A continuous-time observer which converges in finite time

the control law (3) does not only improves the transient performance, but also provides smoother outputs. It is important to stress that a better performance can still be achieved with (28) and (30). However, as discussed in Remark IV.1, increasing gains would not only cause more peaks in the outputs, but it might also yield saturation, especially for 2. V. CONCLUSION The tracking control problem for rigid robots with model parameter uncertainty has been studied in this note. In order to improve the parameter error convergence to zero, robust control techniques have been used. It was shown that with only parameter-dependent persistent ex-citation, the transient response of the parameter and tracking errors can be improved notably. Unlike other existing algorithms, the improvement of the transient performance is not achieved by increasing control gains, but by achieving a fast parameter adaptation, what results in smoother control outputs. Under the assumption of known bounds for the real parameters, it is also guaranteed that even in the absence of excitation the estimated parameter will remain bounded. By using the model of a two-link robot available in the literature, the proposed algorithm was tested in simulation. It was shown that the transient performance of this new adaptive algorithm is better in comparison with other well-known algorithms in the literature. REFERENCES [1] M. Corless, " Tracking controllers for uncertain systems: Application to a manutec r3 robot, " ASME J. Estimation of iner-tial parameters of rigid body links of manipulators, " in Proc. Adaptive computed torque control for rigid link manipulators, " Syst. Exponentially stable trajectory following of robotic manipulators under a class of adaptive controls, " Automatica, vol. 28, no. 3, pp. 579–586, 1992. [7] S. Nader and R. Horowitz, " Stability and robustness analysis of a class of adaptive controllers for robotic manipulators, " Int. , " An exponentially stable adaptive control law for robotic manip-ulators, " IEEE Trans. Adaptive control of robot manipulators with controller/update law modularity, " Automatica, On the adaptive control of robot manipula-tors, " Int. [14] R. Lozano and C. C. de Wit, " Passivity based adaptive control for mechanical manipulators using ls-type estimation, " IEEE Trans. Automat. of robot manipulators: A unified approach based on passivity, " Int. J. [17] A. Yao and M. Tomizuka, " Robust desired compensation adaptive control of robot manipulators with guaranteed transient performance, " in , " Smooth robust adaptive sliding mode control of …