Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation

Abstract

Dependence on the parameters of the set of trajectories of the control system described by a nonlinear Volterra integral equation Applications of Mathematics, Vol. 59 (2014) Abstract. In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius µ in Lp (p > 1). It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to µ for each fixed p, and is continuous with respect to p for each fixed µ. An upper estimate for the diameter of the set of trajectories is given.

On the compactness of the set of L-2 trajectories of the control system

“…Control systems described by the integral equations with geometric constraints on the controls are discussed in [1,3,4,22] (see also the references in these papers). The properties of the set of trajectories of the control systems with integral constraints on the control functions and described by different type integral equations are considered in [13,14]. In [12,15] and [16], the methods for approximate construction of the set of trajectories are discussed.…”

On the existence of ε-optimal trajectories of the control systems with constrained control resources

“…In papers [8], [9] various topological properties of the sets of trajectories of the control systems described by the nonlinear Volterra type integral equations with integral constraint on the control functions are studied. In [7] the approximation of 76 ANAR HUSEYIN the sets of trajectories of the aforementioned systems is discussed.…”

Approximation of the Set of Trajectories of the Nonlinear Control System with Limited Control Resources

“…In [14], [16], [15], [17] approximation and topological properties of the set of trajectories of the control systems described by nonlinear integral equations with integral constraints on the control functions are considered. In this paper the control system described by a Urysohn type integral equation with integral constraint on the control functions is studied, where the trajectory of the system is multivariable continuous function.…”