Set-Theoretic Barrier Lyapunov Function for Handling State Constraints and Uncertainties

Many engineering systems are forced to operate in bounded state-space domains and therefore techniques to incorporate state constraints play an essential role for feedback controller designs. Yet, especially in the presence of system uncertainties, incorporating these constraints becomes a challenge. Motivated by this standpoint, a set-theoretic model reference adaptive control approach is proposed in this paper for uncertain nonlinear systems to keep the state values within the desired bounds. Specifically, three different restricted potential functions are explored to demonstrate that much attention should be shown in the selection of the restricted potential functions in order to result in effective constrained control and also obtain a desirable closed-loop system performance. Illustrative numerical examples are also provided to demonstrate the efficacy of our contributions.