The Role of Uncertainty in Adaptive Control of Switched Euler-Lagrange Systems

Abstract

This work presents a Lyapunov-based approach to adaptive control of uncertain Euler-Lagrange (EL) systems in a slow switching scenario. Fundamental trade-offs arising from considering uncertain dynamics with unknown uncertainty bounds are presented and discussed. Contrary to the non-switched scenario, the use of acceleration feedback seems to be unavoidable in the switched scenario: this is due to the fact that an acceleration feedback and an appropriate Lyapunov function must be adopted to make the switching law independent from the unknown uncertainty bounds. In the absence of such feedback or using different Lyapunov functions, a stabilizing switching law would exist but could not be determined as it would depend on an unknown uncertainty bound.