Richard Bellman and stochastic control systems

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Bellman function in stochastic control and harmonic analysis

The stochastic optimal control uses the differential equation of Bellman and its solution—the Bellman function. We show how the homonym function in harmonic analysis is (and how it is not) the same stochastic optimal control Bellman function. Then we present several creatures from Bellman’s Zoo: a function that proves the inverse Hölder inequality, as well as several other harmonic analysis Bel...

Hamilton-Jacobi-Bellman Equations and the Optimal Control of Stochastic Systems

In many applications (engineering, management, economy) one is led to control problems for stochastic systems : more precisely the state of the system is assumed to be described by the solution of stochastic differential equations and the control enters the coefficients of the equation. Using the dynamic programming principle E. Bellman [6] explained why, at least heuristically, the optimal cos...

Bellman Equations for Stochastic Programs

This is a revised version of a paper entitled \World Modeling vs. World Axiomatizing" which accompanied an invited talk at LPNMR-99. Abstract. This paper gives a model-checking style algorithm for verifying the decision-theoretic utility of a handwritten robot controller. The paper presents a simple Turing-complete programming language for expressing robot control programs. The robot control la...

Richard Bellman on the Birth of Dynamic Programming

W follows concerns events from the summer of 1949, when Richard Bellman first became interested in multistage decision problems, until 1955. Although Bellman died on March 19, 1984, the story will be told in his own words since he left behind an entertaining and informative autobiography, Eye of the Hurricane (World Scientific Publishing Company, Singapore, 1984), whose publisher has generously...