Optimal Control of Port-Hamiltonian Descriptor Systems with Minimal Energy Supply
Timm Faulwasser, Bernhard Maschke, Friedrich Philipp, Manuel Schaller, Karl Worthmann
Abstract
We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems. We study the reachability properties of the system and prove that optimal states exhibit a turnpike behavior with respect to the conservative subspace. Further, we derive a input-state turnpike toward a subspace for optimal control of port-Hamiltonian ordinary differential equations with a feed-through term and a turnpike property for the corresponding adjoint states toward zero. In an appendix we characterize the class of dissipative Hamiltonian matrices and pencils.
Topics & Concepts
MathematicsReachabilityHamiltonian systemDissipative systemOptimal controlSubspace topologyHamiltonian (control theory)Applied mathematicsOrdinary differential equationControl theory (sociology)Pure mathematicsMathematical analysisMathematical optimizationDifferential equationControl (management)CombinatoricsComputer sciencePhysicsArtificial intelligenceQuantum mechanicsControl and Stability of Dynamical SystemsATP Synthase and ATPases ResearchAdvanced Control Systems Optimization