Other than learning basic calculus, I don't really have an advanced background. I was curious to learn about Optimal Control (the theory that involves, bang-bang, Potryagin's Maximum Principle etc.) but any article that I start off with, mentions the following: "Consider a control system of the form..." and then goes on to defining partial differential equations. In short, I am lost. 


Can someone suggest me a path I should take to learn more about Optimal Control from the very basics?



How do I approach Optimal Control?
My field is mathematical programming, and I tend to look at optimal control as just optimization with ODEs in the constraint set; that is, it is the optimization of dynamic systems. I would start by studying some optimization theory (not LPs but NLPs) and getting an intuitive feel for the motivations behind stationarity and optimality conditions -- that will lead naturally into optimal control theory.


I should mention there is another facet of optimal control, related to control systems. The systems considered are discrete time (as opposed to continuous in PMP) therefore it's difference equations instead of differential equations. Examples of optimal control laws in this latter sense are Linear Quadratic Regulators (LQRs), Linear Quadratic Gaussian (LQGs), Model Predictive Control (MPC). It is this latter type of optimal control that is actually applied in industry. The Pontryagin principle, while useful for analysis, is generally intractable for real-time application to nontrivial plants.


