Song Jun, Wang Zidong, Niu Yugang, Dong Hongli
IEEE Trans Cybern. 2021 Jul;51(7):3664-3675. doi: 10.1109/TCYB.2020.2980109. Epub 2021 Jun 23.
The sliding-mode control (SMC) problem is studied in this article for state-saturated systems over a class of time-varying fading channels. The underlying fading channels, whose channel fading amplitudes (characterized by the expectation and variance) are allowed to be different, are modeled as a finite-state Markov process. A key feature of the problem addressed is to use a hidden Markov mode detector to estimate the actual network mode. The novel model of hidden Markov fading channels (HMFCs) is shown to be more general yet practical than the existing fading channel models. Based on a linear sliding surface, a switching-type SMC law is dedicatedly constructed by just using the estimated network mode. By exploiting the concept of stochastic Lyapunov stability and the approach of hidden Markov models, sufficient conditions are obtained for the resultant SMC systems that ensure both the mean-square stability and the reachability with a sliding region. With the aid of the Hadamard product, a binary genetic algorithm (GA) is developed to solve the proposed SMC design problem subject to some nonconvex constraints induced by the state saturations and the fading channels, where the proposed GA is based on the objective function for optimal reachability. Finally, a numerical example is employed to verify the proposed GA-assisted SMC scheme over the HMFCs.
本文研究了一类时变衰落信道上状态饱和系统的滑模控制（SMC）问题。潜在的衰落信道，其信道衰落幅度（由期望和方差表征）允许不同，被建模为有限状态马尔可夫过程。所解决问题的一个关键特征是使用隐马尔可夫模式检测器来估计实际网络模式。结果表明，隐马尔可夫衰落信道（HMFCs）的新模型比现有的衰落信道模型更具一般性且更实用。基于线性滑模面，仅利用估计的网络模式专门构造了一种切换型SMC律。通过利用随机李雅普诺夫稳定性的概念和隐马尔可夫模型的方法，为所得的SMC系统获得了充分条件，确保了均方稳定性和具有滑动区域的可达性。借助哈达玛积，开发了一种二进制遗传算法（GA）来解决由状态饱和和衰落信道引起的一些非凸约束下的SMC设计问题，其中所提出的GA基于最优可达性的目标函数。最后，通过一个数值例子验证了所提出的GA辅助SMC方案在HMFCs上的有效性。
