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Passivity-based control of implicit port-Hamiltonian systems

The main contribution of this paper is the generalisation of well-known energy-based control techniques (i.e., energy-balancing passivity-based control and passivity-based control with state modulated source), to the case in which the plant is a port-Hamiltonian system in implicit form. A typical situation is when (part of) the system is obtained from the spatial discretization of an infinite dimensional port-Hamiltonian system: in this case, the dynamics is not given in standard input-state-output form, but as a set of DAEs. Consequently, the control by energy-shaping has to be extended to deal with dynamical systems with constraints. The general methodology is discussed with the help of a simple but illustrative example, i.e. a transmission line interconnected with an RLC circuit.