DOI: 10.4018/978-1-5225-2385-7.ch001
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The book presents a foundational and comprehensive treatment of the analysis and design tasks for large-scale nonlinear interconnected systems based on the Takagi-Sugeno (T-S) model. Expect stability analysis, an emphasis is laid on the derivation of methods which have a decentralized or a distributed control structure. These include sampled-data control, event-triggered control, sliding mode control, practical applications, and last but not the least, conclusions and future research. The proposed methodologies provide effective techniques to overcome specific difficulties in the considered systems, such as high dimensionality, interconnections, and coupling nonlinearities.
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1.1 Large-Scale Interconnected Systems

The demand for rapid and sustained development has pushed control scholars and engineers to focus on increasingly higher dimensional and more complex systems. Such kind of systems is referred to as large-scale systems, which relies on the cooperation of several subsystems (Šiljak, 1978; Šiljak & Zečević, 2005). In large-scale systems, two kinds of analytical models are developed with respect to interconnections and non-interconnections among subsystems, respectively. Such general models for large-scale systems with non-interconnections are multi-agent systems. Control community has studied extensively coordination control of multi-agent systems, including unmanned aerial vehicles, unmanned underwater vehicles, and unmanned ground vehicles. Some important results and progress in coordination control of multi-agent have been published in major control systems and robotics journals (Ren, Beard & Atkins, 2005; Oh, Park & Ahn, 2015). Large-scale interconnected systems exist widely in the real world, such as power networks, transportation systems, ecological systems, and river pollution systems (Lunze, 1992; Mahmoud, 2011). A distinguish property of such large-scale interconnected systems is that a perturbation of one subsystem can affect the other subsystems as well as the overall stability and performance, its structure is shown in Figure 1.

Figure 1.

Structure of large-scale interconnected systems

Large-scale interconnected systems invoke control theory with the following challenges:

  • The large size of the plants leads to the high dimension of its mathematical model. This condition requires a control restriction on hardware and software costs;

  • Every subsystem has several interconnections connecting to other subsystems, which have to be considered explicitly in the stability analysis and controller design;

  • The dynamics among all subsystems can be different each other. The design aims at including not only stability or optimality for systems with simple dynamics, but also a variety of hybrid dynamics in interconnections, such as continuous-discrete time, coupling nonlinearity, and network-induced uncertainties.

On the other hand, computer systems undergo several revolutions. From 1945, when the modern computer began to emerge, until 1985, computers became large and expensive. Since 1980, however, two technologies began to change the situation. One was the development of powerful microprocessors, and the other was the invention of high-speed computer networks (Tanenbaum & Steen, 2007). A network allows that hundreds of machines within different areas could be connected. Put together the systems with a large numbers of computers over a network, they are usually called computer networks or distributed systems. Recently, complex networks have been developed for large-scale systems, such as communication protocols (Simon, Volgyesi, Maróti, & Ákos, 2003), synchronization and consensus of nodes (Tang, Qian, Gao, & Jürgen, 2014).


1.2 General Methodologies

The control of large-scale systems is one of the foremost challenges facing control engineers today. There exist three approaches adopted for the control of large-scale interconnected systems: the centralized approach, the decentralized approach, and the distributed approach.

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