On feedback invariants of controlled conservative contact systems

Conservative contact systems are defined with respect to an invariant Legendre submanifold and permit to endow thermodynamic systems with a geometric structure. Structure preserving feedback of controlled conservative contact systems involves to determine the existence of closed-loop invariant Legendre submanifolds. General results characterizing these submanifolds are presented. For contact systems arising from the modelling of thermodynamic processes by using pseudo port-controlled Hamiltonian formulation a series of particular results, that permits to constructively design the invariant submanifold and relate them with the stability of the system, are presented. Furthermore, the closed-loop system may again be restricted to some invariant Legendre submanifold and the control reduced to a state-feedback control. A heat transmission example is used to illustrate the approach.