Understanding Costate Variables in Optimal Control Theory

In optimal control theory, we often encounter a method that elegantly combines the objective function and the state equations. This approach bears a striking resemblance to using a Lagrangian in static optimization problems. However, there's a key distinction: the multipliers, denoted as λ(t) and referred to as 'costate variables,' are not constants but functions of time. This dynamic nature of costate variables sets them apart in the realm of dynamic systems.