SYNTHESIS OF OPTIMAL CONTROLS FOR NONLINEAR OBJECTS BY THE CRITERION OF MAXIMUM SPEED

• Main Authors: Yu. P. Korniushin, D. V. Melnikov, A. V. Mazin
• Format: Article
• Language: English
• Published: CRI «Electronics» 2017-11-01
• Series: Радиопромышленность
• Subjects: synthesis; optimal; speedy; nonlinear; matrix; operator
• Online Access: https://www.radioprom.org/jour/article/view/255
• ISSN: 2413-9599; 2541-870X

The  article  presents  an  algorithm  for  synthesizing  optimal  program  controls  for  nonlinear  control-affine  objects  by  the criterion  of  maximum  speedy.  The  mathematical  apparatus  used  is  the  linearization  of  Newton-Kantorovich  and  the apparatus of matrix operators. The structure of the algorithm includes the following steps at the first stage, the linearization of the nonlinear mathematical model of the object is performed by the Newton-Kantorovich method; at the second stage, we carry out the reduction of the synthesis problem by the criterion of minimum time in the presence of constraints on the control energy to the synthesis problem by the energy minimum criterion for finding the (optimal) minimum value of the sought  time;  at  the  third  stage  we  perform  parametrization  of  the  mathematical  model  of  the  control  object  and  a  new quality criterion using the apparatus of matrix operators with the subsequent construction of the optimal control. The fourth final  stage  consists  in  realizing  the  iterative  process  prescribed  by  the  Newton-Kantorovich  method-there  is  an  optimal (minimal) time value. The synthesis algorithm is illustrated by an example.