Orthogonal Functions in Systems and Control (Advanced Electrical and Computer Engineering)

Traditionally, field theory is taught through canonical quantization with a heavy emphasis on high energy physics. However, the techniques of field theory are applicable as well and are extensively used in various other areas of physics such as consdensed matter, nuclear physics and statistical mechanics. The path integral approach brings out this feature most clearly. In this book, the path integral approach is developed in detail completely within the context of quantum mechanics. Subsequently, it is applied to various areas of physics Ch. 1. Orthogonal Functions in Systems and Control: A Historical Perspective -- Ch. 2. Least Squares Approximation of Signals -- Ch. 3. Signal Processing in Continuous Time Domain -- Ch. 4. Analysis of Time-Delay Systems -- Ch. 5. Identification of Lumped Parameter Systems -- Ch. 6. Identification of Distributed Parameter Systems -- Ch. 7. Identification of Linear Time-Varying and Nonlinear Distributed Parameter Systems -- Ch. 8. Optimal Control of Linear Systems A systematic, unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials (such as, Legendre, Laguerre, Hermite, Tchebychef, Jacobi, and Gegenbauer) and via orthogonal functions such as sine-cosine, block-pulse and Walsh. This volume provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials (such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi and Gegenbauer) and via orthogonal functions such as sine-cosine, block-pulse, and Walsh. This book concentrates on the application of orthogonal polynomials in systems and control and aims to establish the superiority of orthogonal polynomials over other orthogonal functions This book provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi, Gegenbauer, and via orthogonal functions such as sine-cosine, block-pulse, and Walsh. This is the first book devoted to the application of orthogonal polynomials in systems and control, establishing the superiority of orthogonal polynomials to other orthogonal functions.