Approximation Property Of Fuzzy Systems Research Articles

Adaptive Fuzzy Velocity Field Control for Navigation of Nonholonomic Mobile Robots

This paper presents a novel contour tracking scheme based on a well-posed kinematic representation of differential-driven nonholonomic mobile robots. Firstly, a fuzzy aggregation of spatial sets in cluttered environments allows designing a velocity field to encode the desired velocity vector pointing to the target (the contour). Thus, the resultant smooth trajectory avoids obstacles by combining spatially distributed velocity fields that enable the robot navigation. Finally, the universal approximation property of fuzzy systems facilitates the design of an adaptive PI-like controller, whose closed-loop stability leads to the precise tracking of the velocity field. The results of the performed numerical simulations illustrate the reliability of the proposed scheme.

Opto-electronic platform tracking control of multi-rotor unmanned aerial vehicles based on composite disturbance compensation

Airborne opto-electronic platforms are very important in unmanned aerial vehicle systems. The stability and tracking performance of airborne opto-electronic platforms are easily affected by disturbance factors, making compensating for those disturbances a very prominent issue. In this paper, compared to the traditional disturbance observer, an improved velocity signal based disturbance observer (IVDOB) is particularly designed to compensate for the disturbance. Then its capability, robustness, and stability are discussed. For improving the stabilization accuracy and tracking performance of airborne opto-electronic platforms, the universal approximation property of fuzzy systems is used to compensate the disturbance further and an adaptive fuzzy control system based on IVDOBs is proposed. To validate the scheme, a series of experiments were carried out. The results show that the proposed control scheme can achieve reliable control precision and satisfy the requirements of airborne opto-electronic platform tasks.

Adaptive Fuzzy Decentralized Control for a Class of Strong Interconnected Nonlinear Systems With Unmodeled Dynamics

The state-feedback decentralized stabilization problem is considered for interconnected nonlinear systems in the presence of unmodeled dynamics. The functional relationship in affine form between the strong interconnected functions and error signals is established, which makes backstepping-based fuzzy control successfully generalized to strong interconnected nonlinear systems. By combining adaptive control with both backstepping design and the approximation property of fuzzy systems, an adaptive decentralized control algorithm is developed. It is demonstrated by both theoretical analysis and simulation study that the proposed control strategy ensures semiglobally uniformly ultimately bounded of all signals within the closed-loop systems.

Adaptive decentralized fuzzy output feedback tracking control for a class of nonlinear large-scale systems with input delays

In this paper, the decentralized tracking control problem of nonlinear large-scale systems with immeasurable states and unknown nonlinearities in each subsystem and their interconnections subject to input delays is proposed. Based on the universal approximation properties of fuzzy systems, a fuzzy observer is designed to estimate the inaccessible states of the system. Subsequently, by defining the appropriate change of coordinates and employing the backstepping technique, an adaptive fuzzy backstepping output feedback control scheme is proposed for nonlinear interconnected systems subject to input delays. Owing to the problem of so-called explosion of complexity that inherently arises in the design procedures of the traditional backstepping technique, an adaptive fuzzy dynamic surface output feedback control approach is also presented for this class of large-scale systems. Moreover, it is shown that the two proposed adaptive decentralized fuzzy observer-based control approaches ensure all the signals of the closed loop system uniformly ultimately bounded and the norms of the tracking errors as well as the norms of the observation errors can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are carried out on the chemical reactor recycle system to illustrate and compare the effectiveness of the two proposed approaches.

Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities

An observer-based output feedback adaptive fuzzy controller is proposed to stabilize a class of uncertain chaotic systems with unknown time-varying time delays, unknown actuator nonlinearities and unknown external disturbances. The actuator nonlinearity can be backlash-like hysteresis or dead-zone. Based on universal approximation property of fuzzy systems the unknown nonlinear functions are approximated by fuzzy systems, where the consequent parts of fuzzy rules are tuned with adaptive schemes. The proposed method does not need the availability of the states and an observer based output feedback approach is proposed to estimate the states. To have more robustness and at the same time to alleviate chattering an adaptive discontinuous structure is suggested. Semi-global asymptotic stability of the overall system is ensured by proposing a suitable Lyapunov–Krasovskii functional candidate. The approach is applied to stabilize the time-delayed Lorenz chaotic system with uncertain dynamics amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of coping well with the modeling uncertainties, nonlinearities in actuators, unknown time-varying time-delays and unknown external disturbances while maintaining asymptotic convergence.

