Robust Control of Networked Control Systems with Random Communication Delays
Networked control systems (NCSs) refer to a class of systems where the components such as plants, sensors, actuators and controllers are connected via a communication network. This configuration provides several advantages over the traditional point-topoint structure such as modularity, ease of maintenance and low construction cost. NCSs enable several practical applications such as unmanned aerial vehicle and remote control of the plant, which are difficult to achieve with the traditional point-to-point structure. The presence of network inevitably, however, introduces delays and data loss as signals travel through the network, meaning that the controllers in NCSs are to stabilize the system while overcoming the adverse effects caused by the presence of the network. As continuous signals are transmitted via a network, they are converted to clusters of data called packets and these packets of data are transmitted through the network. Hence, it is natural to consider the plant and the controller in discrete-time domain where new information about the systems components are available at each sampling instance. In this thesis, discrete-time representation of the plant is considered and the controller/filter design methodologies are developed based on Lyapunov-Krasovskii functional. The focus of the research is to develop controller and filter design methodologies for NCSs which takes the aforementioned network constraints into account. Hence the network needs to be modelled and taken into consideration when designing the controller/ filter. In particular, a finite state Markov chain is used in this research to model the network-induced delays and data loss where each mode in the Markov chain corresponds to the delays in the network. Difficulties of obtaining a completely known transition probability matrix, which describes the transitions between the modes of the Markov chain, in real world is acknowledged in this research and some of the elements in the transition probability matrix are allowed to be unknown. In this thesis, a robust H1 state feedback controller design for linear and nonlinear NCSs are first developed where the transition probability matrix of the Markov chain is assumed to be completely known. Based on theses methodologies, robust H1 state feedback controller, robust H1 filter and robust H1 dynamic output feedback controller design methodologies for NCSs are presented where the transition probability matrix is allowed to be partially known. It is shown that the case with either completely known or unknown transition probability matrix can be considered as a special case of the presented approaches. Study of nonlinear systems is important as every real system contains nonlinearities. Takagi-Sugeno (T-S) fuzzy model has been shown to be effective in modelling nonlinear systems which describes a global nonlinear system with a series of local linear models blended using membership functions. In this thesis, robust fuzzy H1 state feedback, robust fuzzy H1 filter and robust fuzzy H1 dynamic output feedback controller design are considered where the nonlinear NCSs are described by T-S fuzzy model, with main focus on partially known transition probability matrix in the Markov chain. Special attention is given to premise variables of the plant to correctly model NCSs where there exists a network between the plant and the controller. It has been addressed that many existing literature on nonlinear NCSs modelled by T-S fuzzy model fail to acknowledge this issue, making the existing approaches impractical. Furthermore, a methodology to incorporate membership functions into the controller/filter designs via sum-of-squares approach is presented to ensure that the controller is specific for the membership functions of the system. This has not been considered in existing studies of nonlinear NCSs, making the existing results conservative as the controllers are valid for any shape of membership functions. Iterative algorithms to convert nonconvex problems into optimization problems are also presented so that existing mathematical tools can be used to obtain a controller/filter. Finally, the effectiveness of the proposed design methodologies are demonstrated using numerical examples in this thesis. The simulation results show that the proposed design methodologies achieve the prescribed performance requirements. Comparisons with existing methodologies without considering membership functions are made for robust fuzzy H1 state feedback controller and robust fuzzy H1 dynamic output feedback controller to illustrate that incorporating membership functions results a larger stabilization region, demonstrating the advantage of the presented methodologies.
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