A bidimensional optimal landing problem (Q1298277)

The author proposes the following model for the evolution of the height \(x(t)\) above the ground and velocity \(y(t)\) of a landing airplane: \[ \begin{aligned} dx(t) &= -y(t) dt,\\ dy(t) &= 2y(t)\left[1-\sqrt{y(t)}\right] dt + bu(t) dt+ \sqrt{8y^2(t)} dW(t), \end{aligned} \] where \(u(t)\) is a control and \(W\) is a Wiener process. The optimal control is found explicitly. The properties of the model are discussed to show that it is a better, more realistic model than models considered previously.