Controllability And Optimal Control Of Bilinear Systems

Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.

This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections ... Lie algebraic conditions for local controllability... the use of the Campbell-Hausdorff series to derive properties of optimal trajectories... the Fuller phenomenon ... the theory of orbits ... and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .

This book is designed to be a comprehensive treatment of linear methods to optimal control of bilinear systems. The unified theme of this book is the use of dynamic programming in order to simplify and decompose required computations for the optimal control of bilinear-quadratic systems. There are numerous examples of bilinear control systems that provide great challenges to engineers, mathematicians and computer scientists: these include nuclear reactors, missile intercept problems and mechanical brake systems. The book also examines two special classes of bilinear-quadratic control problems: namely singularly perturbed and weakly coupled bilinear control systems. The usefulness of the presented methods to these two types of control problem is demonstrated by several real control system examples.

Bilinear Control Processes: with Applications to Engineering, Ecology, and Medicine