Abstract:
In a stochastic control problem described by a nonlinear hyperbolic equation with a Goursat-Darboux type boundary condition, first-order necessary optimality condition in the form of linearized Pontryagin maximum principle is obtained. The case of degeneration of the linearized maximum principle is considered, and various necessary optimality conditions are established for quasi-singular (i.e., controls for which the linearized maximum condition degenerates) controls.
Key words and phrases:necessary optimality conditions, nonlinear Goursat-Darboux stochastic system, linearized optimality condition, quasi-singular controls.
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