Teaching linear-quadratic optimal control to undergraduate students

In this paper we show that the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear-quadratic optimal controller) can be solved using elementary mathematics as a static optimization problem. The derivations require only a basic (undergraduate) usage of linear algebra and state space linear system analysis. Having full understanding of derivations of the linear-quadratic optimal controller, students and engineers will feel confident to use these controllers in numerous engineering and scientific applications.