Adaptive Override Control under High-Relative-Degree Nonovershooting Constraints

Abstract: This paper considers the problem of adaptively overriding unsafe actions of a nominal controller in the presence of high-relative-degree nonovershooting constraints and parametric uncertainties. To prevent the design from being coupled with high-order derivatives of the parameter estimation error, we adopt a modular design approach in which the controller and the parameter identifier are designed separately. The controller module ensures that any safety violations caused by parametric uncertainties remain bounded, provided that the parameter estimation error and its first-order derivative are either bounded or square-integrable. The identifier module, in turn, guarantees that these requirements on the parameter estimation error are satisfied. Both theoretical analysis and simulation results demonstrate that the closed-loop safety violation is bounded by a tunable function of the initial estimation error. Moreover, as time increases, the parameter estimate converges to the true value, and the amount of safety violation decreases accordingly.