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The Euler-Lagrangenonlinear system with both uncertain parameters and input noises (ENUI) is a common model of many plants in practice as, robot manipulators, mechanical Tora systems, Lavitat mechanical systems, etc. The previous studiesare most oriented to control problems for separate cases: parameters uncertainty or input noises. In papers [1], [2], [3] we introduced a new adaptive tracking control method based on disturbance attenuation and ISS stabilization of ENUI. This both methods compensate the uncertain parameters and eliminate the effect of noise on the inputs of systems. The advantage of this adaptive tracking control is the ability to converge the tracking error to be arbitrary sufficiently small around  the neighbourhood of the origin. In this paper, we continue to present a parameter modifying method of an adaptive tracking controller to get an optional transient time. With this modification, we can adjust independently the dimension of tracking errors attractor and the transient time.

Adaptive tracking control of Euler-Lagrange nonlinear systems in the presence of uncertainty and input noise with guaranteed tracking errors