Gradient-Free High-Order Accelerated Self Optimizing Control of Processes with Time Delay

A self-optimizing controller (SOC) adds an upper optimization layer to closed-loop systems, enhancing self-awareness and improving performance during repetitive tasks. However, most SOC optimization algorithms use only the current and previous cost function evaluations to determine the next optimal parameters (first-order optimization methods). This paper introduces a high-order self-optimizing controller (HOSOC) that accelerates the optimization algorithm's convergence by utilizing the history of optimal parameters within a sliding window. A modified version of the Globalized Constrained Nelder Mead optimization method is implemented to account for the past centroids within a memory window to compute the upcoming solution. The algorithm is tested on a general delay-aware First-Order plus Dead Time (FOPDT) system with varying lag, balanced, and delay time dynamics. Results show that the high-order SOC controller speeds up convergence and meets the desired performance specifications effectively.