Finite-dimensional approximations of neutral-type conflict-controlled systems

M. I. Gomoyunov ; A. R. Plaksin

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 49 (2017), pp. 111-122

Résumé

The paper deals with a conflict-controlled dynamical system which motion is described by neutral-type functional-differential equations in J. Hale's form. Approximations of this system by controlled high-dimensional systems of ordinary differential equations are investigated. A mutual aiming procedure between the initial system and its finite-dimensional approximation that guarantees proximity between their motions is elaborated. Stability properties of the procedure with respect to measurement errors are established, an illustrative example is considered. An application of the procedure is given for solving a guarantee optimization problem in which a motion of the dynamical system is described by linear functional-differential equations of neutral type in J. Hale's form and the quality index evaluates a motion history and realizations of control and disturbance actions. For this purpose an auxiliary control problem for the approximating system is formulated and its solution is constructed by the upper convex hulls method. It is shown that the optimal guaranteed result in the auxiliary problem approximates the optimal guaranteed result in the initial problem, and with the use of optimal in the auxiliary problem motions of the approximating system as guides an optimal control law is constructed. An illustrative example is considered, numerical simulation results are shown.

Détail

Keywords: control theory, differential games, neutral-type systems.