Control of stochastic chaos using sliding mode method

AbstractStabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As some case studies, the stabilization of 1-cycle and 2-cycle orbits of chaotic Duffing and Φ6 Van der Pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems. Simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper

SYNCHRONIZATION OF CHAOTIC SYSTEMS USING VARIABLE STRUCTURE CONTROLLERS

ABSTRACT In this paper a variable structure system based upon sliding mode control with time varying sliding surface and variable boundary layer is introduced to synchronize two different chaotic systems with uncertain parameters. The method is applied to Lur'e-Genesio chaotic systems, as drive-response systems to investigate the effectiveness and robustness of the controlling method. In addition the simulation is repeated with a conventional sliding mode to compare the performance of the proposed sliding mode technique with a simple sliding mode control. The results show the high quality and improved performance of the method presented in the paper for synchronization of different drive-response chaotic systems

Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance

Augmenting Inertial Motion Capture with SLAM Using EKF and SRUKF Data Fusion Algorithms

Inertial motion capture systems widely use low-cost IMUs to obtain the orientation of human body segments, but these sensors alone are unable to estimate link positions. Therefore, this research used a SLAM method in conjunction with inertial data fusion to estimate link positions. SLAM is a method that tracks a target in a reconstructed map of the environment using a camera. This paper proposes quaternion-based extended and square-root unscented Kalman filters (EKF & SRUKF) algorithms for pose estimation. The Kalman filters use measurements based on SLAM position data, multi-link biomechanical constraints, and vertical referencing to correct errors. In addition to the sensor biases, the fusion algorithm is capable of estimating link geometries, allowing the imposing of biomechanical constraints without a priori knowledge of sensor positions. An optical tracking system is used as a reference of ground-truth to experimentally evaluate the performance of the proposed algorithm in various scenarios of human arm movements. The proposed algorithms achieve up to 5.87 (cm) and 1.1 (deg) accuracy in position and attitude estimation. Compared to the EKF, the SRUKF algorithm presents a smoother and higher convergence rate but is 2.4 times more computationally demanding. After convergence, the SRUKF is up to 17% less and 36% more accurate than the EKF in position and attitude estimation, respectively. Using an absolute position measurement method instead of SLAM produced 80% and 40%, in the case of EKF, and 60% and 6%, in the case of SRUKF, less error in position and attitude estimation, respectively.Comment: 8 pages, 8 figures, 4 tables, 21 reference

Vibration suppression of a strain gradient micro-scale beam via an adaptive lyapunov control strategy,”

Vibration suppression of a strain gradient Euler-Bernoulli beam in presence of disturbance and uncertainties is considered in this investigation. Vibration of the system is suppressed by an adaptive boundary controller which has robustness to the environmental and control effort disturbances. The direct Lyapunov stability theorem is used to design the controller and adaptation law. The numerical results are presented to demonstrate the effectiveness of the proposed controller