fundamental matrix

Approximation of Control for Singularly Perturbed System with Delay with Integral Quadratic Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The purpose of the work is the development and theoretical substantiation of analytical approximate or asymptotic methods for solving optimal control problems for singularly perturbed systems with constant delay in phase variables under conditions of uncertainty with respect to the initial data. For achievement of a goal the control problem for the singularly perturbed system with delay with indeterminate initial conditions and integral quadratic constraints on the control resources according to the minimax criterion is considered.

On Iterative Method of Constructing Optimal Control for Singularly Perturbed Systems with Delay

Authors: Grebennikova I. V.

The control problem for the singularly perturbed system with delay according to the minimax criterion is considered. Iterative procedure of constructing control response that approximates the optimal solution with givenac curacy with respect toasmall positive parameter is proposed.

Iterative Procedure of Constructing Optimal Solving in the Minimax Problem of Control for Singularly Perturbed System with Delay with Geometric Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. Iterative procedure of constructing control response that approximates the optimal solution with given accuracy with respect to a small positive parameter is proposed.

Approximation of Control for Singularly Perturbed System with Delay with Geometric Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. A limiting problem is formulated for which a specially selected quality functional is chosen. We propose the procedure for initial approximation construction of a control response in the control minimax problem.