Controlling Chaotic Systems via Time-delayed Control

Based on Lyapunov stabilization theory, this paper proposes a proportional plus integral time-delayed controller to stabilize unstable equilibrium points (UPOs) embedded in chaotic attractors. The criterion is successfully applied to the classic Chua's circuit. Theoretical analysis and numerical simulation show the effectiveness of this controller.

Design and Optimization of Generalized PD-Based Control Scheme to Stabilize and to Synchronize Fractional-Order Hyperchaotic Systems

This chapter will establish the importance and significance of studying the fractional-order control of nonlinear dynamical systems and emphasize the link between the factional calculus and famous PID control design. It will lay the foundation related to the research scope, problem formulation, objectives and contributions. As a case study, a fractional-order PD-based feedback (Fo-PDF) control scheme with optimal knowledge base is developed in this work for achieving stabilization and synchronization of a large class of fractional-order chaotic systems (FoCS). Based and derived on Lyapunov stabilization arguments of fractional-order systems, the stability analysis of the closed-loop control system is investigated. The design and multiobjective optimization of Fo-PDF control law is theoretically rigorous and presents a powerful and simple approach to provide a reasonable tradeoff between simplicity, numerical accuracy, and stability analysis in control and synchronization of FoCS. The feasibility and validity of this developed Fo-PDF scheme have been illustrated by numerical simulations using the fractional-order Mathieu-Van Der Pol hyperchaotic system.

Laser-range-finder localization based fuzzy control for mobile robots

Purpose Based on laser-range-finder (LRF) sensing, the control design of location and orientation stabilization for the mobile robot is investigated. However, the practical limitation of the LRF sensing is usually ignored in the control design, which leads to incorrect localization and unexpected control results. The purpose of this study is to design the fuzzy controller subject to the practical limitation on the LRF-based localization for a differentially driven wheeled mobile robot. Design/methodology/approach First, the Takagi–Sugeno (T-S) fuzzy model is derived from the polar kinematic model of a differentially driven mobile robot. Then, the fuzzy controller is designed to the derived T-S fuzzy kinematic model in accordance with the Lyapunov stabilization theorem. The derived Lyapunov stabilization conditions for the fuzzy control design are expressed as the linear matrix inequality (LMI) form and effectively solved by LMI tools. The practical limitation on the LRF-based localization is also expressed as the LMI form and simultaneously solved with the control design. Finding The location and posture stabilization experiments are carried out on a mobile robot with LRF-based localization to prove the effectiveness of the proposed T-S fuzzy model-based control design. Furthermore, the ground truth experiment evaluates the accuracy of LRF-based localization. Originality/value The contribution of this study is to develop the fuzzy control law for a differentially driven wheeled mobile robot under the practical limitation on LRF-based localization. The proposed control design can be applied to other robots with practical limitations on the sensors.

Recent Trends in Stabilization and Control of Distributed Parameter Dynamic Systems

The field of control and stabilization of distributed parameter systems described by partial differential equations has recently seen an increasing number of results published by very respected researchers in excellent control engineering and applied mathematics journals. This paper presents a survey of control and stabilization results with emphasis on controls. Various distributed parameter dynamic control and stabilization problems have been studied corresponding to heat conduction, wave propagation, Schrodinger equation, crowd (swarm) dynamics, magneto-hydro-dynamic channel flow, string and beam equations, viscous Burger equation, and general diffusion equations. Various techniques have been used for control and stabilization of such systems: Lyapunov stabilization, backstepping, gain scheduling, singular perturbations, sliding mode control, observer driven controller, tracking control, sampled-data control, neural networks. The field still remains widely open for future research. Applications of surveyed results to various areas including robots, aircraft, networks, transmission lines, electrochemical processes in energy systems are indicated.