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In control engineering, robust control is an area that explicitly deals with uncertainty in its approach to the design of the system controller [7,10,24]. The methods of robust control are designed to operate properly as long as disturbances or uncertain parameters are within a compact set, where robust methods aim to accomplish robust performance and/or stability in the presence of bounded modeling errors. A robust control policy is static in contrast to the adaptive (dynamic) control policy where, rather than adapting to measurements of variations, the system controller is designed to function assuming that certain variables will be unknown but, for example, bounded. An early example of a robust control method is the high-gain feedback control where the effect of any parameter variations will be negligible with using sufficiently high gain. The overall goal of a control system is to cause the output variable of a dynamic process to follow a desired reference variable accurately. This complex objective can be achieved based on a number of steps. A major one is to develop a mathematical description, called dynamical model, of the process to be controlled [7,10,24]. This dynamical model is usually accomplished using a set of differential equations that describe the dynamic behavior of the system, which can be further represented in state-space using system matrices or in transform-space using transfer functions [7,10,24]. In system modeling, sometimes it is required to identify some of the system parameters. This objective maybe achieved by the use of artificial neural networks (ANN), which are considered as the new generation of information processing networks [5,15,17,28,29]. Artificial neural systems can be defined as physical cellular systems which have the capability of acquiring, storing and utilizing experiential knowledge [15,29], where an ANN consists of an interconnected group of basic processing elements called neurons that perform summing operations and nonlinear function computations. Neurons are usually organized in layers and forward connections, and computations are performed in a parallel mode at all nodes and connections. Each connection is expressed by a numerical value called the weight, where the conducted learning process of a neuron corresponds to the changing of its corresponding weights.

intech ebooks

Robust Control Using LMI Transformation and Neural-Based Identification for Regulating Singularly-Perturbed Reduced Order Eigenvalue-Preserved Dynamic Systems