Network-Based Control And Filtering Of A Class Of Nonlinear Systems Under Variational Communication Capability

With the rapid development of networked control technology, network-based control has become an important research front in the field of automatic control. Through networked control systems have many advantages, such as low costs, modular design, resources sharing, flexible allocation as well as easy expansion, upgrade and maintenance,due to the limited communication capacity of the network media, there may be a nonzero probability that some transmitted signals experience transmission delays, signal quantizations, and packet dropouts and disorders during their transmissions, which can deteriorate the performance of networked control systems, even result in the problem of instability. Researches on networked control systems mainly focus on exploring valid control methods to overcome the above-mentioned network-induced imperfections. It should be noted that in practice, these types of network-induced imperfections are variational, such as time-variation of transmission delays, variability and uncertainty of packet dropout rates, variation of quantization density and variation of network parameters induced by the switchings among the main channel and the redundant channels. These dynamics bring new challenges to the analyses and syntheses of networked control systems.The thesis aims to deal with the issues of stability analyses, control and filtering for a class of nonlinear networked control systems under the variations of communication capability, in which time-varying transmission delays, uncertain packet dropout rates, variational quantization density and channels switchings with the usage of redundant channels are considered. As most practical control systems are nonlinear systems, this thesis focuses on nonlinear control systems that are approximated by Takagi–Sugeno(T–S) fuzzy models. Main results and contributions are summarized as follows:Chapter 2 is concerned with the H∞ control problem for a class of discrete-time T–S fuzzy Markov jump systems with time-varying delays under unreliable communication links. It is assumed that the data transmission between the plant and the controller are subject to randomly occurred packet dropouts satisfying Bernoulli distribution. The dropout rate is uncertain as well as the upper bound and lower bound of the packet dropout rate can be asymmetric to the “nominal”rate. By adopting the two-term approximation method to deal with the time-varying delay term and transforming the original closed-loop system into an interconnected form, then based on a fuzzy-basis-dependent and mode-dependent Lyapunov–Krasovskii functional, the existence conditions of the desired mode-dependent H∞state-feedback controllers are derived by employing the scaled small gain theorem such that the closed-loop system is stochastically stable and achieves a guaranteed H∞performance. Finally, a practical example of robot arm is provided to illustrate the performance of the proposed approach.Chapter 3 addresses the distributed H∞ filtering problem for a class of discrete-time T–S fuzzy systems with time-varying delays. The data communications among sensor nodes are equipped with a main channel and a redundant channel. Both channels are subject to random packet dropouts modeled by mutually independent Bernoulli stochastic processes. Meanwhile, the practical phenomenon of the uncertain packet dropout rates is considered. By utilizing the two-term approximation method to approximating the time-varying term and transforming the original distributed filtering error system into an interconnected form, sufficient conditions on the existence of the desired distributed filters are established with the aid of the scaled small gain theorem to ensure that the closed-loop interconnected system is stochastically stable and achieves a prescribed average H∞ performance index. Finally, a modified Henon mapping system is employed as an illustrative example to verify the superiorities of redundant channels.Chapter 4 investigates the issue of asynchronous H∞ filtering for a class of discretetime T–S fuzzy affine systems against time-varying signal transmission delays and measurement quantization. The so-called asynchrony is caused by the situation that the plant state and the filter state locate different local regions of the state space, and the quantization density can be adjusted to satisfy different performance requirements at different time instants. By transforming the filtering error system into an input–output form consisting of two interconnected subsystems, sufficient conditions on the existence of the desired piecewise filters are established via the scaled small gain theorem to ensure that the underlying interconnection system is asymptotically stable with a prescribed H∞ performance index with the aid of a novel piecewise Lyapunov–Krasovskii functional and the S-procedure approach. Finally, a practical example of cart-pendulum with modified model is provided to illustrate the effectiveness of the obtained theoretical results and advantages of variational quantization density.