Умовно стійкі системи з фазі-регулятором

Розглянуто нелінійну динамічну систему n-го порядку, для якої побудовано нечіткий регулятор типу Такагі-Сугено. Встановлено критерій стійкості, що не залежить від виду функції перемикання, для системи 2 – 5 порядків, для яких відома передавальна функція.Рассмотрена нелинейная динамическая система n-го порядка, для которой построен нечёткий регулятор типа Такаги-Сугено. Установлен критерий устойчивости, который не зависит от вида функции переключения для систем 2 – 5 порядков, для которых известна передаточная функция.Nonlinear dynamic system of n-th order is considered. Takagi-Sugeno fuzzy control is constructed for it. Stability criterion is presented which does not depend on the type of switching function for the 2 – 5 order systems for which the transfer function is known

Neural feedback linearization adaptive control for affine nonlinear systems based on neural network estimator

In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system

A CENTER MANIFOLD THEORY-BASED APPROACH TO THE STABILITY ANALYSIS OF STATE FEEDBACK TAKAGI-SUGENO-KANG FUZZY CONTROL SYSTEMS

The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system

Stability analysis of the simplest Takagi-Sugeno fuzzy control system using circle criterion

In this paper, we present two sufficient conditions in the frequency domain for the global stability analysis of the simplest Takagi-Sugeno (T-S) fuzzy control system, based on the circle criterion and its graphical interpretation. These conditions are significant in graphically designing the simplest T-S fuzzy controller in the frequency domain. Four numerical examples are provided to demonstrate the efficiency of our two frequency domain-based conditions. Furthermore, this T-S fuzzy controller and the linear proportional controllers are also compared. It is concluded that the simplest T-S fuzzy controller can outperform the linear proportional controllers in a noisy environment with external disturbances. © 2007 Elsevier Inc. All rights reserved