Abstract
A controllability problem for a Fokker-Planck equation is termedProblem A. Under proper assumptions, a solution (v*, Ф*) to that problem is constructed by a Theorem of Jamison. Theorem 2 gives a sufficiency condition concerning the given initial and terminal data for that solution to exist. Theorem 3 states that v* is an optimal feedback control for a stochastic optimal control problem with constraint on the end-state, termedProblem B. Further, v* corresponds to the minimum of an entropy distance. Finally, Problem A is transformed into a controllability problem for a stochastic differential equation, termedProblem C: the solution to Problem C corresponding to the one constructed in Problem A is the Markovian process satisfying the given end conditions in a set of reciprocal processes of Jamison.
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Blaquiére, A. Controllability of a Fokker-Planck equation, the Schrödinger system, and a related stochastic optimal control (revised version). Dynamics and Control 2, 235–253 (1992). https://doi.org/10.1007/BF02169515
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DOI: https://doi.org/10.1007/BF02169515