The relationship between the maximum principle and dynamic programming

  title={The relationship between the maximum principle and dynamic programming},
  author={F. H. Clarke and R. Vinter},
  journal={Siam Journal on Control and Optimization},
  • F. H. Clarke, R. Vinter
  • Published 1987
  • Mathematics
  • Siam Journal on Control and Optimization
  • Let $V(t,x)$ be the infimum cost of an optimal control problem, viewed as a function of the initial time and state $(t,x)$. Dynamic Programming is concerned with the properties of $V( \cdot , \cdot )$ and in particular with its characterization as a solution to the Hamilton–Jacobi–Bellman equation. Heuristic arguments have long been advanced relating the Maximum Principle to Dynamic Programming according to \[p(t) = - V_x \left( {t,x_0 (t)} \right).\] Here $x_0 ( \cdot )$ is the minimizing… CONTINUE READING
    103 Citations
    New results on the relationship between dynamic programming and the maximum principle
    • R. Vinter
    • Mathematics, Computer Science
    • Math. Control. Signals Syst.
    • 1988
    • 39
    Is the costate variable the state derivative of the value function?
    • R. Vinter
    • Mathematics
    • 1986 25th IEEE Conference on Decision and Control
    • 1986
    • 1
    • PDF
    Combining Pontryagin's Principle and Dynamic Programming for Linear and Nonlinear Systems
    Infinite horizon optimal control: Transversality conditions and sensitivity relations
    Reflections on optimality and dynamic programming
    • E. Galperin
    • Mathematics, Computer Science
    • Comput. Math. Appl.
    • 2006
    • 4