Advice to Students
Optimal control is learned by moving repeatedly among a physical system, a mathematical formulation, necessary conditions, numerical computation, and independent verification.
For each problem:
identify states, controls, parameters, information, and units;
state the objective, dynamics, boundary conditions, and path constraints;
predict the qualitative structure of a good solution;
choose a solution method that matches the problem structure;
inspect feasibility, optimality residuals, scaling, and discretization error;
re-simulate the control with an independent dynamics solver; and
explain what the solution means physically and what assumptions limit it.
A solver’s success message is evidence about an algorithm, not by itself evidence that the engineering conclusion is correct.