Linear Optimal Control

Abstract

In certain problems, control variables enter the Hamiltonian linearly, either via the objective function or the dynamic system or both. This type of problem is called Linear Optimal Control. For example, in the Optimal growth model discussed earlier (see 5.6.2), if the utility funtion is u(c)= c, then the maximization of $\int\limits_0^T {c{e^{ - rt}}dt}$ subject to $\mathop k\limits^ \bullet = f(k) - \lambda k - c$ leads to the Hamiltonian $H \equiv ({e^{ - rt}} - p)c + p[f(k) - \lambda k$ which is linear in the control variable c.