An efficient PID-based optimizer loop and its application in De Jong’s functions minimization and quadratic regression problems

• Published in: Systems & control letters Vol. 159; p. 105090
• Main Authors: Alagoz, Baris Baykant, Deniz, Furkan Nur, Koseoglu, Murat
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2022
• Subjects: De Jong’s function; Nonlinear optimization; PID-based optimizers; Quadratic regression; PID-based optimizers; Quadratic regression; Nonlinear optimization; De Jong’s function
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2021.105090

The Proportional–Integral–Derivative (PID) control law has been commonly used for process control in control engineering applications. However, it has potential to work as a solver in optimization problems. This study introduces a PID-based optimizer loop that is designed to solve nonlinear, unconstrained, multi-parameter optimization problems. To achieve the minimization of multi-parameter positive real objective functions by using a closed loop PID control loop, a slope sentient objective function model is suggested to allow zero-crossing of the error signal. Thus, this objective function model enhances the convergence efficiency of the PID-based optimizer loop by indicating slope direction of the objective function and operating in both positive and negative error regions. The boundedness and convergence theorems for the proposed PID optimizer loop are presented, and a theoretical background for the PID-based minimization is established. To demonstrate practical minimization performance, numerical applications of the proposed PID optimizer loops are illustrated in the solution of two fundamental optimization problems. These are the minimization of 30 parameters De Jong’s functions and the solution of quadratic regression problems. Also, an experimental study is presented for the quadratic regression modeling of measurement data from a hole-drilling experiment. Optimization results reveal that the proposed PID-based optimizer system can improve convergence speed and accuracy compared to performances of fundamental nonlinear optimization techniques. •A novel closed loop PID-based optimizer system is proposed to solve optimization problems.•The proposed PID optimizer loop uses a slope sentient objective function model.•The slope sentient objective function model provides slope direction info.•The PID optimizer loop is compared with gradient-based optimization methods.•Test results indicate improved minimization performance of PID optimizer loops.