Semi-heuristic optimization techniques performance in robust control systems design

Abstract

Designing a robust controller for systems with parameter uncertainties is a complex and demanding task since they are prone to changes regardless of the external impact forced upon these systems. This change might not only yield poor controller performance, but it can also lead to instability based on the change magnitude. Traditional deterministic control approaches may not provide a convenient solution due to combined computational complexity, and probabilistic approaches may also fall short in providing efficient and satisfactory solutions due to their time-intensive behavior and not guarantee of convergence. To address this challenge, we propose a semi-heuristic approach that works as a mild algorithm, leveraging the advantages of both deterministic and heuristic approaches and overcoming the drawbacks obtained from these two types of control strategies. The proposed semi-heuristic approach exploits the Kharitonov theorem to establish an initial stable controller using system nominal values. Then this controller is used as a starting point for the gradient descent algorithm. The random search technique propagates based on cost function/s implemented for the whole of the uncertainty region. The iterative optimization process by gradient descent incorporates user-defined performance criteria, our approach provides a robust controller with respect to the presence of uncertainties for systems with interval polynomial characteristic equations. We further enhanced the semi-heuristic approach by utilizing a more effective random optimization technique known as the Adaptive Moment Estimation (Adam) optimizer. We applied this proposal to the rotary inverted pendulum system, which is a well-known nonlinear and unstable system in control theory. We managed to demonstrate the efficiency of the semi-heuristic approaches in stabilizing a linearized rotary inverted pendulum model with a parametric approach used for uncertainty representation. Extensive numerical simulations done on the proposed semi-heuristic approaches and the designed model validate the effectiveness of our proposed algorithms for both of the systems considered during this thesis study. Consequently, the semi-heuristic approaches emerge as a moderate solution to our initial problem introduced by the deterministic and stochastic approaches. We further compared the controller results with common control strategies in state-of-the-art and proved their superiority in addressing robust control problems with uncertain parameters.