Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control

Abstract

An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.

A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

“…We leave the long algebra outside the scope of this paper. The complete details of the transformations can be found in [50][51][52][53], where the same idea is applied to different control problems. However, for the sake of completeness, we briefly present some derivations from the mentioned papers here.…”

“…In ( 50) and ( 51), the constants K 0 , K h , K 0 and K h depend on the domain ( 5), ( 26), (38) and τ. It follows from ( 51) and (50), that if the function z(τ) belongs to the domain ( 5), ( 26) over the interval [0, τ]; then, it exponentially decreases over the interval τ ∈ [τ 1 , τ]. Let us fix τ, τ > τ 1 > 0 in the domain (39), so that…”

“…In the present paper, the method developed and applied in [50][51][52][53] to various systems is modified for systems with a delayed control.…”

Boundary Value Problem for a Two-Time-Scale Nonlinear Discrete System

“…by using an algorithmic technique we developed firstly for perturbed difference equations (see [10], [11], [16], [17], [18], [19]). Recently, many researchers have studied discrete versions of boundary value problems (BVPs) (see [1], [4], [5], [8]), and applications of two-point BVP algorithms arise in pollution control problems, nuclear reactor heat transfer and vibration. For an abbreviated writing, we denote the partial derivative…”