I was watching some excellent videos on DSGE models by Klaus Pretner. The author was able to solve some simple model such as the Ramsey-Cass-Koopman's model, and a New Keynesian model with frictions, using either analytic first order conditions, or using an analytic derivation of the HJB conditions as well.
However, I keep hearing that economists often have to use the Linear Quadratic Regulator to simulate models. This is what is described in the Ljungquvist and Sargent book and even Sargent's Youtube videos. I am familiar with the Linear Quadratic Regulator from Optimal Control Theory, but can someone explain the reasons for using LQR control in simulating DSGE models? Is there a good article or chapter on this question. I tried to read the Ljunqvist and Sargent text on this topic, but they don't really explain the reason for using it as much as saying that there is no way around using it. So the justification or basis is still not clear to me.
My sense is that is has something to do with stochastic variations around the equilibrium point of a model. But that is just a guess and I don't have a comfortable intuition about what the issue is there.
