Synchronisation of uncertain chaotic systems via fuzzy-regulated adaptive optimal control approach

This study investigates the adaptive synchronisation of uncertain chaotic systems with unmodelled nonlinearities, dynamic mismatch, parametric perturbations, and external disturbances. A fuzzy-regulated adaptive optimal control (FRAOC) scheme is derived to realise chaotic synchronisation under both structure and parameter uncertainties. In the proposed scheme, the uncertain chaotic dynamics is firstly captured and estimated using a self-organising learning algorithm in an online fuzzy rule database. Based on the complicated and uncertain chaotic information, control strategy is adaptively regulated and configured in the form of weighting matrix for the subsequent optimal controller by the use of fuzzy logic inference. An adaptive optimal controller is then developed, so that its control behaviour and performance are adaptively adjusted for the chaotic synchronisation and compound uncertainty compensation. A supervisory compensator with recursive adaptation law is also designed to attenuate the residual compensation error and guarantee the synchronisation stability. Chaotic synchronisation convergence using the proposed approach can be mathematically ensured and speeded up with satisfactory robustness. Simulation results also demonstrate the effectiveness of the proposed control method in comparison with robust quadratic optimal control based on linear matrix inequality approach.