Dynamic programming and stochastic control processes

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Consider a system S specified at any time t by a finite dimensional vector x(t) satisfying a vector differential equation dx/dt = g[x, r(t), f(t)], x(0) = c, where c is the initial state, r(t) is a random forcing term possessing a known distribution, and f(t) is a forcing term chosen, via a feedback process, so as to minimize the expected value of a functional J(x) = f{hook}0T h(x - y, t) dG(t), where y(t) is a known function, or chosen so as to minimize the functional defined by the probability that max0 ≦ t ≦ T h(x - y, t) exceed a specified bound. It is shown how the functional equation technique of dynamic programming may be used to obtain a new computational and analytic approach to problems of this genre. The limited memory capacity of present-day digital computers limits the routine application of these techniques to first and second order systems at the moment, with limited application to higher order systems. © 1958.




Bellman, R. (1958). Dynamic programming and stochastic control processes. Information and Control, 1(3), 228–239. https://doi.org/10.1016/S0019-9958(58)80003-0

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