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- W2005367169 abstract "Conditions have been obtained in Theorems 1 and 2 for the solution u*(·) of the problem minimize J(u)=∫L(x,u)dt subject to dx/dl=f(x,u), x(t0)=x0 to be characterized by a non-linear, first-order differential equation, called the optimal differential equation. These conditions are not affected by the imposition of constraints, such as c1≤u≤c2. But the trajectory of u*(t) has to be reinterpreted, and the durations of time during which u*(t) makes a sojourn between the boundaries and stays on the boundaries have to be computed. The uniqueness of these durations is considered in Theorem 3. The optimal differential equation can always be discretized in time and phase, to obtain the system of difference equations u-skk+1/*=Fi(uk*) for uk*∃Ii, an interval in the phase space. It is shown that when the Fi(·) are linear, the system Ii is a Markov chain. Some analysis is made of the efficiency of discretization in terms of certain invariants of the system; the theorems relating to this analysis are stated without proof." @default.
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- W2005367169 date "1971-01-01" @default.
- W2005367169 modified "2023-10-16" @default.
- W2005367169 title "A contribution to the theory of optimization with Markovian controls" @default.
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- W2005367169 doi "https://doi.org/10.1016/s0020-0255(71)80022-1" @default.
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