Search results for "fuzzy system"
showing 10 items of 20 documents
Asymptotic comparison of the implicative fragments of certain fuzzy logics
2022
An asymptotic similarity of some fragments of two fuzzy logics is proved. We focus on two 3-valued fuzzy logics: the Gödel-Dummett one and the Łukasiewicz one and we consider their purely implicative fragments of two variables. This paper shows the existence of the densities of truth of these logics and determines their values. For this purpose we build the appropriate Tarski-Lindenbaum algebra and use extensively generating functions. Our method can be generalized to n-valued logics, n > 3, but all computations will be extremely complicated.
Finite-Time Hâ Filtering for T-S Fuzzy Discrete-Time Systems with Time-Varying Delay and Norm-Bounded Uncertainties
2015
In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are propose…
Neural Petri Control: an application on a mobile robot
2006
In the present work, an innovative nonlinear controller of nonholonomic mechanical systems, characterized by a dynamic not well known model a priori, using a new neural model obtained by the combination of a Petri net with a neural network, is proposed. The performances of the control algorithm are evaluated for tasks of tracking of time trajectories. The study of the stability of the total system to closed loop is based on the Lyapunov theory. Simulation experiments, made taking into consideration a nonholonomic mobile robot, to two wheels, allowed to verify the theoretical results.
On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems
2014
This paper deals with the problem of robust stability and robust stabilization for a class of continuous-time singular Takagi-Sugeno fuzzy systems. Sufficient conditions on stability and stabilization are proposed in terms of strict LMI (Linear Matrix Inequality) for uncertain T-S fuzzy models. In order to reduce the conservatism of results developed using quadratic method, an approach based on non-quadratic Lyapunov functions and S-procedure is proposed. Illustrative examples are given to show the effectiveness of the given results Refereed/Peer-reviewed
Design on fuzzy control for a class of stochastic nonlinear systems
2014
The problem of Hankel-norm output feedback control is solved for a class of T-S fuzzy stochastic systems. The dynamic output feedback controller design technique is proposed by employing fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms Refereed/Peer-reviewed
Novel Stability Criteria for T--S Fuzzy Systems
2014
In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature. Then, new membership-dependent stability conditions are developed by the new Lyapunov function approach. It is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical resul…
Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes
2008
Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The result…
Probabilistic Fuzzy Approach to Evaluation of Logistics Service Effectiveness
2014
Received: 9 September 2014 Abstract Accepted: 11 October 2014 Logistics service providers offer a whole or partial logistics business service over a certain time period. Between such companies, the effectiveness of specific logistics services can vary. Logistics service providers seek the effective performance of logistics service. The purpose of this paper is to present a new approach for the evaluation of logistics service effectiveness, along with a specific computer system implementing the proposed approach – a sophisticated inference system, an extension of the Mamdani probabilistic fuzzy system. The paper presents specific knowledge concerning the relationships between effectiveness i…
Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach
2009
Classical Takagi-Sugeno (T-S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T-S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is…
Stability and l1-gain analysis for positive 2D T–S fuzzy state-delayed systems in the second FM model
2014
This paper considers the problems of delay-dependent stability and l"1-gain analysis for a class of positive two-dimensional (2D) Takagi-Sugeno (T-S) fuzzy linear systems with state delays described by the second FM model. Firstly, the co-positive type Lyapunov function method is applied to establish sufficient conditions of asymptotical stability for the addressed positive 2D T-S fuzzy system. Then, the l"1-gain performance analysis for the positive 2D T-S fuzzy delayed system is studied. All the obtained results are formulated in the form of linear matrix inequalities (LMIs) which are computationally tractable. Finally, an illustrative example is given to verify the effectiveness of the p…