Page - VII - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

internalize the concepts and make them your own. You must ultimately learn to thinksimplyandclearlyaboutproblemsof control andhowsuchproblems relate to the broad corpus of existing knowledge. At every stage of learning, this tutorial provides the next natural step tomove ahead. I present each step in thequickest andmost illustrativemanner. If that quick stepworks for you, then you canmove along. If not, then you should turn to the broad resources provided by the classic texts. In this way, you can build your understanding rapidly,with emphasis onhow the piecesfit together tomake a rich andbeautiful conceptualwhole.Throughout your study, youcan take advantageof other sources to fill in technical gaps, practical exercises, and basic principles of appliedmathematics. Youwill have tobuildyourowncourse of study,whichcanbechallenging.But with this tutorial guide, you can do it with the confidence that you are working toward the broad conceptual understanding that can be applied to awide range of real-world problems. Although the size of this tutorial guide is small, it will lead you toward thekeyconcepts in standardfirst coursesplusmanyof theprinciples in thenext tier of advanced topics.For scientistsoutsideofengineering, I cannot think of another source that can guide your study in such a simple and direct way. For engineering students, this tutorial supplements theusual courses andbooks tounify theconceptualunderstandingof the individual toolsandskills thatyou learn inyour routine studies. This tutorial is built around an extensive core of software tools and examples. I designed that software to illustrate fundamental concepts, to teach youhow to do analyses of your own problems, and to provide tools that can be used to develop your own research projects. I provide all of the software code used to analyze the examples in the text and to generate the figures that illustrate the concepts. The software is written inWolframMathematica. I usedMathematica rather than the standard MATLAB tools commonly used in engineering courses. Those two systemsaresimilar foranalyzingnumericalproblems.However,Mathematicaprovides muchricher tools for symbolicanalysis and forgraphicpresentationofcomplex results from numerical analysis. The symbolic tools are particularly valuable, because the Mathematica code provides clear documentation of assumptions and mathematical analysis alongwith the series of steps used in derivations. The symbolic analysis also allowseasycouplingofmathematical derivations tonumerical examples andgraphical illustrations. All of the software code used in this tutorial is freely available at http://extras.springer.com/2018/978-3-319-91707-8. TheUSNational Science Foundation and theDonaldBren Foundation support my research. Irvine, USA StevenA. Frank March 2018 viii Preface