Fuzzy remodeling and synchronization of nonlinear systems

2021 ◽  
Author(s):  
Y.V. Talagaev
Keyword(s):  
Nonlinear Systems ◽  
Parametric Uncertainty ◽  
Synchronization Problem ◽  
Candidate Solution ◽  
Initial Task ◽  
Wide Range ◽  
Non Linear ◽  
Behavior Systems ◽  
Fuzzy Description ◽  
Takagi Sugeno

Synchronization is one of the crucial control problems in coordinated behavior systems. A wide range of applications necessitates the development and improvement of approaches to solving the linearization problem for non-linear systems with complex behavior. Hence the paper offers an approach to solving the problem of chaotic system coordinate synchronization based on the use of fuzzy remodeling and superstability conditions. It is shown that transition from general (non-linear) synchronization problem statement to fuzzy description with fuzzy Takagi-Sugeno models allows transforming the initial task to a well understood problem of fuzzy T-S system stabilization that describes the dynamics synchronization error. As a candidate solution for the problem we offer a way of implementing superstability conditions that reduce the task of finding fuzzy regulator to solving a linear programming task. It is shown that implementation of superstability conditions not only presents a simple way of solving the problem, but also has practical value. Superstability provides the monotonesness of the transient process of synchronization without sharp spikes of solution norm. The efficiency of the offered approach is demonstrated by the example of synchronization of two hyperchaotic systems. To prove the efficiency of superstability conditions the solution of the robust synchronization problem with parametric uncertainty in system matrices is given. The presented results can be applied for synchronization of various nonlinear systems demonstrating chaotic dynamics.

Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model

2019 ◽  
Vol 41 (15) ◽  
pp. 4218-4229 ◽  
Author(s):  
Alireza Navarbaf ◽  
Mohammad Javad Khosrowjerdi
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Wide Range ◽  
Satisfy Lipschitz Condition ◽  
Unknown Disturbances ◽  
Takagi Sugeno

In this paper, a new design approach to construct a fault-tolerant controller (FTC) with fault estimation capability is proposed using a generalized Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems in the presence of actuator faults and unknown disturbances. The generalized T-S fuzzy model consists of some local models with multiplicative nonlinear terms that satisfy Lipschitz condition. Besides covering a very wide range of nonlinear systems with a smaller number of local rules in comparison with the conventional T-S fuzzy model and hence having less computational burden, the existence of the multiplicative nonlinear term solves the uncontrollability issues that the other generalized T-S fuzzy models with additive nonlinear terms dealt with. A state/fault observer designed for the considered generalized T-S fuzzy model and then, a dynamic FTC law based on the estimated fault information is proposed and sufficient design conditions are given in terms of linear matrix inequalities (LMIs). It can be shown that the number of LMIs are less than that of previously proposed methods and then feasibility of our method is more likely. The effectiveness of the proposed FTC approach is verified using a nonlinear mass-spring-damper system.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

scholarly journals Fault diagnosis for Takagi-Sugeno nonlinear systems

2009 ◽  
Vol 42 (8) ◽  
pp. 504-509 ◽  
Author(s):  
Dalil Ichalal ◽  
Benoit Marx ◽  
José Ragot ◽  
Didier Maquin
Keyword(s):  
Fault Diagnosis ◽  
Nonlinear Systems ◽  
Takagi Sugeno

scholarly journals Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

2021 ◽  
Author(s):  
Chao Ma ◽  
Liziyi Hao ◽  
Hang Fu
Keyword(s):  
Neural Network ◽  
Hidden Markov ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Markov Jump ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
The Neural Network ◽  
Takagi Sugeno

AbstractThis paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval

2011 ◽  
Vol 34 (7) ◽  
pp. 841-849 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markov Jump ◽  
Non Linear ◽  
Robust Controllability ◽  
Jump Systems ◽  
Takagi Sugeno

In this paper we study the robust control problems with respect to the finite-time interval of uncertain non-linear Markov jump systems. By means of Takagi–Sugeno fuzzy models, the overall closed-loop fuzzy dynamics are constructed through selected membership functions. By using the stochastic Lyapunov–Krasovskii functional approach, a sufficient condition is firstly established on the stochastic robust finite-time stabilization. Then, in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of the stochastic finite-time controller are presented and proved. Finally, the design problem is formulated as an optimization one. The simulation results illustrate the effectiveness of the proposed approaches.

Calculation of Nonlinear Systems Under Narrow Band Excitation Using Equivalent Linearization and Path Continuation

2021 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt
Keyword(s):  
Nonlinear Systems ◽  
Narrow Band ◽  
Gaussian White Noise ◽  
Random Excitation ◽  
Mean Value ◽  
Equivalent Linearization ◽  
Efficient Procedure ◽  
Stochastic Excitations ◽  
Wide Range ◽  
The One

Abstract Turbomachines experience a wide range of different types of excitation during operation. On the structural mechanics side, periodic or even harmonic excitations are usually assumed. For this type of excitation there are a variety of methods, both for linear and nonlinear systems. Stochastic excitation, whether in the form of Gaussian white noise or narrow band excitation, is rarely considered. As in the deterministic case, the calculations of the vibrational behavior due to stochastic excitations are even more complicated by nonlinearities, which can either be unintentionally present in the system or can be used intentionally for vibration mitigation. Regardless the origin of the nonlinearity, there are some methods in the literature, which are suitable for the calculation of the vibration response of nonlinear systems under random excitation. In this paper, the method of equivalent linearization is used to determine a linear equivalent system, whose response can be calculated instead of the one of the nonlinear system. The method is applied to different multi-degree of freedom nonlinear systems that experience narrow band random excitation, including an academic turbine blade model. In order to identify multiple and possibly ambiguous solutions, an efficient procedure is shown to integrate the mentioned method into a path continuation scheme. With this approach, it is possible to track jump phenomena or the influence of parameter variations even in case of narrow band excitation. The results of the performed calculations are the stochastic moments, i.e. mean value and variance.

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