Stability analysis of interval type-2 sampled-data polynomial fuzzy-model-based control system with a switching control scheme

The stability of an interval type-2 (IT2) sampled-data (SD) polynomial fuzzy-model-based control system with a switching control scheme is studied in this paper. The uncertain nonlinear plant is depicted via an IT2 polynomial fuzzy model. To realize control, a switching IT2SD polynomial fuzzy controller is generated. This paper adopts a switching control scheme with a variable sampling period. The modeling domain consists of several sub-domains, and each sub-domain corresponds to a local IT2SD polynomial fuzzy controller. These local IT2SD polynomial fuzzy controllers form the switching IT2SD polynomial fuzzy controller. To aid in the stability analysis, this paper adopts a looped-functional-based technique. The imperfect premise matching concept is brought in to solve the mismatch dilemma caused by the SD control strategy and uncertainties. For decreasing the conservativeness, this paper takes into account the state information as well as the information of IT2 membership functions. The stability analysis is performed for each sub-domain, providing the potential for further relaxation. As polynomials exist in the stability conditions, this paper employs the sum-of-squares method for the stability investigation. The simulation outcomes confirm the efficacy of the proposed method

Event-triggered control for rational and Lur’e type nonlinear systems

In the present work, the design of event-triggered controllers for two classes of nonlinear systems is addressed: rational systems and Lur’e type systems. Lyapunov theory techniques are used in both cases to derive asymptotic stability conditions in the form of linear matrix inequalities that are then used in convex optimization problems as means of computing the control system parameters aiming at a reduction of the number of events generated. In the context of rational systems, state-feedback control is considered and differentialalgebraic representations are used as means to obtain tractable stability conditions. An event-triggering strategy which uses weighting matrices to strive for less events is proposed and then it is proven that this strategy does not lead to Zeno behavior. In the case of Lur’e systems, observer-based state-feedback is addressed with event generators that have access only to the system output and observed state, but it imposes the need of a dwell-time, i.e. a time interval after each event where the trigger condition is not evaluated, to cope with Zeno behavior. Two distinct approaches, exact time-discretization and looped-functional techniques, are considered to ensure asymptotic stability in the presence of the dwell-time. For both system classes, emulation design and co-design are addressed. In the emulation design context, the control law (and the observer gains, when appropriate) are given and the task is to compute the event generator parameters. In the co-design context, the event generator and the control law or the observer can be simultaneously designed. Numerical examples are presented to illustrate the application of the proposed methods.Neste trabalho é abordado o projeto de controladores baseados em eventos para duas classes de sistemas não lineares: sistemas racionais e sistemas tipo Lur’e. Técnicas da teoria de Lyapunov são usadas em ambos os casos para derivar condições de estabilidade assintótica na forma de inequações matriciais lineares. Tais condições são então utilizadas em problemas de otimização convexa como meio de calcular os parâmetros do sistema de controle, visando uma redução no número de eventos gerados. No contexto de sistemas racionais, realimentação de estados é considerada e representações algébrico-diferenciais são usadas como meio de obter condições de estabilidade tratáveis computacionalmente. Uma estratégia de disparo de eventos que usa uma medida de erro ponderado através de matrizes definidas positivas é proposta e é demonstrado que tal estratégia não gera comportamento de Zenão. No caso de sistemas tipo Lur’e, considera-se o caso de controladores com restrições de informações, a saber, com acesso apenas às saídas do sistema. Um observador de estados é então utilizado para recuperar a informação faltante. Neste contexto, é necessária a introdução de um tempo de espera (dwell time, em inglês) para garantir a inexistência de comportamento de Zenão. Todavia, a introdução do tempo de espera apresenta um desafio adicional na garantia de estabilidade que é tratado neste trabalho considerando duas técnicas possíveis: a discretização exata do sistema e o uso de looped-functionals (funcionais em laço, em uma tradução livre). Para ambas classes de sistemas, são tratados os problemas de projeto por emulação e co-design (projeto simultâneo, em uma tradução livre). No projeto por emulação, a lei de controle (e os ganhos do observador, quando apropriado) são dados a priori e a tarefa é projetar os parâmetros do gerador de eventos. No caso do co-design, o gerador de eventos e a lei de controle ou o observador são projetados simultaneamente. Exemplos numéricos são usados para ilustrar a aplicação dos métodos propostos

Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

A delay-product-type Lyapunov functional approach for enhanced synchronization of chaotic Lur'e systems using a quantized controller

The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones

Survey on time-delay approach to networked control

This paper provides a survey on time-delay approach to networked control systems (NCSs). The survey begins from a brief summary on fundamental network-induced issues in NCSs and the main approaches to the modelling of NCSs. In particular, a comprehensive introduction to time-delay approach to sampled-data and networked control is provided. Then, recent results on time-delay approach to event-triggered control are recalled. The survey highlights time-delay approach developed to modelling, analysis and synthesis of NCSs, under communication constraints, with a particular focus on Round-Robin, Try-once-discard and stochastic protocols. The time-delay approach allows communication delays to be larger than the sampling intervals in the presence of scheduling protocols. Moreover, some results on networked control of distributed parameter systems are surveyed. Finally, conclusions and some future research directions are briefly addressed