Tyler Fallis

In many real-world problems in variational calculus, we cannot explicitly set the value of the system state at every point, but rather can steer the trajectory with the use of a control function. Optimal control theory is an extension to variational calculus where we seek external control functions that not only govern a suitable system of differential equations to desired targets but minimize an associated integral cost functional. The key tool in finding such a control function is Pontryagin's Maximal Principle (PMP), which states that the optimal control maximizes the Hamiltonian of the state/co-state system at every point of continuity. In this talk, we will use the PMP to do straightforward computations of select optimization problems with real-world applications, as well as give a brief idea of the proof of the PMP.