Genetic-Algorithm-Assisted Sliding-Mode Control for Networked State-Saturated Systems Over Hidden Markov Fading Channels

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.

Automated summary

This article investigates the sliding-mode control problem for state-saturated systems over time-varying fading channels, utilizing a hidden Markov mode detector to estimate the actual network mode. The novel model of hidden Markov fading channels is shown to be more general yet practical than existing fading channel models. By exploiting stochastic Lyapunov stability and hidden Markov models, sufficient conditions are obtained for the SMC systems to ensure mean-square stability and reachability within a sliding region.