Optimal Control with Engineering Applications: Polymers and Colloids in Personal Care (ACS Symposium Series (No. 961))

Because the theoretical part of the book is based on the calculus of variations, the exposition is very transparent and requires mostly a trivial mathematical background. In the case of open-loop optimal control, this leads to Pontryagin’s Minimum Principle and, in the case of closed-loop optimal control, to the Hamilton-Jacobi-Bellman theory which exploits the principle of optimality. Many optimal control problems are solved completely in the body of the text. Furthermore, all of the exercise problems which appear at the ends of the chapters are sketched in the appendix. The book also covers some material that is not usually found in optimal control text books, namely, optimal control problems with non-scalar-valued performance criteria (with applications to optimal filtering) and Lukes’ method of approximatively-optimal control design. Furthermore, a short introduction to differential game theory is given. This leads to the Nash-Pontryagin Minimax Principle and to the Hamilton-Jacobi-Nash theory. The reason for including this topic lies in the important connection between the differential game theory and the H~infinity~-control theory for the design of robust controllers. "Because the theoretical part of the book is based on the calculus of variations, the exposition is very transparent and requires mostly a trivial mathematical background. In the case of open-loop optimal control, this leads to Pontryagin's Minimum Principle and, in the case of closed-loop optimal control, to the Hamilton-Jacobi-Bellman theory which exploits the principle of optimality." "Many optimal control problems are solved completely in the body of the text. Furthermore, all of the exercise problems which appear at the ends of the chapters are sketched in the appendix." "The book also covers some material that is not usually found in optimal control text books, namely, optimal control problems with non-scalar-valued performance criteria (with applications to optimal filtering) and Lukes' method of approximatively-optimal control design."--BOOK JACKET In this book, the reader is introduced to a variety of problem statements in classical optimal control, in optimal control problems with non-scalar performance criteria, and in optimal estimation and filtering. The optimal control theory is based on rather basic methods in the calculus of variation, in particular on the Lagrange multiplier methods. The theory is explained in a very transparent way. Many engineering optimal control problems are solved completely. Each chapter contains a small collection of additional statements of optimal control problems. Their solutions are sketched in the appendix. This book introduces a variety of problem statements in classical optimal control, in optimal estimation and filtering, and in optimal control problems with non-scalar-valued performance criteria. Many example problems are solved completely in the body of the text. All chapter-end exercises are sketched in the appendix. The theoretical part of the book is based on the calculus of variations, so the exposition is very transparent and requires little mathematical rigor. Front Matter....Pages i-2 Introduction....Pages 3-22 Optimal Control....Pages 23-74 Optimal State Feedback Control....Pages 75-101 Differential Games....Pages 103-115 Back Matter....Pages 117-134