Optimal control of the motion of a quasilinear oscillating system with the aid of small forces
Abstract
A firstapproximation solution in the small parameter is given for some problems in the optimal control of singlefrequency oscillating systems consisting, in the unperturbed state, of an arbitrary number of oscillating elements. It is assumed that the frequency depends on the 'slow' time, defined as normal time multiplied by the small parameter plus a constant, and the control affects only perturbing members, so that the system is formally weakly controllable. Cases of practical interest are studied where the controlling forces are small but of long duration. The analysis is applied to the problem of a plane oscillator.
 Publication:

Prikladnaia Matematika i Mekhanika
 Pub Date:
 December 1975
 Bibcode:
 1975PriMM..39..995A
 Keywords:

 Boundary Value Problems;
 Maximum Principle;
 Mechanical Oscillators;
 Nonlinear Systems;
 Optimal Control;
 Canonical Forms;
 Frequency Response;
 Functional Analysis;
 Stable Oscillations;
 Time Dependence;
 Physics (General)