2.2 Linear-quadratic system	Contents	2.4 Push-cart system

2 Optimization of dynamic systems

2.3 Harvest system

The harvest system [Mic92] is a one-dimensional equation of growth with one constraint:

x(k+1)=a·x(k)-u(k), k=1,2,...,N; such that x(0)=x(N).

The objective function for minimization is therefore defined as:

f(u)=-sum(sqrt(u(k))), k=1:N.

The exact solution can be analytically found by:

Minimum=-sqrt((x(0)·(a^N-1)^2/(a^(N-1)·(a-1))).

Figure 1 shows the control vector for the harvest system with N=20.

Fig. 1: Optimal control vector for the harvest system with N=20

This function is implemented in objharv.