2.3 Harvest system	Contents

2 Optimization of dynamic systems

2.4 Push-cart system

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.