Discrete-time optimal control and games on large intervals (Q511301)

The author in the book presents and discusses properties of approximate solutions of optimal control problems for discrete-time systems and of dynamic non-cooperative discrete-time games on infinite or sufficiently large intervals. The book summarizes and extends results obtained by the author and his coworkers published in a number of mathematical, control engineering and economic journals. A key notion applied by the author to get these results is a so-called turnpike property. To have this property means that the approximate solutions of the problems are determined mainly by the objective functions and are essentially independent of the choice of intervals and endpoint conditions except in regions close to the endpoints. The author proves that the turnpike property is generic for all the problems considered in the book, i.e. Lagrange and Bolza problems for discrete-time systems and for zero-sum discrete-time dynamic games. In the latter case unconstrained and constrained games without convexity-concavity assumptions are studied. Special properties of approximate solutions for problems satisfying convexity-concavity assumptions are also discussed. Where it is possible, the author studies also the structure of approximate solutions in regions close to the endpoints of the time intervals and their stability under small perturbations of the objective functions. All theorems and propositions presented in the book are endowed with rigorous proofs. On the other hand, the book may disappoint some potential readers because it does not contain simple examples illustrating the theory.