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Available energy-based interconnection and entropy assignment (ABI-EA) boundary control of the heat equation: an Irreversible Port Hamiltonian approach

In this paper, we consider the boundary control of the 1D heat equation using an irreversible port Hamiltonian systems (IPHS) formulation. This formulation allows to cope with the second principle of Thermodynamics and exhibits the physical properties of the system. We extend the Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) method developed for port Hamiltonian systems to the available energy-based boundary control of IPHS. This method allows to achieve the desired equilibrium profile without constraints on the boundary conditions or on the initial profile of the plant. The method is illustrated by means of simulations considering the boundary control of the 1D heat diffusion in a copper rod.