10 papers
On the minimal integral energy of majorants of the Wiener process
S. E. Nikitin
We consider the asymptotic behavior (over long time intervals) of the minimal integral energy \[ |h|_T^ψ= \int_0^T ψ(h^\prime(t)) \, \mathrm{d}t \] of majorants of the Wiener proce…
Leap Gradient Algorithm
Sergey Nikitin
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of targ…
Stabilization of nonlinear systems with semi-quadratic cost
S. Nikitin
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effect…
Stochastic extrema as stationary phases of characteristic functions
S. Nikitin
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The…
Pontryagin's principle of stabilization
Sergey Nikitin
The paper presents necessary and sufficient conditions for a nonlinear system to be stabilized by a feedback. The conditions are based on the ideas related to the well-known Pontry…
Generalized persistency of excitation
Sergey Nikitin
The paper presents the generalized persistency of excitation conditions. They are not only valid for much broader range of applications than their classical counterparts but also e…