Approximation of the attainable sets of the nonlinear control systems with integral constraint on controls

In this article the attainable sets of a control system are investigated. It is assumed that the behavior of the control system is described by a differential equation which is nonlinear with respect to the phase state vector and control vector. The admissible control functions are chosen from the closed ball centered at the origin with radius μ0μ0 in Lp([t0,θ];Rm)Lp([t0,θ];Rm) with p∈(1,+∞)p∈(1,+∞). An approximation method has been obtained for numerical construction of the attainable sets.