Unified approach for open-loop optimal control

We develop a unified approach for the necessary conditions for optimization of open-loop control systems, starting from the basic principles of calculus of variations. The unified approach results are simultaneously applicable to both shift (q)-operator-based, discrete-time systems and the derivative (d/dt)-operator-based, continuous-time systems. It is shown that the optimal condition results that are now obtained separately for continuous-time and discrete-time systems can be easily obtained from the unified approach. An illustrative example is given.