Exponential tracking of adaptive control systems

Dear editor, In the last decades, extensive efforts have been focused on the adaptive control problem of uncertain nonlinear systems (e.g., [1–5]). In this study, the problem of exponential tracking control is addressed for a class of nonlinear systems with parametric uncertainty. A design method based on adaptive control, capable of guaranteeing the exponential tracking with zero tracking error, is proposed. In the control design, the following techniques are applied: (a) several technical lemmas which can guarantee the exponential tracking are introduced; (b) two exponential functions with different exponent constants are incorporated into the control law and adaptive law, respectively; (c) all the unknown parameters in the controlled system are lumped together, and only one integrated parameter is adaptively updated. The presented controller has simple structure and the estimated parameter is carefully chosen. To ensure that the control function avoids singularity and remains smooth enough, the hyperbolic tangent function is incorporated into the control law. For stability analysis, the Lyapunov function weighted by an exponential function is appropriately constructed. It is shown that the presented robust adaptive scheme can guarantee the boundedness of all the closed-loop system signals and the convergence of the tracking error to zero exponentially fast. A simulation example is provided to clarify and verify the proposed approach.