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The Dynamic Programming Approach

Chapter
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Part of the Systems & Control: Foundations & Applications book series (SCFA, volume 85)

Abstract

This chapter describes general schemes of the Dynamic Programming approach. It introduces the notion of value function and its role in these schemes. They are dealt with under either classical conditions or directional differentiability of related functions, leaving more complicated cases to later chapters. Here the emphasis is on indicating solutions to forward and backward reachability problems for “linear-convex” systems and the design of closed-loop control strategies for optimal target and time-optimal feedback problems.

Keywords

Dynamic programming Value function HJB equation Reachability Linear-convex systems Colliding tubes Terminal control Time-optimal control 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State (Lomonosov) UniversityMoscowRussia
  2. 2.Electrical Engineering and Computer SciencesUniversity of California, BerkeleyBerkeleyUSA

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