Mehmet Önder Efe

An algorithm for fast convergence in training neural networks

In this work, two modifications on Levenberg-Marquardt (LM) algorithm for feedforward neural networks are studied. One modification is made on performance index, while the other one is on calculating gradient information. The modified algorithm gives a better convergence rate compared to the standard LM method and is less computationally intensive and requires less memory. The performance of the algorithm has been checked on several example problems.

Fractional Fuzzy Adaptive Sliding-Mode Control of a 2-DOF Direct-Drive Robot Arm

This paper presents a novel parameter adjustment scheme to improve the robustness of fuzzy sliding-mode control achieved by the use of an adaptive neuro-fuzzy inference system (ANFIS) architecture. The proposed scheme utilizes fractional-order integration in the parameter tuning stage. The controller parameters are tuned such that the system under control is driven toward the sliding regime in the traditional sense. After a comparison with the classical integer-order counterpart, it is seen that the control system with the proposed adaptation scheme displays better tracking performance, and a very high degree of robustness and insensitivity to disturbances are observed. The claims are justified through some simulations utilizing the dynamic model of a 2-DOF direct-drive robot arm. Overall, the contribution of this paper is to demonstrate that the response of the system under control is significantly better for the fractional-order integration exploited in the parameter adaptation stage than that for the classical integer-order integration.

A general backpropagation algorithm for feedforward neural networks learning

A general backpropagation algorithm is proposed for feedforward neural network learning with time varying inputs. The Lyapunov function approach is used to rigorously analyze the convergence of weights, with the use of the algorithm, toward minima of the error function. Sufficient conditions to guarantee the convergence of weights for time varying inputs are derived. It is shown that most commonly used backpropagation learning algorithms are special cases of the developed general algorithm.

A comparative study of neural network structures in identification of nonlinear systems

Abstract This paper investigates the identification of nonlinear systems by neural networks. As the identification methods, Feedforward Neural Networks (FNN), Radial Basis Function Neural Networks (RBFNN), Runge–Kutta Neural Networks (RKNN) and Adaptive Neuro Fuzzy Inference Systems (ANFIS) based identification mechanisms are studied and their performances are comparatively evaluated on a three degrees of freedom anthropomorphic robotic manipulator.

Proper orthogonal decomposition for reduced order modeling: 2D heat flow

Modeling issues of infinite dimensional system is studied in this paper. Although the modeling problem has been solved to some extent, use of decomposition techniques still poses several difficulties. A prime one of this is the amount of data to be processed. Method of snapshots integrated with POD is a remedy. The second difficulty is the fact that the decomposition followed by a projection yields an autonomous set of finite dimensional ODEs that is not useful for developing a concise understanding of the input operator of the system. A numerical approach to handle this issue is presented in this paper. As the example, we study 2D heat flow problem. The results obtained confirm the theoretical claims of the paper and emphasize that the technique presented here is not only applicable to infinite dimensional linear systems but also to nonlinear ones.

A hierarchical motion planning strategy for a uniform self-reconfigurable modular robotic system

Describes a multi-layered hierarchical motion planning strategy for a class of self-reconfigurable modular robotic systems, I-Cubes. The approach is based on the synthesis of motion on the basis of metacubes, which have a particular structure possessing 8 Cubes and 16 Links. The developed strategy organizes the metacube motions and the corresponding cube-level motions. At the lowest level, link motions are generated. The resulting system is demonstrated to be capable of performing a pre-specified task of moving from one position/shape to another. The paper describes the latest results of our planning strategy through some experimentally justified examples.

Variable structure control of a class of uncertain systems

This brief paper proposes a method for tuning the parameters of a variable structure controller. The approach presented extracts the error at the output of the controller and applies a nonlinear tuning law using this error measure. The adaptation mechanism drives the state tracking error vector to the sliding hypersurface and maintains the sliding mode. In the simulations, the approach presented has been tested on the control of Duffing oscillator and the analytical claims have been justified under the existence of measurement noise, uncertainty and large nonzero initial errors.

Autonomous quadrotor flight with vision-based obstacle avoidance in virtual environment

In this paper, vision-based autonomous flight with a quadrotor type unmanned aerial vehicle (UAV) is presented. Automatic detection of obstacles and junctions are achieved by the use of optical flow velocities. Variation in the optical flow is used to determine the reference yaw angle. Path to be followed is generated autonomously and the path following process is achieved via a PID controller operating as the low level control scheme. Proposed method is tested in the Google Earth(R) virtual environment for four different destination points. In each case, autonomous UAV flight is successfully simulated without observing collisions. The results show that the proposed method is a powerful candidate for vision based navigation in an urban environment. Claims are justified with a set of experiments and it is concluded that proper thresholding of the variance of the gradient of optical flow difference have a critical effect on the detectability of roads having different widths.

Low dimensional modelling and Dirichlét boundary controller design for Burgers equation

Modelling and boundary control for the Burgers equation is studied in this paper. Modelling has been done via processing of numerical observations through proper orthogonal decomposition (POD) with Galerkin projection. This results in a set of spatial basis functions together with a set of ordinary differential equations (ODEs) describing the temporal evolution. Since the dynamics described by the Burgers equation are non-linear, the corresponding reduced-order dynamics turn out to be non-linear. The presented analysis explains how the free boundary condition appears as a control input in the ODEs and how controller design can be accomplished. The issues of control system synthesis are discussed from the point of practicality, performance and robustness. The numerical results obtained are in good compliance with the theoretical claims. A comparison of various different approaches is presented.

Control input separation by actuation mode expansion for flow control problems

A control input separation method is proposed for reduced-order modelling in boundary control problems. The dynamics of flow systems are typically described by partial differential equations where the input affects the system through boundary conditions. From a control design perspective it is most desirable and natural to employ finite-dimensional representations in which the input enters the dynamics directly. The method proposed here to resolve the input from the boundary conditions is based on obtaining a proper orthogonal decomposition of the unforced flow of the system, and then augmenting this decomposition by optimally computed actuation modes, built using snapshots of the actuated flow. A reduced-order Galerkin model is then derived for this expansion, in which the input appears as an explicit term in the system dynamics. The model reduces exactly to the original baseline case under zero input conditions. The proposed method is then compared to an existing input separation technique, namely the sub-domain separation method. A boundary control example regarding the 2D incompressible Navier–Stokes equation is considered to illustrate the proposed method, where a controller is designed to achieve tracking of a desired 2D spatial profile for the flow velocity.