“…Therefore, OGY scheme on the basis of the linearization of the Poincare´map can generate a small control input using these properties. [11][12][13][14] In order to estimate the Poincare´map in the OGY controller, SVM technique is proposed due to the training network with high speed and appropriate performance in the system with sensitivity to initial conditions. The estimation function based on the least square SVM results in a convex optimization of the performance index with linear inequality constrains using the Lagrangian method.…”
Section: Mathematical Modelmentioning
confidence: 99%
“…Therefore, OGY scheme on the basis of the linearization of the Poincaré map can generate a small control input using these properties. 11–14 Figure 5.Control structure of the chaotic half-car model based on the optimal OGY.…”
Section: Chaos Control Strategymentioning
confidence: 99%
“…The OGY system was introduced by Ott-Grebogi-Yorke on the basis of the linearization of the Poincare´map. [11][12][13][14] The superiority of OGY algorithm persuaded researchers recently to extend the theory and applications of this method. The estimation of the Poincare´map in the OGY is one of the main problems.…”
The chaotic dynamics along with the control of chaos in a half-car model with semi-active suspension system is considered in this paper. The time series responses, phase space trajectories, Poincaré sections, and Lyapunov exponent methods are used to analyze the chaotic behavior in the open-loop system. In order to suppress the chaotic responses in the system, a chaos controller is applied based on the development of Ott-Grebogi-Yorke algorithm. In this new control strategy, the Poincaré map of the system is estimated using the support vector machine innovatively. After linearization of the Poincaré map, the optimal discrete-time linear quadratic regulator is designed for the linear map as a main contribution. The discrete optimal Ott-Grebogi-Yorke controller improves the performance of the system along with the rejection of chaos in the responses. This improvement involves the reduction in settling time, control effort, and energy consumption in the suspension system.
“…Therefore, OGY scheme on the basis of the linearization of the Poincare´map can generate a small control input using these properties. [11][12][13][14] In order to estimate the Poincare´map in the OGY controller, SVM technique is proposed due to the training network with high speed and appropriate performance in the system with sensitivity to initial conditions. The estimation function based on the least square SVM results in a convex optimization of the performance index with linear inequality constrains using the Lagrangian method.…”
Section: Mathematical Modelmentioning
confidence: 99%
“…Therefore, OGY scheme on the basis of the linearization of the Poincaré map can generate a small control input using these properties. 11–14 Figure 5.Control structure of the chaotic half-car model based on the optimal OGY.…”
Section: Chaos Control Strategymentioning
confidence: 99%
“…The OGY system was introduced by Ott-Grebogi-Yorke on the basis of the linearization of the Poincare´map. [11][12][13][14] The superiority of OGY algorithm persuaded researchers recently to extend the theory and applications of this method. The estimation of the Poincare´map in the OGY is one of the main problems.…”
The chaotic dynamics along with the control of chaos in a half-car model with semi-active suspension system is considered in this paper. The time series responses, phase space trajectories, Poincaré sections, and Lyapunov exponent methods are used to analyze the chaotic behavior in the open-loop system. In order to suppress the chaotic responses in the system, a chaos controller is applied based on the development of Ott-Grebogi-Yorke algorithm. In this new control strategy, the Poincaré map of the system is estimated using the support vector machine innovatively. After linearization of the Poincaré map, the optimal discrete-time linear quadratic regulator is designed for the linear map as a main contribution. The discrete optimal Ott-Grebogi-Yorke controller improves the performance of the system along with the rejection of chaos in the responses. This improvement involves the reduction in settling time, control effort, and energy consumption in the suspension system.
“…In recent years, a number of publications on the application and extension of the OGY algorithm have appeared in the literature. Much of this literature focuses on the notion of decreasing the calculation time and better performance for the chaos control system . Besides the advantages of the OGY controller, the main problem of this control system is the derivation of the related Poincaré map.…”
Quasi-periodic and chaotic behavior, along with the control of chaos for a Gyrostat satellite (GS), is investigated in this work. The quaternion-based dynamical model of the GS is first derived, and then the influences of the reaction wheels in the GS structure, under the gravity gradient perturbation that causes a route to chaos through quasi-periodicity mechanism, is investigated. For the suppression of chaos in the system, a chaos control system with the quaternion feedback is designed for the GS based on the extension of the Ott-Grebogi-Yorke (OGY) method using the linearization of the Poincaré map. In the extended OGY controller, the Poincaré map is estimated using the Least Square Support Vector Machine (LSSVM) technique. After linearization of the Poincaré map, the Discrete-time Linear Quadratic Regulator (DLQR) is applied on the linearized Poincaré map, making the DLQR-OGY controller for chaos. The DLQR-OGY control system stabilizes the orbits to the fixed points providing a small control input signal, which leads to a decrease in the control effort and energy consumption in the GS system.
“…In the real application, the chattering phenomenon may cause electronic circuits to be superheated and broken. In order to solve this problem, quasi-sliding mode control method is studied recently [21][22][23][24][25]. Based on the quasi-sliding mode controller, when the trajectories of dynamic systems converge to the sliding manifold, the trajectories can be bounded in the settled region along the sliding surface and the impulse and chattering phenomenon can be avoided.…”
This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on theH∞theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, theH∞quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
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