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Download or read book State Estimation and Stabilization of Nonlinear Systems written by Abdellatif Ben Makhlouf and published by Springer Nature. This book was released on 2023-11-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).
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Download or read book Analytical Techniques for Trace Elements in Geochemical Exploration written by Raghaw Saran and published by Royal Society of Chemistry. This book was released on 2022-12-07 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trace element analysis plays a prominent role in various fields, from mineralogy and geology to semiconductor manufacture and foods. In geochemical exploration, the analysis of trace elements assumes high significance due to the multifaceted role played by them. The analyte is at the detection limit of many instrumental techniques. This makes their determination difficult This book covers a wide spectrum of destructive and non-destructive analytical techniques and recent developments in them used all over the world, including developing countries, for quantitation of trace elements. With revolutionary progress in the last three to four decades in analytical techniques, several ICP-based techniques like ICP-OES and ICP-MS and other nuclear analytical techniques have enabled determination of trace elements at the ppb level. However, these methods require expensive instrumentation and cannot be made available everywhere. The quality of analytical data is dependent on valid reference standards. The book contains detailed sample preparation in varying matrices and an important chapter on statistical treatment of analytical data for the purpose of quality control and quality assurance. Pulling together, the book, containing the work carried out by the author’s group in India, will be useful to analysts involved in geochemical explorations.
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