R.O. Mastaliyev.
Optimal control of a stochastic diffusion process with functional equality and inequality constraints
We consider a problem of optimal control of a multidimensional process specified by Ito stochastic differential equation, in the presence of functional equality and inequality constraints on the phase trajectory, with the control acting on the drift coefficient. Sufficiently general and at the same time constructively verifiable first- and second-order necessary optimality conditions are formulated in terms of variations of functionals.
Keywords: Ito equation, Stochastic control problem with constraints, Optimal control, Stochastic analogue of the Euler equation, Analogue of the Legendre-Klebsch condition
DOI: https://www.doi.org/10.54381/icp.2021.2.05
Optimal control of a stochastic diffusion process with functional equality and inequality constraints
We consider a problem of optimal control of a multidimensional process specified by Ito stochastic differential equation, in the presence of functional equality and inequality constraints on the phase trajectory, with the control acting on the drift coefficient. Sufficiently general and at the same time constructively verifiable first- and second-order necessary optimality conditions are formulated in terms of variations of functionals.
Keywords: Ito equation, Stochastic control problem with constraints, Optimal control, Stochastic analogue of the Euler equation, Analogue of the Legendre-Klebsch condition
DOI: https://www.doi.org/10.54381/icp.2021.2.05