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- W1490837526 abstract "We consider the problem of the optimal control of the terminal state of a linear system containing random perturbations in the form of Gaussian white noise. We propose a method for the approximate solution of Bellman's equation for one class of such systems in the case when the solution of the deterministic Bellman equation has discontinuities of the first kind in its values or in the values of its derivatives. As an application of the results obtained we give an approximate solution of Bellman's equation corresponding to one model problem in the control of entry into the atmosphere (see [1, 2]) and we compare the result obtained with the results of the numerical calculations in [2]. Some methods for the approximate solution of Bellman's equation have been studied earlier, for example, in [3–6]. Asymptotic expansions with respect to a small parameter, being the noise intensity, were constructed in [4–6] for the case when the deterministic Bellman equation corresponding to a system without random perturbations has a smooth solution. Exact solutions of Bellman's equation were obtained in [3] in certain cases when the system has a dimension of one." @default.
- W1490837526 created "2016-06-24" @default.
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- W1490837526 date "1973-01-01" @default.
- W1490837526 modified "2023-09-30" @default.
- W1490837526 title "Approximate solution of Bellman's equation for a class of optimal terminal state control problems" @default.
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- W1490837526 doi "https://doi.org/10.1016/0021-8928(73)90083-x" @default.
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