This article is concerned with the extended dissipative fuzzy proportional–integral–derivative (PID) control problem for nonlinear systems subject to controller parameter perturbations over a class of mixed fading channels. The sensors of plant are divided into two groups according to engineering practice, where the individual sensor group transmits the measurements to the controller via a respective communication channel undergoing specific fading effects. Considering the complicated nature of the signal fading with the transmission channels, two stochastic models (i.e., the independent and identically distributed fading model and the Markov fading model) are simultaneously employed to describe the mixed fading effects of the two communication channels corresponding to the two sensor groups. The objective of this article is to design a nonfragile PID controller such that the closed-loop system is exponentially stable in mean square and extended stochastically dissipative. With the assistance of the Lyapunov stability theory and stochastic analysis method, sufficient conditions are obtained to analyze the system performance. Then, within the established theoretical framework, an iterative optimization algorithm is proposed to design the desired controller parameters by using the convex optimization technique. Finally, two simulation examples are given to verify the effectiveness of the proposed control schemes.

中文翻译：

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具有混合衰落测量的非脆弱耗散模糊 PID 控制


本文关注一类混合衰落信道上受到控制器参数扰动的非线性系统的扩展耗散模糊比例积分微分 (PID) 控制问题。根据工程实践，工厂的传感器分为两组，其中各个传感器组通过经历特定衰落效应的各自通信通道将测量结果传输到控制器。考虑到信号衰落随传输信道的复杂性，同时采用两种随机模型（即独立同分布衰落模型和马尔可夫衰落模型）来描述两个通信信道对应的混合衰落效应。传感器组。本文的目标是设计一种非脆弱 PID 控制器，使闭环系统在均方上呈指数稳定，并具有扩展随机耗散性。借助Lyapunov稳定性理论和随机分析方法，获得了分析系统性能的充分条件。然后，在已建立的理论框架内，提出了一种迭代优化算法，利用凸优化技术来设计所需的控制器参数。最后，给出两个仿真例子来验证所提出的控制方案的有效性。