Passivity-Based Control with Guaranteed Safety via Interconnection and Damping Assignment

In this paper, we study a Passivity-Based Control (PBC) design that solves asymptotic stability with guaranteed safety problem via Interconnection and Damping Assignment (IDA) approach. Akin to the classical IDA-PBC method, the original system is transformed via a state-feedback to a port-Hamiltonian system where the corresponding interconnection and damping matrices and the energy function are shaped according to the given set of unsafe states and to the desired equilibrium point. By embedding it in a hybrid control framework, we show how the global results can also be obtained. We illustrate the efficacy of our proposed method on a nonlinear second-order system.