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Control of functional differential equations with function space boundary conditions
Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Relative controllability of linear difference equations
In this paper, we study the relative controllability of linear difference
equations with multiple delays in the state by using a suitable formula for the
solutions of such systems in terms of their initial conditions, their control
inputs, and some matrix-valued coefficients obtained recursively from the
matrices defining the system. Thanks to such formula, we characterize relative
controllability in time in terms of an algebraic property of the
matrix-valued coefficients, which reduces to the usual Kalman controllability
criterion in the case of a single delay. Relative controllability is studied
for solutions in the set of all functions and in the function spaces and
. We also compare the relative controllability of the system for
different delays in terms of their rational dependence structure, proving that
relative controllability for some delays implies relative controllability for
all delays that are "less rationally dependent" than the original ones, in a
sense that we make precise. Finally, we provide an upper bound on the minimal
controllability time for a system depending only on its dimension and on its
largest delay
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