Open AccessOn the optimal control of the n-fold integrator
Author(s) -
Yu. N. Gorelov
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-10-114-133
Subject(s) - mathematics , optimal control , maximum principle , singular control , equivalence (formal languages) , boundary value problem , impulse (physics) , integrator , mathematical analysis , impulse control , quadratic equation , mathematical optimization , pure mathematics , computer science , geometry , psychology , computer network , physics , bandwidth (computing) , quantum mechanics , psychotherapist
The optimal control problem n-fold integrator with arbitrary boundary conditions and functionals of type norms in spaces of Lq[t0; tf ], q = 1; 2;1 is considered. First, it is the problem of minimizing the total controling impulse, which boils down to L1- problem of moments; secondly, the problem of minimizing the maximum values of the control parameter (represented as L1-problem of moments), and, finally, it is the problem of minimizing ”generalized work control” (as L2-problem of moments). Solving problems is obtained by using the method of moments in the form of the maximum principle by N.N. Krasovsky. It is shown that optimal control in the first problem is approximated by a -impulsive control. Conditions for the existence of regular and singular solutions to this problem depending on the boundary conditions are also specified. The general solution of the second problem, which is the conditions for existence of regular and singular solutions and not equivalence with the mutual problem of time-optimal control is obtained. Examples of solution for the considered control tasks are given. In case of a quadratic functional general relations required for constructing a program optimal control were obtained.