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Convex Analysisの二,三の進展について

Fractional Differential Equations

System Identification I

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L2 Gain And Passivity Techniques In Nonlinear Control

This paper presents a new adaptive sliding-mode control (ASMC) scheme that uses the time-delay estimation (TDE) technique, then applies the scheme to robot manipulators. The proposed ASMC uses a new adaptive law to achieve good tracking performance with small chattering effect. The new adaptive law considers an arbitrarily small vicinity of the sliding manifold, in which the derivatives of the adaptive gains are inversely proportional to the sliding variables. Such an adaptive law provides remarkably fast adaptation and chattering reduction near the sliding manifold. To yield the desirable closed-loop poles and simplify a complicated system model by adapting feedback compensation, the proposed ASMC scheme works together with a pole-placement control (PPC) and a TDE technique. It is shown that the tracking errors of the proposed ASMC scheme are guaranteed to be uniformly ultimately bounded (UUB) with arbitrarily small bound. The practical effectiveness and the fast adaptation of the proposed ASMC are illustrated in simulations and experiments with robot manipulators, and compared with those of an existing ASMC.

A New Adaptive Sliding-Mode Control Scheme for Application to Robot Manipulators

Containment control of heterogeneous linear multi-agent systems

In this study, an adaptive fractional-order terminal sliding mode controller is proposed for controlling robot manipulators with uncertainties and external disturbances. An adaptive tuning method is utilised to deal with uncertainties which upper bounds are unknown in practical cases. Fast convergence is achieved using non-singular fast terminal sliding mode control. Also, fractional-order controller is used to improve tracking performance of controller. After proposing a new stable fractional-order non-singular and non-linear switching manifold, a sliding mode control law is designed. The stability of the closed-loop system is proved by Lyapunov stability theorem. Simulation results demonstrate the effectiveness and high-precision tracking performance of this controller in comparison with integer-order terminal sliding mode controllers.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2015.1218

Adaptive fractional-order non-singular fast terminal sliding mode control for robot manipulators

Fuzzy approach to select machining parameters in electrical discharge machining (EDM) and ultrasonic-assisted EDM processes

In this paper, the problem of finite-time stabilization and control of an n -degree of freedom (DOF) robotic manipulator is concerned. Factors such as model nonlinearity, uncertainties, and external disturbances can interfere in a closed-loop system performance. In order to attenuate these effects and improve the response characteristics of the system, a proper controller is developed. This paper is the pioneering one on integrating adaptive backstepping control approach into fractional-order controller design for an integer-order dynamic system. An analytic proof is provided based on the fractional Lyapunov stability theorem to guarantee global asymptotic stability of the controlled system. Ensuring finite-time convergence of the system regardless of initial states values is another important aspect of this study. Furthermore, model uncertainties and external disturbances are taken into account and the controller is developed to attenuate these effects. The developed fractional-order adaptive backstepping controller (FOABC) is experimentally implemented on a manipulator and extensive experiments are carried out. Moreover, an exact comparison between FOABC, integer-order adaptive backstepping controller (ABC), and two of the recently released adaptive control approaches is drawn which gives an evidence of superiority of the controller.

Fractional-Order Adaptive Backstepping Control of Robotic Manipulators in the Presence of Model Uncertainties and External Disturbances

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.

Mohammad Ali Badamchizadeh

Papers

Containment control of heterogeneous linear multi-agent systems

Adaptive fractional-order non-singular fast terminal sliding mode control for robot manipulators

Fuzzy approach to select machining parameters in electrical discharge machining (EDM) and ultrasonic-assisted EDM processes

Fractional-Order Adaptive Backstepping Control of Robotic Manipulators in the Presence of Model Uncertainties and External Disturbances

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.