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On the controllability of a class of nonlinear stochastic systems. (English) Zbl 0986.93007
Summary: We study the controllability properties of a class of stochastic differential systems characterized by a linear controlled diffusion perturbed by a smooth, bounded, uniformly Lipschitz nonlinearity. We obtain conditions that guarantee the weak and strong controllability of the system. Also, given any open set in the state space, we construct a control, depending only on the Lipschitz constant and the infinity-norm of the nonlinear perturbation, such that the hitting time of the set has a finite expectation with respect to all initial conditions.
MSC:
93B05Controllability
93E03General theory of stochastic systems
93C73Perturbations in control systems