-time control and sensory data, which aggravate and compress within real-time flows. Such real-time are vulnerable to synchronization to synchronization problems, if combined with poor Internet links. Apart from the use of differentiated QoS and MPLS services, several haptic transport protocols have been proposed to confront such issues, focusing on minimizing flows rate disruption while maintaining a steady transmission rate at the sender. Nevertheless, these protocols fail to cope with network variations and queuing delays posed by the Internet routers. This paper proposes a new haptic protocol that tries to alleviate such inadequacies using three different metrics: mean frame delay, jitter and frame loss calculated at the receiver end and propagated to the sender. In order to dynamically adjust flow rate in a fuzzy controlled manners, the proposed protocol includes a fuzzy controller to its protocol structure. The proposed FRTPS protocol (Fuzzy Real-Time haPticS protocol), utilizes crisp inputs into a fuzzification process followed by fuzzy control rules in order to calculate a crisp level output service class, denoted as Service Rate Level (SRL). The experimental results of FRTPS over RTP show that FRTPS outperforms RTP in cases of congestion incidents, out of order deliveries and goodput

A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

Measurements, Models, Systems and Design

531 s.