Control of port-Hamiltonian systems with minimal energy supply

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable st...

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Bibliographic Details
Published in:European journal of control 2021-11, Vol.62, p.33-40
Main Authors: Schaller, Manuel, Philipp, Friedrich, Faulwasser, Timm, Worthmann, Karl, Maschke, Bernhard
Format: Article
Language:English
Subjects:
Control systems
Decomposition
Dissipation
Dissipativity
Eigenvalues
Energy
Hamiltonian functions
Initial conditions
Mathematical functions
Minimal energy supply
Optimal control
Port-Hamiltonian systems
Steady state
Subspaces
Toll roads
Trajectory optimization
Turnpike property
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Summary:We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.
ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2021.06.017