Boundary port Hamiltonian control of a class of nanotweezers

Boundary controlled-port Hamiltonian systems have proven to be of great use for the analysis and control of a large class of systems described by partial differential equations. The use of semi-group theory, combined with the underlying physics of Hamiltonian systems permits to prove existence, well-possessedness and stability of solutions using constructive techniques. On other hand, the differential geometric representation of these systems has lead to finite dimension approximation methods that conserves physical properties such as the interconnection structure and the energy. These results are applied to the modelling and control of a class of nanotweezers used for DNA-manipulation. The Nanotweezer may be modelled as a flexible beam interconnected with a finite dimensional dynamical system representing the manipulated object. A boundary controlled-port Hamiltonian model for the ensemble and an exponentially stabilizing controller are proposed. A geometric approximation scheme is used to reduce the infinite dimensional system and numerical simulations of the closed-loop system presented.