Saturated RISE Controllers With Exponential Stability Guarantees: A Projected Dynamical Systems Approach

The Robust Integral of the Sign of the Error (RISE) control approach results in a powerful continuous controller that yields exponential tracking error convergence despite the presence of time-varying and state-dependent disturbances. However, designing the RISE controller to yield exponential tracking error convergence in the presence of actuator saturation has been an open problem. Although there are existing results that provide a saturation scheme for RISE controllers, these results only guarantee asymptotic tracking error convergence using a Lyapunov-based analysis. In this paper, a new design strategy is developed using a projection algorithm and auxiliary filters to yield exponential tracking error convergence. This new strategy does not employ trigonometric or hyperbolic saturation functions inherent to previous saturated (or amplitude limited) controllers. As a result, a Lyapunov-based analysis can be constructed that yields exponential convergence of the tracking errors. Comparative simulation results demonstrate the performance of the developed method in comparison with a baseline controller. The developed method can operate at a lower saturation limit than the baseline method while maintaining stability and achieving exponential tracking error convergence.