Suppression and synchronization of chaos in uncertain time-delay physical system

The mechanical horizontal platform (MHP) system exhibits a rich chaotic behavior. The chaotic MHP system has applications in the earthquake and offshore industries. This article proposes a robust adaptive continuous control (RACC) algorithm. It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances. The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system; it improves the efficiency of the closed-loop. The proposed RACC approach (a) accomplishes faster convergence of the perturbed state variables (synchronization errors) to the desired steady-state, (b) eradicates the effect of unknown state-dependent and time-dependent disturbances, and (c) suppresses undesirable chattering in the feedback control inputs. This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique. It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values. The computer simulation results endorse the theoretical findings and provide a comparative performance.