• International Journal of Control, Automation, and Systems
• /
• v.4 no.3
• /
• pp.293-301
• /
• 2006

A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well-known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.2562-2567
• /
• 2005

This paper suggests a new method discretization of nonlinear system using Taylor series expansion and zero-order hold assumption. This method is applied into the sampled-data representation of a nonlinear system with input time delay. Additionally, the delayed input is time varying and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. Them mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. And 'hybrid' discretization scheme that result from a combination of the ‘scaling and squaring' technique with the Taylor method are also proposed, especially under condition of very low sampling rates. The computer simulation proves the proposed algorithm discretized the nonlinear system with the variable time-delayed input accurately.

• Journal of Institute of Control, Robotics and Systems
• /
• v.13 no.6
• /
• pp.581-588
• /
• 2007

In this paper, we propose a delayed feedback guaranteed cost controller design method for linear time-delay systems with norm-bounded parameter uncertainties and nonlinear perturbations. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, an LMI optimization problem is formulated to design a controller such that the closed-loop cost function value is not more than a specified upper bound for all admissible system uncertainties and nonlinear perturbations. Numerical example show the effectiveness of the proposed method.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.50 no.7
• /
• pp.253-257
• /
• 2013

This paper proposes the robust observer design for nonlinear systems with delayed output and external disturbance. It is shown that by considering a nonlinear term of error dynamics as an additional state variable, the nonlinear error dynamics with time delay can be transformed into the linear one with time delay. Sufficient conditions for existence of a robust observer are characterized by linear matrix inequalities. Finally, an illustrative example is given in order to show the effectiveness of our design method.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.12 no.3
• /
• pp.239-245
• /
• 2002

In this Paper, we present a method for designing fuzzy $H_2/H_{\infty}$ controllers of delayed nonlinear systems with saturating input. Takagi-Sugeno fuzzy model is employed to represent delayed nonlinear systems with saturating input. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. And a sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is given in terms of linear matrix inequalities(LMIs). The designing fuzzy $H_2/H_{\infty}$ controllers minimize an upper bound on a linear quadratic performance measure. Finally, a design example of fuzzy $H_2/H_{\infty}$ controller for uncertain delayed nonlinear systems with saturating input.

• Proceedings of the KIEE Conference
• /
• 2007.04a
• /
• pp.89-91
• /
• 2007

In this paper, a new approach for a sampled-data representation of nonlinear system that has time-delayed multi-input is proposed. That is largely devoid of illconditioning and is suitable for any nonlinear problem. The new scheme is applied to nonlinear systems with two or three inputs; and then the delayed multi-input general equation is derived. The method is based on thematrix exponential theory. Itdoes not require excessive computational resources and lends itself to a short and robust piece of software that can be easily inserted into large simulation packages. A performance of the proposed method is evaluated using a nonlinear system with time-delay: maneuvering an automobile.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2004.07b
• /
• pp.1234-1238
• /
• 2004

A Controlled neural networks are proposed in order to measure nonlinear environments in adaptive and in realtime. The structure of it is similar to recurrent neural networks: a delayed output as the input and a delayed error between tile output of plant and neural networks as a bias input. In addition, we compute the desired value of hidden layer by an optimal method instead of transfering desired values by backpropagation and each weights are updated by RLS(Recursive Least Square). Consequently, this neural networks are not sensitive to initial weights and a learning rate, and have a faster convergence rate than conventional neural networks. This new neural networks is Error Estimated Neural Networks. We can estimate nonlinear models in realtime by the proposed networks and control nonlinear models. To show the performance of this one, we have various experiments. And this controller call prove effectively to be control in the environments of various systems.

• International Journal of Control, Automation, and Systems
• /
• v.4 no.4
• /
• pp.448-455
• /
• 2006

This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2002.11a
• /
• pp.573-577
• /
• 2002

A new estimated neural networks are proposed in order to measure nonlinear road environments in realtime. This new neural networks is Error Estimated Neural Networks. The structure of it is similar to recurrent neural networks; a delayed output as the input and a delayed error between the output of plant and neural networks as a bias input. In addition, we compute the desired value of hidden layer by an optimal method instead of transfering desired values by backpropagation and each weights are updated by RLS(Recursive Least Square). Consequently, this neural networks are not sensitive to initial weights and a learning rate, and have a faster convergence rate than conventional neural networks. We can estimate nonlinear models in realtime by the proposed networks and control nonlinear models. To show the performance of this one, we control 7 degree simulation, this controller and driver were proved to be effective to drive a car in the environments of nonlinear road systems.

• Journal of Mechanical Science and Technology
• /
• v.20 no.7
• /
• pp.950-960
• /
• 2006

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.