- Varvara Turova, TU München
- Nikolai Botkin, TU München
Dynamic Programming Approach to Optimal Control Methods and Applications
programming method proposed by R. Bellman at the end of the 1950s
became a powerful tool of modern control theory. It is applicable to
problems with fixed and non-fixed time of termination, to processes
with infinite time horizon, as well as to problems with various
boundary conditions and state constraints.
method is also suitable for solving optimal control problems in the
presence of uncertainties, if the uncertain factors are interpreted as
counteractions of an opponent who tries to do maximal harm, whereas the
aim of the control is to ensure the best guaranteed result. In problems
with continuous time, dynamic programming approach leads to
Hamilton-Jacobi-Bellman (HJB) equations whose theory is being
At the same time, the development of effective numerical methods is of great importance for applications.
section focuses on recent achievements both in the theory of viscosity
solutions (existence, proximal analysis, regularity, etc.) of HJB
equations and in approximation techniques that provide stable numerical
algorithms for the treatment of HJB equations arising from nonlinear control problems with state constraints.
approaches to overcoming the curse of dimensionality including parallel
algorithms and the usage of modern computing technologies will be
Some important applications of dynamic programming method
in different areas, e.g., in civil aviation, acoustics, and ecology
will be presented.