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Energy-Based Control of Nonlinear Infinite-Dimensional Port-Hamiltonian Systems with Dissipation (1807.05362v1)
Published 14 Jul 2018 in math.OC, math.AP, math.DG, and math.DS
Abstract: In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet-bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation models that can be incorporated in the port- Hamiltonian framework by means of appropriate differential operators. For this system class, energy-based control by means of Casimir functionals as well as energy balancing is analysed and demonstrated using a nonlinear Euler-Bernoulli beam.