Sangchul Won

A new fuzzy Lyapunov function approach for a Takagi--Sugeno fuzzy control system design

In this paper, a new fuzzy Lyapunov function approach is presented for a class of continuous-time Takagi-Sugeno fuzzy control system. The proposed fuzzy Lyapunov function is formulated as a line-integral of a fuzzy vector which is a function of the state, and it can be regarded as the work done from the origin to the current state in the fuzzy vector field. Unlike the approaches using a fuzzy blending of multiple quadratic Lyapunov functions, the time-derivatives of membership functions do not appear in the proposed approach. The effectiveness of the proposed approach is shown through numerical examples.

Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling

Abstract This paper proposes an adaptive control method to achieve the lag synchronization between uncertain complex dynamical network having delayed coupling and a non-identical reference node. Unknown parameters of both the network and reference node are estimated by adaptive laws obtained by Lyapunov stability theory. With the estimated parameters, the proposed method guarantees the globally asymptotical synchronization of the network in spite of unknown bounded disturbances. The effectiveness of our work is verified through a numerical example and simulation.

An improvement on "Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty"

In this paper, an improvement on the stability result in the above paper by Jin-Hoon (see ibid. vol.46 (2001)) is given based on a modified Lyapunov function. It is shown that our result is much less conservative than that in the paper, especially when the size of derivative of the time delay increases. For comparison, we give two examples.

H∞ synchronization of time-delayed chaotic systems

Abstract This paper considers H ∞ synchronization of a class of time-delayed chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the dynamic feedback controller is established to not only guarantee synchronization between derive and response systems, but also reduce the effect of external disturbance to an H ∞ norm constraint. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme.

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.

Synchronization of singular complex dynamical networks with time-varying delays

Abstract This paper considers delay dependent synchronizations of singular complex dynamical networks with time-varying delays. A modified Lyapunov–Krasovskii functional is used to derive a sufficient condition for synchronization in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Numerical examples show the effectiveness of the proposed method.

Adaptive synchronization for uncertain chaotic neural networks with mixed time delays using fuzzy disturbance observer

This paper proposes a robust adaptive control method for synchronization of uncertain chaotic neural networks with mixed delays. Uncertainty and disturbance in the networks are estimated by fuzzy disturbance observer without any prior information about them. The proposed control scheme with adaptive laws is derived based on Lyapunov-Krasovskii stability theory to guarantee the globally asymptotical synchronization between the networks. An example is illustrated to show the effectiveness of the proposed method.

A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system

Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems

In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.

Improved delay-dependent stability criteria for uncertain Lur'e systems with sector and slope restricted nonlinearities and time-varying delays

Abstract This paper deals with the absolute stability analysis for uncertain time delay Lur’e systems that have time-varying delays and sector and slope restricted nonlinearities. New delay-dependent stability criteria are derived via linear matrix inequality (LMI) formulation that can be easily solved by various optimization techniques. Sector bounds and slope bounds are employed to the Lyapunov–Krasovskii functional through convex representation of the nonlinearities so that less conservative stability conditions are obtained. Numerical examples show effectiveness of the proposed stability condition.