DESIGNING CONTROL SCHEMS FOR CHAOTIC SYSTEMS VIA SLIDING MODE CONTROL

Abstract

Among various robust control methods, Sliding Mode Control (SMC) has attracted considerable interest in theoretical research due to its unique features. SMC is well known for its robustness to matched and bounded uncertainties, reduction in the order of the system during the sliding phase, simplified decoupling of system dynamics, and its ability to achieve zero steady-state error. These characteristics make SMC a powerful tool in designing control systems for uncertain and nonlinear environments. This thesis presents a comprehensive study on the control and synchronization of chaotic systems, focusing on the Modified Lorenz System (MLS) and the Liu financial dynamical system. Chaotic behavior, with its sensitivity to initial conditions, presents major challenges in nonlinear control. Sliding Mode Control (SMC) is applied to coupled MLS to ensure robust synchronization through a designed sliding surface and control law, with convergence proven via Lyapunov stability and validated through numerical simulations. In the Liu financial system, both SMC and Passive Control (PC) are implemented and compared. While SMC provides rapid synchronization (within 𝑡 ≥ 1, error reduced from 5.67 to 0.02), PC achieves synchronization more gradually (within 𝑡 ≤ 13, error reduced from 6.21 to 0.03) using a simpler, single-controller strategy. The results highlight key trade-offs between speed, robustness, and implementation complexity, offering valuable insights into managing chaos in nonlinear and financial systems. These limitations have motivated ongoing research aimed at improving SMC design. The core challenge remains how to develop a simple yet effective sliding mode control technique that retains its robustness and zero-error tracking while minimizing chattering and relaxing the need for precise uncertainty bounds.