Tong Shaocheng

Interval number and fuzzy number linear programmings

Abstract In this paper, we focus on two kinds of linear programmings with fuzzy numbers. They are called interval number and fuzzy number linear programmings, respectively. The problems of linear programmings with interval number coefficients are approached by taking maximum value range and minimum value range inequalities as constraint conditions, reduced it into two classical linear programmings, and obtained an optimal interval solution to it. The problems of fuzzy linear programming with fuzzy number coefficients are approached in two ways: i.e. “fuzzy decisive set approach” and “interval number linear programming approach for several membership levels”. Finally, we gave the numerical solutions of the illustrative examples.

Direct adaptive fuzzy control for unknown multivariable nonlinear systems with fuzzy logic

In this paper, a fuzzy, adaptive tracking control scheme for a class of unknown dynamical nonlinear systems is presented. Since both parametric uncertainties and unmodeled dynamics are present in the nonlinear system, we design different controllers, respectively. Based on Lyapunov theory, we discussed the stability of the closed loop system and the convergence of the tracking errors.

Fuzzy indirect adaptive control for a class of decentralized nonlinear systems

A stable fuzzy indirect control scheme is presented for a class of interconnected nonlinear systems for which an explicit linear parametrization of the uncertainty is either unknown or impossible. In the control algorithm, fuzzy logic systems, are employed to approximate the unknown dynamics in each subsystems, the feedback and adaptation mechanisms for each subsystems depend only upon local measurements to provide asymptotic tracking of a reference trajectory. In addition, a fuzzy sliding mode controller is developed to compensate for the fuzzy approximating errors or neural network approximating, and to attenuate the interactions between subsystems. Global asymptotic stability is established in the Lyapunov sense, with the tracking errors converging to a neighbourhood of zero

Adaptive fuzzy sliding mode control for nonlinear systems

This paper proposes a kind of adaptive fuzzy control scheme for a nonlinear system. In the design, we employ fuzzy systems to approximate nonlinear functions, then combine the sliding mode principle and Lyapunov function to obtain a stable adaptive controller. Furthermore, we apply fuzzy inference control to attenuate the chattering phenomenon being inherent in the conventional sliding mode controller, and prove that the closed-loop system is stable with the tracking error converging to a neighbourhood of zero.

Notes on multivariable fuzzy controller under Gödel's implication

In this paper, we obtain the upper bounds and lower bounds for a multivariable fuzzy logic controller under Godels implication without any constraint conditions, and gave a sufficient condition in which fuzzy outputs can reach their upper and lower bounds.

H/sup /spl infin// tracking of unknown nonlinear systems using neural network

A stable neural adaptive control scheme, is proposed to achieve H/sup /spl infin// performance for a class of unknown nonlinear SISO systems with external disturbances. In the control design, the controller comprises a certainty equivalence control term and an H/sup /spl infin// compensating term. The neural network is used to approximate the unknown nonlinear functions for the design of the equivalence controller, and the Lyapunov method is used for the update of the parameters of the neural network, the stability of the proposed control algorithm can be guaranteed. The performance of the proposed method is demonstrated through the control of the inverted pendulum system.

Fuzzy indirect adaptive control and robustness analysis for unknown multivariable nonlinear systems

In this paper, we deal with the problem of controlling an unknown nonlinear dynamical system that is modeled by fuzzy logic systems. In the ideal case of complete model matching, convergence of the state of zero plus boundedness of all signals in the closed loop system is ensured. Moreover, the robustness of the controller designed in the ideal case is given in the framework of singular perturbation theory.

Robust control of nonlinear uncertain systems under generalized matching conditions using neuro-compensator

The robust adaptive control scheme with neural-compensator is developed for a class of uncertain systems satisfied the generalized matching condition. In the control procedure, the neural compensator is combined with the feedback linearization method, and the neural network is implemented to learn and compensate the uncertainty, rescale the uncertainty of nonlinear systems to the reconstruction error of the network, and a sliding mode controller is used to deal with the uncertainty due to the reconstruction of the network. No property of the uncertainty is used for the design, it is more practical than the existing ones in the literature.