Asymptotic Stability of Uncertain Lagrangian Systems with Prescribed Transient Response

This paper considers the asymptotic tracking problem for 2nd-order nonlinear Lagrangian systems subject to predefined constraints for the system response, such as maximum overshoot or minimum convergence rate. In particular, by employing discontinuous adaptive control protocols and nonsmooth analysis, we extend previous results on funnel control to guarantee at the same time asymptotic trajectory tracking from all the initial conditions that are compliant with the given funnel. The considered system contains parametric and structural uncertainties, with no boundedness or approximation/parametric factorization assumptions. The response of the closed loop system is solely determined by the predefined funnel and is independent from the control gain selection. Finally, simulation results verify the theoretical findings.

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