GENERATING CHAOS VIA FEEDBACK CONTROL FROM A STABLE TS FUZZY SYSTEM THROUGH A SINUSOIDAL NONLINEARITY

2002 ◽  
Vol 12 (10) ◽  
pp. 2283-2291 ◽  
Author(s):  
ZHONG LI ◽  
JIN BAE PARK ◽  
GUANRONG CHEN ◽  
YOUNG HOON JOO ◽  
YOON HO CHOI
Keyword(s):  
Feedback Control ◽  
Fuzzy System ◽  
Controller Design ◽  
State Feedback Control ◽  
Small Magnitude ◽  
Controlled System ◽  
Bounded State ◽  
System States ◽  
Takagi Sugeno ◽  
Uniformly Bounded

An approach is proposed for making chaotic a given stable Takagi–Sugeno (TS) fuzzy system using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.

Adaptive state feedback control for nonlinear systems with multiple interval time-varying delays and non-symmetric dead-zone input: A Lyapunov-Krasovskii approach

2019 ◽  
Vol 41 (14) ◽  
pp. 3979-3990
Author(s):  
Wei Zheng ◽  
Zhiming Zhang ◽  
Hongbin Wang ◽  
Shuhuan Wen ◽  
Hongrui Wang
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Controller Design ◽  
Dead Zone ◽  
Nonlinear Function ◽  
State Feedback Control ◽  
Time Varying ◽  
Interval Time ◽  
System States ◽  
The Stability

This paper addresses the stability analysis and adaptive state feedback control for a class of nonlinear discrete-time systems with multiple interval time-varying delays and non-symmetric dead-zone input. The multiple interval time-varying delays uncertainties are bounded by the nonlinear function with unknown coefficients. The non-symmetric dead-zone input without the knowledge of the dead-zone parameters is considered for the nonlinear system. The smooth adaptive state feedback controller is designed. By introducing the new Lyapunov-Krasovskii functional, it can be seen that the solutions of the closed-loop error system converge to an adjustable bounded region. In general, the proposed adaptive state feedback control strategy does not require the knowledge of maximum and minimum values for the characteristic slopes, and the knowledge of all system states. The control design conditions are relaxed because the system output is available for the controller design. Finally, three simulation examples are performed to show the effectiveness of the proposed methods.

A tube-based robust MPC for duty-cycled rotation needle steering systems with bounded disturbances

2021 ◽  
pp. 014233122110430
Author(s):  
Zhi Qi ◽  
Qianyue Luo ◽  
Hui Zhang
Keyword(s):  
Model Predictive Control ◽  
Linear Model ◽  
Predictive Control ◽  
Control Method ◽  
Controller Design ◽  
Control Approach ◽  
Bounded State ◽  
Non Linear ◽  
System States ◽  
Trajectory Tracking Controller

In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios.

scholarly journals A Systematic Controller Design for a Photovoltaic Generator with Boost Converter Using Integral State Feedback Control

2019 ◽  
Vol 9 (2) ◽  
pp. 4030-4036 ◽  
Author(s):  
Z. R. Labidi ◽  
H. Schulte ◽  
A. Mami
Keyword(s):  
Feedback Control ◽  
State Space ◽  
State Feedback ◽  
Controller Design ◽  
State Space Model ◽  
Boost Converter ◽  
State Feedback Control ◽  
Solar Irradiation ◽  
Photovoltaic Array ◽  
Pv Generator

In this paper, a systematic controller design for a photovoltaic generator with boost converter using integral state feedback control is proposed. It is demonstrated that the state–space feedback enables the extraction of maximum available power under variable loads. For this purpose, a control-oriented state-space model of a photovoltaic array connected to a DC load by a boost converter is derived. This model is then linearized by one working point, but no further simplifications are made. The design-oriented model contains the dynamics of PV generator, boost converter, and the load. The controller design is based on the augmented model with an integral component. The controller is validated by a detailed plant model implemented in Simscape. The robustness of the controller with variable solar irradiation and DC load changes is demonstrated.

Current controller design for DFIG‐based wind turbines using state feedback control

2019 ◽  
Vol 13 (11) ◽  
pp. 1938-1948 ◽  
Author(s):  
Ahmed G. Abo‐Khalil ◽  
Ali Alghamdi ◽  
I. Tlili ◽  
Ali M. Eltamaly
Keyword(s):  
Feedback Control ◽  
Wind Turbines ◽  
State Feedback ◽  
Controller Design ◽  
State Feedback Control ◽  
Current Controller

Rule Reduction and Robust Control of Generalized Takagi-Sugeno Fuzzy Systems

2000 ◽  
Vol 4 (5) ◽  
pp. 373-379 ◽  
Author(s):  
Tadanari Taniguchi ◽  
◽  
Kazuo Tanaka ◽  
Keyword(s):  
Robust Control ◽  
Model Reduction ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Controller Design ◽  
Main Idea ◽  
Linear Matrix ◽  
Robust Controller ◽  
Reduction Error ◽  
Takagi Sugeno

This paper presents model reduction and robust control using a generalized form of Takagi-Sugeno fuzzy systems. We first define a generalized form of TakagiSugeno fuzzy systems. The generalized form has a decomposed structure for each element of <I>Ai</I> and <I>Bi</I> matrices in consequent parts. The key feature of this structure is that it is suitable for reducing the number of rules. Conditions to reduce the number of rules are represented in terms of linear matrix inequality (LMIs). The main idea is to find a structure of if-then rules of the reduced model that agrees well with dynamics of the original model. Furthermore, we estimate the lower bound of the norm of model uncertainty of the Takagi-Sugeno fuzzy system that can cover the reduction error. Finally, we present an example of model reduction and robust control for a nonlinear system. In this example, we achieve a robust controller design to compensate for the uncertainly of the Takagi-Sugeno fuzzy system.

CHAOTIFICATION OF DISCRETE DYNAMICAL SYSTEMS IN BANACH SPACES

2006 ◽  
Vol 16 (09) ◽  
pp. 2615-2636 ◽  
Author(s):  
YUMING SHI ◽  
PEI YU ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Banach Spaces ◽  
Original System ◽  
Real Space ◽  
Discrete Dynamical Systems ◽  
State Feedback Control ◽  
Controlled System ◽  
Partial Difference ◽  
Finite Dimensional

This paper is concerned with chaotification of discrete dynamical systems in Banach spaces via feedback control techniques. A criterion of chaos in Banach spaces is first established. This criterion extends and improves the Marotto theorem. Discussions are carried out in general and some special Banach spaces. All the controlled systems are proved to be chaotic in the sense of both Devaney and Li–Yorke. As a consequence, a controlled system described in a finite-dimensional real space studied by Wang and Chen is shown chaotic not only in the sense of Li–Yorke but also in the sense of Devaney. The original system can be driven to be chaotic by using an arbitrarily small-amplitude state feedback control in a certain space. In addition, the Chen–Lai anti-control algorithm via feedback control with mod-operation in a finite-dimensional real space is extended to a certain infinite-dimensional Banach space, and the controlled system is shown chaotic in the sense of Devaney as well as in the sense of both Li–Yorke and Wiggins. Differing from many existing results, it is not here required that the map corresponding to the original system has a fixed point in some cases. An application of the theoretical results to a class of first-order partial difference equations is given with some numerical simulations.

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