Model-free time-varying controller parameters optimization based on constrained extremum seeking approach for batch processes

Abstract

This paper presents a novel constrained identification-based extremum seeking (ES) algorithm to address model-free constrained optimization challenges in batch processes. The significance of this work lies in its ability to handle constrained optimization problems of time-varying controller parameters under the scenario of unknown system. Time-varying parameters are represented using an interpolation method to reduce optimization dimensions. A key point is the design of an interior-point penalty approach with an adaptive coefficient in the constrained ES problem, ensuring feasibility and avoiding obtaining inaccurate solutions in comparison with traditional interior-point penalty methods. Meanwhile, the quasi-Newton direction and the attenuation dither signal are constructed by estimated gradient facilitating the fast and asymptotic convergence of the optimization problem. Rigorous convergence properties of the proposed ES algorithm are established. Furthermore, numerical illustrations for time-varying controllers optimization demonstrate the effectiveness and practicality of the proposed method.