Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics.

This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discrete-time analogs of Bolza problems in calculus of variations are studied. The structures of approximate solutions of two-player zero-sum games are analyzed through standard convexity-concavity assumptions. Finally, turnpike properties for approximate solutions in a class of nonautonomic dynamic discrete-time games with convexity-concavity assumptions are examined.

Investigates individual turnpike results for discrete-time optimal control problems and for dynamic discrete-time two-player zero-sum games Contains solutions to a number of problems in optimal control Presents new approaches, techniques, and methods Includes supplementary material: sn.pub/extras

Autorentext

Alexander J. Zaslavski is professor in the Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel. He has authored numerous books with Springer, the most recent of which include Turnpike Theory for the Robinson-Solow-Srinivasan Model (978-3-030-60306-9), The Projected Subgradient Algorithm in Convex Optimization (978-3-030-60299-4), Convex Optimization with Computational Errors (978-3-030-37821-9), Turnpike Conditions in Infinite Dimensional Optimal Control (978-3-030-20177-7), Optimization on Solution Sets of Common Fixed Point Problems (978-3-030-78848-3).

Inhalt

1. Introduction. -2. Lagrange problems. -3. Bolza problems. -4. Stability Results for Bolza problems. -5. Unconstrained games without Convexity-Concavity
   Assumptions. -6. Constrained Games without Convexity-Concavity
   Assumptions. -7.Nonautonomous Games with Convexity-ConcavityAssumptions. -8.Constrained Games with Convexity-Concavity Assumptions. -References.