Design of an Adaptive Fuzzy Estimator for Force/Position Tracking in Robot Manipulators

This paper presents a stable new algorithm for force/position con- trol in robot manipulators. In this algorithm, position vectors are measured by sensors and then used in the control law. Since using force sensor has some issues such as high costs and technical problems, an approach is presented to overcome these issues. In this respect, force sensor is replaced by an adaptive fuzzy estimator to estimate the external force based on position and veloc- ity measurements. In this approach, force can be properly estimated using universal approximation property of fuzzy systems. Therefore, robots can be controlled in dierent environments even when no exact mathematical model is available. Since this approach is adaptive, accuracy of the system can be improved with time. Through a theorem the stability of the control system is analyzed using Lyapunov direct method. At last, satisfactory performances of the proposed approach are veried via some numerical simulations and the results are compared with some previous approaches.

Adaptive Fuzzy Sliding Mode Control Based on Genetic Optimization for Rotary Steering Drilling Stabilized Platform

Considering the robust control of stabilized platform of rotary steering drilling system, an adaptive fuzzy sliding mode control strategy based on genetic optimization is presented. Firstly, the universal approximation property of fuzzy system is used to approximate the uncertain external disturbance upper bound of stabilized platform under wording condition. Subsequently, sliding mode controller is designed to guarantee the robustness of the closed-loop system and sign function is replaced by bipolar sigmoid function to weaken chattering. Finally, genetic algorithm (GA) is applied to search the optimal controller parameters, including switching function coefficient, membership function of fuzzy system, adaptive coefficient of fuzzy system and sigmoid function coefficient. Simulation results show that this control strategy can make stabilized platform achieve optimal control performance and robustness.

Approximation properties of fuzzy systems for smooth functions and their first-order derivative

The problem of simultaneous approximations of a given function and its derivatives, has been addressed frequently in pure and applied mathematics. In pure mathematics, Bernstein polynomials get their importance from the fact that they provide simultaneous approximation of a function and its derivatives. In neural network theory, feedforward networks were shown to be universal approximators of an unknown function and its derivatives. In this paper, we consider fuzzy logic systems with the membership functions of each input variables are chosen as the translations and dilations of one appropriately fixed function. We prove, by a constructive proof based on discretization of the convolution operator, that under certain conditions made on the input variables membership functions, fuzzy logic systems of Sugeno type are universal approximators of a given function and its derivatives.

The fuzzy rule-base solution of differential equations

The equivalence between differential equation models and fuzzy logic models is demonstrated for a certain family of fuzzy systems—those which use fuzzy spline wavelets as membership functions. The universal approximation property of fuzzy systems built with spline wavelets is exploited for replacing operational representations of differential equations with sparse matrix equations. The solution of the matrix equations has a direct interpretation as a set of fuzzy rules. The fuzzy rule base thus generated provides an approximate solution to the original differential equation while retaining the explanatory power of fuzzy systems. The proposed method enjoys the excellent numerical and computational characteristics of the fast wavelet transform.

Approximation properties of fuzzy systems generated by the min inference

This paper discusses the approximation properties of fuzzy systems generated by the min inference. Firstly, the paper analyzes the properties of fuzzy basis functions (FBFs); Then based on the properties of FBPs, several basic approximation properties concerning approximation mechanisms, uniform approximation bounds, uniform convergency, and universal approximation are obtained. Further, the similarity and difference between the fuzzy systems generated by the product inference and by the min inference are discussed.

Approximation theory of fuzzy systems-MIMO case

In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FBF's) and present several properties of FBF's. Based on these properties of FBF's, we obtain several basic approximation properties of fuzzy systems: 1) basic approximation property which reveals the basic approximation mechanism of fuzzy systems; 2) uniform approximation bounds which give the uniform approximation bounds between the desired (control or decision) functions and fuzzy systems; 3) uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions; and 4) universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect. The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Approximation theory of fuzzy systems-SISO case

In this paper, the approximation problem of SISO fuzzy systems is discussed. Based on the fact that fuzzy systems can be represented by a linear combination of fuzzy basic functions (FBF's), we first give a systematic and detailed analysis of FBF's and present five properties of FBF's: structure similarity and compatibility between the membership functions and FBF's, complementarity and less fuzziness of FBF's, and composition of fuzzy systems. These properties provide a clear picture of the shape and features of FBF's. Based on these properties of FBF's, we obtain some basic approximation properties of fuzzy systems: basic approximation property, uniform approximation property, uniform convergent property and universal approximation property. These results reveal the basic approximation mechanism of fuzzy systems and verify a few basic ideas in the design of fuzzy systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>