A Generalized Hamilton—Jacobi—Bellman Equation for Deterministic Optimal Control Problems

  • Leonard D. Berkovitz
Part of the Systems & Control: Foundations & Applications book series (SCFA)


We shall be concerned with the following problem. Minimize g(t 1, x 1) subject to
$$\frac{{dx\left( t \right)}}{{dt}} = f\left( {t,x\left( t \right),u\left( t \right)} \right) x\left( \tau \right) = \xi $$
$$u\left( t \right) \in Z {\text{a}}{\text{.e}}{\text{.}}$$
$$\left( {{t_1}{x_1}} \right) \in \mathcal{T}{\text{,}}$$
where t 1 is the first time that the solution x(·) of (1) hits a preassigned set T and x 1 = x(t 1).


Viscosity Solution Optimal Trajectory Differential Inclusion Optimal Synthesis Terminal Time 
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© Springer Science+Business Media New York 1999

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  • Leonard D. Berkovitz

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