Tracking control of nonlinear systems with improved performance via transformational approach

In this work, we present a transformation-based adaptive control design, for uncertain strict-feedback nonlinear systems, to achieve given performance specifications in terms of convergence rate/time, overshoot, steady-state (zero-error) precision, in addition to the primary stability requirement. For the case with no uncertainty and known control coefficient, by introducing a time-varying scaling function and an error-dependent transformation, we develop a control strategy that is able to achieve exponential and uniform convergence of the tracking error and at the same time maintain the output tracking overshoot to be as small as desired without the need for trajectory initialization resetting. For the case with nonparametric uncertainties and unknown control directions, by employing an additional time-varying scaling function together with a self-tuning Nussbaum function, we develop a control scheme that not only secures asymptotic tracking but also guarantees finite time transient process in that the tracking error, prior to converging to zero, is regulated into a prespecified residual set within a prescribed time. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.