Unified approach for closed-loop optimal control

We develop a unified approach for the optimization of closed-loop control systems, based on our earlier results on Euler-Langrange equation [1] and open-loop optimal control [2]. 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 provided to demonstrate the results developed in this paper.