• Korean Journal of Computational Design and Engineering
• /
• v.17 no.4
• /
• pp.282-293
• /
• 2012

This paper presents an error-bounded B-spline fitting technique to approximate unorganized data within a prescribed error tolerance. The proposed approach includes two main steps: leastsquares minimization and error-bounded approximation. A B-spline hypervolume is first described as a data representation model, which includes its mathematical definition and the data structure for implementation. Then we present the least-squares minimization technique for the generation of an approximate B-spline model from the given data set, which provides a unique solution to the problem: overdetermined, underdetermined, or ill-conditioned problem. We also explain an algorithm for the error-bounded approximation which recursively refines the initial base model obtained from the least-squares minimization until the Euclidean distance between the model and the given data is within the given error tolerance. The proposed approach is demonstrated with some examples to show its usefulness and a good possibility for various applications.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.8 no.1
• /
• pp.31-40
• /
• 2004

In this paper we point out an approximation for the Fourier transform for functions of bounded variation and study the approximation error of certain associated quadrature rules.

• Korean Journal of Computational Design and Engineering
• /
• v.11 no.1
• /
• pp.1-10
• /
• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.5
• /
• pp.527-532
• /
• 2005

In this paper, we proposed an adaptive fuzzy sliding control for unknown nonlinear systems using estimation of bounds for approximation errors. Unknown nonlinearity of a system is approximated by the fuzzy logic system with a set of IF-THEN rules whose consequence parameters are adjusted on-line according to adaptive algorithms for the purpose of controlling the output of the nonlinear system to track a desired output. Also, using assumption that the approximation errors satisfy certain bounding conditions, we proposed the estimation algorithms of approximation errors by Lyapunov synthesis methods. The overall control system guarantees that the tracking error asymptotically converges to zero and that all signals involved in controller are uniformly bounded. The good performance of the proposed adaptive fuzzy sliding mode controller is verified through computer simulations on an inverted pendulum system.

• Journal of KIISE:Software and Applications
• /
• v.28 no.9
• /
• pp.681-687
• /
• 2001

In order to raise a class discrimination power by combining multiple classifiers under the Bayesian decision theory, the upper bound of a Bayes error rate bounded by the conditional entropy of a class variable and decision variables obtained from training data samples should be minimized. Wang and Wong proposed a tree dependence first-order approximation scheme of a high order probability distribution composed of the class and multiple feature pattern variables for minimizing the upper bound of the Bayes error rate. This paper presents an extended high order product approximation scheme dealing with higher order dependency more than the first-order tree dependence, based on the minimization of the upper bound of the Bayes error rate. Multiple recognizers for unconstrained handwritten numerals from CENPARMI were combined by the proposed approximation scheme using the Bayesian formalism, and the high recognition rates were obtained by them.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.634-637
• /
• 1994

This paper presents a CMAC network based controller on the basis of Lyapunov theory. CMAC network is employed to approximate and to compensate the uncertainties induced by inaccurate modelling of the system. For the improvement of robustness under the bounded disturbances and the approximation error of the CMAC, the adaptation scheme with a deadzone and an additional control input are developed.

• Proceedings of the KIEE Conference
• /
• 2003.11b
• /
• pp.187-190
• /
• 2003

In this paper, we address the robust adaptive backstepping controller using fuzzy neural network (FHIN) for a class of uncertain output feedback nonlinear systems with disturbance. A new algorithm is proposed for estimation of unknown bounds and adaptive control of the uncertain nonlinear systems. The state estimation is solved using K-fillers. All unknown nonlinear functions are approximated by FNN. The FNN weight adaptation rule is derived from Lyapunov stability analysis and guarantees that the adapted weight error and tracking error are bounded. The compensated controller is designed to compensate the FNN approximation error and external disturbance. Finally, simulation results show that the proposed controller can achieve favorable tracking performance and robustness with regard to unknown function and external disturbance.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.11 no.5
• /
• pp.1597-1600
• /
• 2010

In this paper, a direct controller for nonlinear plants using a neural network is presented. The composed of the control input by using RBF neural networks and auxiliary input to compensate for effects of the approximation errors and disturbances. In the results, using this scheme, the output tracking error between the plant and the reference model can asymptotically converge to zero in the presence of bounded disturbances and approximation errors. Simulation results show that it is very effective and can realize a satisfactory control of the nonlinear system.

• Journal of Institute of Control, Robotics and Systems
• /
• v.22 no.10
• /
• pp.779-787
• /
• 2016

A nonlinear control law for the quad-rotor of a low-complexity, global approximation-free from system uncertainties and external disturbances are described in this paper. The control law guarantees convergence to a small bounded error using a prescribed performance function. The stability of the proposed nonlinear control system is also proven by the Lyapunov stability theorem. The advantage of this technique is that it has a simpler form than any other nonlinear compensators and is applicable to any nonlinear systems without precise knowledge of the systems. In this paper, the proposed approach is applied to attitude/altitude control of a quad-rotor. Numerical simulations are performed to investigate the proposed nonlinear attitude control law by applying it to an uncertain quadcopter system with external disturbances.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.85.4-85
• /
• 2001

A learning controller is presented for repetitive walking motion of biped robot. The learning control scheme learns the approximate inverse dynamics input of biped walking robot and uses the learned input pattern to generate an input profile of different walking motion from that learnt. In the learning controller, the PID feedback controller takes part in stabilizing the transient response of robot dynamics while the feedforward learning controller plays a role in computing the desired actuator torques for feedforward nonlinear dynamics compensation in steady state. It is shown that all the error signals in the learning control system are bounded and the robot motion trajectory converges to the desired one asymptotically. The proposed learning control scheme is ...