ISSN:
1573-2878
Keywords:
Optimal control
;
nonlinear large systems
;
decomposition and coordination
;
modification of performance index
;
improvement of convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper proposes a coordination algorithm for multilevel control of a nonlinear dynamical system. The overall system under consideration is composed of subsystems with relatively strong interactions or relatively strong nonlinearities, or both. The objective is to minimize a performance index of quadratic type. The idea of the present algorithm is to replace the system variables associated with interactions and nonlinearities by artificially introducedinteraction variables and to decompose the overall problem into a number of smaller and simpler subproblems. At the same time, the appearance of the performance index is modified by using the interaction variables. Parameters, called weights, are introduced into the modified performance index. Choice of the values of these parameters has significant influence on the convergence rate of the algorithm, and hence is one of the major factors determining the total computing time. The interaction variables are adjusted directly by a nearly steepest-descent algorithm, without using Jacobian matrix, until the interactions attain consistency. In the paper, some sufficient conditions for convergence of the iterative algorithm are discussed in detail, and several features of the present algorithm are illustrated by examining an example.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933215
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