Two-Point Boundary Optimization Problem for Bilinear Control Systems

DOI

10.2991/jnmp.1997.4.1-2.33How to use a DOI?

Abstract

This paper presents a new approach to the optimization problem for the bilinear system x = {x, } (1) based on the well-known method of continuous parametric group reconstruction using of its structure constants defined by the Brockett equation z = {z, }. (2) Here x is the system state vector, {·, ·} are the Lie brackets, z = {x, y}, y is the vector of cojoint variables, = A-1 z is the control vector, A is the inertion matrix. The quadratic control functional has to reach an extremum at the optimal solution of the equation (2) and the boundary optimization problem is to find such z0 that solution (2) makes evolution from the state x(t0) = x0 up to the final state x(t1) = x1 during the time delay T = t1 -t0. Therefore it is necessary to define a transformation group of the state space which is parametrized by components of the vector and then to solve the Cauchy problem for an arbitrary smooth curve joining x(t0) with x(t0). Key words. Bilinear system, Lie group, optimization, boundary problem, structure constants.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Alla V. Vinogradskaya
PY  - 1997
DA  - 1997/05/01
TI  - Two-Point Boundary Optimization Problem for Bilinear Control Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 209
EP  - 213
VL  - 4
IS  - 1-2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1997.4.1-2.33
DO  - 10.2991/jnmp.1997.4.1-2.33
ID  - Vinogradskaya1997
ER  -