Optimal control problem for nonlinear stochastic difference second kind Volterra equations
type: Item
instance of: scholarly article
title: Optimal control problem for nonlinear stochastic difference second kind Volterra equations
zbMATH Open document ID: 0898.93036
DOI: 10.1016/S0898-1221(97)00189-2
author: N. V. Kuchkina
author: Leonid Shaikhet
publication date: 1998-11-05T00:00:00Z
review text: The author considers the optimal stochastic control problem for the discrete-time system \[ x(i+1) =\eta (i+1) +\Phi (i+1, x_{i+1}) +\sum^i_{j=0} a\bigl(i,j,x_j,u(j) \bigr)+ \sum ^i_{j=0} b\bigl(i,j,x_j, u(j)\bigr) \xi(j), \tag{1} \] \[ x(0)= \eta(0) \] and the cost functional \[ J(u)= E\Biggl[F(x_N) +\sum^{N-1}_{j=0} G\bigl(j,x_j, u(j)\bigr) \Biggr].\tag{2} \] Under suitable assumptions, necessary optimality conditions are derived. As an example a linear-square optimal control problem is considered.
reviewed by: L. Socha
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1107101
zbMATH Keywords: Volterra integral equation
zbMATH Keywords: optimal stochastic control problem
zbMATH Keywords: discrete-time system
MaRDI profile type: Publication
cites work: Q4868382
cites work: Opial-type inequalities involving higher order differences
cites work: Necessary and sufficient conditions of asymptotic mean square stability for stochastic linear difference equations
cites work: Linear square optimal control problem for stochastic difference equations with unknown parameters
cites work: Riccati equations in the stability of retarded stochastic linear systems
full work available at URL: s0898-1221(97)00189-2
OpenAlex ID: W1980676428
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1107101