Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Xanthi, Greece.
Int J Neural Syst. 2013 Oct;23(5):1350022. doi: 10.1142/S0129065713500226. Epub 2013 Jul 16.
In this paper, we investigate the indirect adaptive regulation problem of unknown affine in the control nonlinear systems. The proposed approach consists of choosing an appropriate system approximation model and a proper control law, which will regulate the system under the certainty equivalence principle. The main difference from other relevant works of the literature lies in the proposal of a potent approximation model that is bilinear with respect to the tunable parameters. To deploy the bilinear model, the components of the nonlinear plant are initially approximated by Fuzzy subsystems. Then, using appropriately defined fuzzy rule indicator functions, the initial dynamical fuzzy system is translated to a dynamical neuro-fuzzy model, where the indicator functions are replaced by High Order Neural Networks (HONNS), trained by sampled system data. The fuzzy output partitions of the initial fuzzy components are also estimated based on sampled data. This way, the parameters to be estimated are the weights of the HONNs and the centers of the output partitions, both arranged in matrices of appropriate dimensions and leading to a matrix to matrix bilinear parametric model. Based on the bilinear parametric model and the design of appropriate control law we use a Lyapunov stability analysis to obtain parameter adaptation laws and to regulate the states of the system. The weight updating laws guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. Moreover, introducing a method of "concurrent" parameter hopping, the updating laws are modified so that the existence of the control signal is always assured. The main characteristic of the proposed approach is that the a priori experts information required by the identification scheme is extremely low, limited to the knowledge of the signs of the centers of the fuzzy output partitions. Therefore, the proposed scheme is not vulnerable to initial design assumptions. Simulations on selected examples of well-known benchmarks illustrate the potency of the method.
在本文中，我们研究了控制非线性系统中未知仿射项的间接自适应调节问题。所提出的方法包括选择适当的系统近似模型和适当的控制律，这些控制律将根据等价原理调节系统。与文献中的其他相关工作的主要区别在于提出了一种有效的近似模型，该模型与可调参数呈双线性关系。为了部署双线性模型，非线性植物的组件最初通过模糊子系统进行近似。然后，使用适当定义的模糊规则指示函数，将初始动态模糊系统转换为动态神经模糊模型，其中指示函数由经过采样系统数据训练的高阶神经网络 (HONN) 取代。初始模糊组件的模糊输出分区也基于采样数据进行估计。这样，要估计的参数是 HONN 的权重和输出分区的中心，这些参数都排列在适当维度的矩阵中，导致矩阵到矩阵的双线性参数模型。基于双线性参数模型和适当控制律的设计，我们使用 Lyapunov 稳定性分析来获得参数自适应律，并调节系统状态。权重更新律保证了识别误差和系统状态都以指数方式快速达到零，同时保持闭环中的所有信号有界。此外，通过引入“并发”参数跳跃方法，修改更新律，以确保控制信号的存在。所提出方法的主要特点是，识别方案所需的先验专家信息极低，仅限于模糊输出分区中心的符号知识。因此，所提出的方案不易受到初始设计假设的影响。对选定的知名基准示例的仿真说明了该方法的有效性。
