Anup Parikh

Anup Parikh, Rushikesh Kamalapurkar, Warren E. Dixon

Concurrent learning is a recently developed adaptive update scheme that can be used to guarantee parameter convergence without requiring persistent excitation. However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. A novel integral concurrent learning method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties. A Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation.

Rushikesh Kamalapurkar, Joel A. Rosenfeld, Anup Parikh et al.

This paper generalizes the Lasalle-Yoshizawa Theorem to switched nonsmooth systems. Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A candidate common Lyapunov function that has a negative semidefinite derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle-Yoshizawa results for the switched system. Results for regular and non-regular candidate Lyapunov functions are presented using an appropriate generalization of the time derivative. The developed generalization is motivated by adaptive control of switched systems where the derivative of the candidate Lyapunov function is typically negative semidefinite.