- The push-cart system [Mic92]
is a two-dimensional system described by the following equations:
x1(k+1)=x2(k),
k=1,2,...,N
,
x2(k+1)=2·x2(k)-x1(k)+(1/N^2)·u(k)
.
- The objective function for minimization is therefore defined
as:
f(x,u)=-x1(N+1)+1/(2·N)·sum(u(k)^2),
k=1:N
.
- The exact solution can be analytically found by:
Minimum=-(1/3)+((3·N-1)/(6·N^2))+1/(2·N^3)·sum(k^2),
k=1:N-1
.
Figure 1 shows the control vector
for the push-cart system with N=20.
Fig. 1: Optimal control vector
for the push-cart system with N=20
This function is implemented in the m-file objpush.m.
This document is part of
version 3.3 of the
GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab -
www.geatbx.com.
The Genetic and Evolutionary Algorithm Toolbox is
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© 1994-2000 Hartmut Pohlheim, All Rights Reserved,
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