Precompactness of the Set of Trajectories of the Controllable System Described by a Nonlinear Volterra Integral Equation

Abstract

In this paper the controllable system whose behaviour is described by a nonlinear Volterra integral equation, is studied. The set of admissible control functions is the closed ball of the space L _p (p > 1) with radius µ ₀ and centered at the origin. It is shown that the set of trajectories of the system is a bounded and precompact subset of the space of continuous functions.

Keywords:

• nonlinear Volterra integral equation
• controllable system
• integral constraint
• set of trajectories

AMS Subject Classification:

• 93C23
• 45D05