This paper proposes an adaptive dynamic surface control (DSC) approach for disturbance attenuation of uncertain nonlinear systems in the parametric strict-feedback form. In the proposed control system, a smooth projection algorithm is employed to train uncertain parameters. The proposed DSC system can overcome the complexity of an actual controller caused by the recursive differentiation of virtual controllers and parameter adaptation laws in the backstepping design procedure. From Lyapunov stability analysis, it is shown that the proposed controller has H ∞ tracking performance to attenuate external disturbances
-In this paper, a formation control method based on the leader-following approach for nonholonomic mobile robots is proposed. In the previous works, it is assumed that the followers know the leader's velocity by means of communication. However, it is difficult that the followers correctly know the leader's velocity due to the contamination or delay of information. Thus, in this paper, an adaptive approach based on the parameter projection algorithm is proposed to estimate the leader's velocity. Moreover, the adaptive backstepping technique is used to compensate the effects of a dynamic model with the unknown time-invariant and time-varying parameters. From the Lyapunov stability theory, it is proved that the errors of the closed-loop system are uniformly ultimately bounded. Simulation results illustrate the effectiveness of the proposed control method.
In this paper, an adaptive formation control based on the leader-following approach is proposed for multiple mobile robots with time varying parameters. The proposed controller does not require the velocity information of the leader robot, which is commonly assumed that it is either measured or telecommunicated. In order to estimate time varying velocities of the leader robot, the smooth projection algorithm is employed. From the Lyapunov stability theory, it is proved that the proposed control scheme can guarantee the uniform ultimate boundedness of error signals of the closed-loop system. Finally, the computer simulations are performed to demonstrate the performance of the proposed control system.
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