A class of PSO-tuned controllers in Lorenz chaotic system

Abstract

This paper considers the optimal robust control of chaotic systems subject to parameter perturbations and measurement noise. Three novel dynamic tracking controllers are designed herein to suppress the chaotic behaviour in Lorenz systems under practical constraints. The dynamic controllers allow for extra improvements towards optimal and robust tracking but their design is challenging in the chaotic system. Given a single measured state only, the single-state feedback controllers are optimally tuned using high-performance heuristic Particle Swarm Optimization (PSO) algorithm with a constrained multi-objective function focusing mainly on the Integral Absolute Error (IAE). The controlled system stability is ensured through Routh–Hurwitz stability criteria where control parameters are further tuned using a metaheuristic PSO algorithm to ensure faster transients with minimum errors when tracking desired state trajectories and also to ensure robustness to parameter variations and external disturbances in the chaotic system. Different designs are tested through extensive simulations and comparisons where the proposed PSO-tuned PD-tracking controller is proved superior for not only suppressing the chaotic behaviour and reducing the transients but also for their high robustness to parameter uncertainties and external disturbances.