Textbook in PDF format The first chapter defines the problems of deterministic optimum control, state estimation, stochastic control, parameter estimation, and adaptive control, which arise in optimum systems control. Chapter 2 provides an introduction to the calculus of extrema of two and more variables. In Chapter 3, the authors treat the classical calculus of variations. Chapter 4 is a natural extension of Chapter 3 where more general solutions are obtained. Chapter 5 deals with optimum systems control examples. Chapter 6 discusses the discrete variational calculus and the discrete maximum principle. Chapter 7 is the major coverage in the book which gives a valuable insight into the systems concepts. Chapter 8 contains an account of optimum state estimation. Chapter 9 is devoted to the LQG problem for discrete and continuous cases, extensions of the LQG problem, and sensitivity analysis of combined estimation and control algorithms. Chapter 10 contains several methods for solving optimal control problems. Appendix A discusses the algebra, calculus, and differential equations of vectors and matrices. Appendix B is devoted to “Abstract Spaces.” Appendix C treats random variables and stochastic processes. Appendix D develops the matrix inversion lemma