Examples
A common solution strategy in many optimal control problems is to solve for the costate (sometimes called the shadow price) . The costate summarizes in one number the marginal value of expanding or contracting the state variable next turn. The marginal value is not only the gains accruing to it next turn but associated with the duration of the program. It is nice when can be solved analytically, but usually the most one can do is describe it sufficiently well that the intuition can grasp the character of the solution and an equation solver can solve numerically for the values.
Having obtained, the turn-t optimal value for the control can usually be solved as a differential equation conditional on knowledge of . Again it is infrequent, especially in continuous-time problems, that one obtains the value of the control or the state explicitly. Usually the strategy is to solve for thresholds and regions that characterize the optimal control and use a numerical solver to isolate the actual choice values in time.
Read more about this topic: Optimal Control
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