Exponentially Stable Combined Adaptive Control under Finite Excitation Condition

The parameter convergence relies on a stringent persistent excitation (PE) condition in adaptive control. Several works have proposed a memory term in the last decade to translate the PE condition to a feasible finite excitation (FE) condition. This work proposes a combined model reference adaptive control for a class of uncertain nonlinear systems with an unknown control effectiveness vector. The closed-loop system is exponentially stable under the FE condition. The exponential rate of convergence is independent of the excitation level of the regressor vector and is lower-bounded in terms of the system parameters and user-designed gains. Numerical simulation is illustrated, validating the results obtained with the proposed adaptive control.