in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands.

Preface.- 1. Introduction.- 2. Control systems with periodic convex integrands.- 3. Control systems with non convex integrands.- 4. Stability properties.- 5. Linear control systems with discounting.- 6. Dynamic zero-sum games with linear constraints.- 7. Genericity results.- 8. Variational problems with extended-value integrands.- 9. Dynamic games with extended-valued integrands.- References.- Index.

Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems.  The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis.Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands.  Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integrands.

“The monograph is designed to be useful to specialists, being especially well suited for researchers interested in the latest advances in turnpike theory. One of the main features of the book is that it collects together, in a unified way, results of the author published elsewhere, and uses standard notation.” (Juan Pablo Rincón Zapatero, Mathematical Reviews, April, 2016)

Establishes turnpike properties for linear optimal control problems with non convex integrands and of approximate solutions for zero-sum continuous-time games with two players Shows the stability of the turnpike phenomenon for linear optimal control problems Obtains the description of solutions in the regions close to the endpoints of the time intervals Includes supplementary material: sn.pub/extras