The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

Abstract

This paper investigates the control of chaotic systems in the presence of unknown parameters, model uncertainties, and external disturbance. We first discuss the control of a class of chaotic systems and then investigate the control of general chaotic systems. Based on the adaptive control scheme, some novel criteria are proposed via a backstepping-like procedure. As an example, the control of the Zhang hyperchaotic system is investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach.

Observer and descriptor satisfying incremental quadratic constraint for class of chaotic systems and its applications in a quadrotor chaotic system

“…and D 1 is any positive real number. Then, we construct the full-order observer for system (16) of the form; ˙…”

“…Corollary 3.6. If we consider Z equals to zero in (16) , we get observer given in [34] Corollary 3.7. If original system 16 has only linear output, then we get observer given in [35] Corollaries 3.6 and 3.7 show generalization of observer given in our work.…”

“…8 in the form of long row of a matrix having dimension 128 × 128 is considered. Meanwhile, observer system (17) synchronizes with original system (16) , but this all is possible to set pulses of sequences;…”

An Adaptive Neural Network Control Scheme for Stabilizing Chaos to the Stable Fixed Point

“…In Eqs. 17, (18), second terms are calculated as: (22) where z η is also changed adaptively as: (23) where 1 > φ and 1 < ς are appropriate constants. With above updating rules, the output of the network converges to the target stable fixed point.…”

Generation of chaotic attractors using neurons with multidentrites

“…Therefore, the control of such unpredictable systems has caught the attention of researcher since 1990s. Luo (2015) investigated an easy control implementation of the unpredictable behaviour of a hyperchaotic system with model uncertainties, external noise and anonymous parameters. A class of chaotic systems are characterised by the coexistence of many different types of attractors, a phenomenon referred to the multi-stability which has become a very important research topic and received much attention recently (Yu et al, 2020;Lin et al, 2020).…”