Hwang Chih-Lyang, Chang Li-Jui
Department of Electrical Engineering, Tamkang University, Tamsui 25137, Taiwan, ROC.
IEEE Trans Syst Man Cybern B Cybern. 2007 Dec;37(6):1471-85. doi: 10.1109/tsmcb.2007.903448.
In this paper, a partially known nonlinear dynamic system with time-varying delays of the input and state is approximated by N fuzzy-based linear subsystems described by a state-space model with average delay. To shape the response of the closed-loop system, a set of fuzzy reference models is established. Similarly, the same fuzzy sets of the system rule are employed to design a fuzzy neural-based control. The proposed control contains a radial-basis function neural network to learn the uncertainties caused by the approximation error of the fuzzy model (e.g., time-varying delays and parameter variations) and the interactions resulting from the other subsystems. As the norm of the switching surface is inside of a defined set, the learning law starts; in this situation, the proposed method is an adaptive control possessing an extra compensation of uncertainties. As it is outside of the other set, which is smaller than the aforementioned set, the learning law stops; under this circumstance, the proposed method becomes a robust control without the compensation of uncertainties. A transition between robust control and adaptive control is also assigned to smooth the possible discontinuity of the control input. No assumption about the upper bound of the time-varying delays for the state and the input is required. However, two time-average delays are needed to simplify the controller design: 1) the stabilized conditions for every transformed delay-free subsystem must be satisfied; and 2) the learning uncertainties must be relatively bounded. The stability of the overall system is verified by Lyapunov stability theory. Simulations as compared with a linear transformed state feedback with integration control are also arranged to consolidate the usefulness of the proposed control.
在本文中，一个输入和状态具有时变延迟的部分已知非线性动态系统由N个基于模糊的线性子系统近似，这些子系统由具有平均延迟的状态空间模型描述。为了塑造闭环系统的响应，建立了一组模糊参考模型。同样，采用系统规则的相同模糊集来设计基于模糊神经网络的控制。所提出的控制包含一个径向基函数神经网络，用于学习由模糊模型的近似误差（例如，时变延迟和参数变化）引起的不确定性以及其他子系统产生的相互作用。当切换面的范数在定义的集合内时，学习律启动；在这种情况下，所提出的方法是一种具有额外不确定性补偿的自适应控制。当它在另一个比上述集合小的集合之外时，学习律停止；在这种情况下，所提出的方法成为一种没有不确定性补偿的鲁棒控制。还分配了鲁棒控制和自适应控制之间的过渡，以平滑控制输入可能的不连续性。不需要对状态和输入的时变延迟的上限进行假设。然而，需要两个时间平均延迟来简化控制器设计：1）必须满足每个变换后的无延迟子系统的稳定条件；2）学习不确定性必须相对有界。通过李雅普诺夫稳定性理论验证了整个系统的稳定性。还安排了与带有积分控制的线性变换状态反馈相比的仿真，以巩固所提出控制的有效性。
