Exponential Control Lyapunov-Barrier Function Using a Filtering-Based Concurrent Learning Adaptive Approach
Vahid Azimi, Seth Hutchinson
Abstract
The state-of-the-art quadratic-program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This article presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline concurrent learning technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing safety with the largest safe region. Under this unification, all results are exponential in the presence of modeling error without the need for numerical methods to estimate state derivatives. This is formally proven by employing a Lyapunov argument. Simulations are finally carried out to validate the theoretical results.