Control of port-Hamiltonian systems with minimal energy supply

Schaller, Manuel; Philipp, Friedrich; Faulwasser, Timm; Worthmann, Karl; Maschke, Bernhard

doi:10.1016/j.ejcon.2021.06.017

Cited by 20 publications

(31 citation statements)

References 21 publications

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“…In [31] we made first observations concerning the special case with P = 0, D = 0, and Q > 0. Subsequently, we go beyond [31], i.e.…”

Section: Optimal Control Of Ph Ode Systems With Feed-throughmentioning

confidence: 99%

“…In [31] we made first observations concerning the special case with P = 0, D = 0, and Q > 0. Subsequently, we go beyond [31], i.e. we explore the reachability properties of ( 14) and prove novel results concerning input-state subspace turnpikes as well as an adjoint turnpike for the ODE-constrained OCP (13).…”

Section: Optimal Control Of Ph Ode Systems With Feed-throughmentioning

confidence: 99%

“…In spite of this unfavorable situation, we have shown in [31] that in the special ODEcase with E = I and Q > 0 the OCP is strictly dissipative at least with respect to a subspace and that optimal controls are completely characterized by the state and its adjoint. 1 First steps towards the infinite-dimensional case are taken in [28].…”

Section: Introductionmentioning

confidence: 98%

“…Despite the widespread interest of pH system for modeling, simulation and control of dynamic systems, surprisingly little has been done in terms of optimal control. In [31] we have shown in the ODE case, i.e. E = I in (1), that the inherent dissipativity can be exploited in Optimal Control Problems (OCPs) which require to transfer the system state from a prescribed initial condition at t = 0 to some target set at t = T , while minimizing the supplied energy T 0 u(t) y(t) dt.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal control of port-Hamiltonian descriptor systems with minimal energy supply

Faulwasser¹,

Maschke²,

Philipp³

et al. 2021

Preprint

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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 towards 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 towards zero. In an appendix we characterize the class of dissipative Hamiltonian matrices and pencils.

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“…In [31] we made first observations concerning the special case with P = 0, D = 0, and Q > 0. Subsequently, we go beyond [31], i.e.…”

Section: Optimal Control Of Ph Ode Systems With Feed-throughmentioning

confidence: 99%

Section: Optimal Control Of Ph Ode Systems With Feed-throughmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal control of port-Hamiltonian descriptor systems with minimal energy supply

Faulwasser¹,

Maschke²,

Philipp³

et al. 2021

Preprint

Self Cite

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“…In this work, we consider optimal control of irreversible pH systems [25,24] accounting both for the energy conservation and the entropy creation. Thereby, we extend our previous works on minimzing the energy supply in the linear pH setting [30,19,8] to the class of nonlinear irreversible pH systems, that is, we aim for a state transition with minimal energy, entropy, or exergy supply, respectively linear combinations thereof. We prove that, under suitable assumptions, a state transition that is optimal with respect to these metrics is always performed in a neighborhood of the set of thermodynamical equilibria for the majority of the time.…”

Section: Introductionmentioning

confidence: 98%

Optimal control of thermodynamic port-Hamiltonian Systems

Maschke¹,

Philipp²,

Schaller³

et al. 2022

Preprint

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We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions exhibit the manifold turnpike phenomenon with respect to the manifold of thermodynamic equilibria. We illustrate our analytical findings via numerical results for a heat exchanger.

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Stage‐cost design for optimal and model predictive control of linear port‐Hamiltonian systems: Energy efficiency and robustness

Şen,

Schaller,

Worthmann

2023

Proc Appl Math and Mech

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We consider singular optimal control of port‐Hamiltonian systems with minimal energy supply. We investigate the robustness of different stage‐cost designs w.r.t. time discretization and show that alternative formulations that are equivalent in continuous time, differ strongly in view of discretization. Furthermore, we consider the impact of additional quadratic control regularization and demonstrate that this leads to a considerable increase in energy consumption. Then, we extend our results to the tracking problem within model predictive control and show that the intrinsic but singular choice of the cost functional as the supplied energy leads to a substantial improvement of the closed‐loop performance.

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Control of port-Hamiltonian systems with minimal energy supply

Cited by 20 publications

References 21 publications

Optimal control of port-Hamiltonian descriptor systems with minimal energy supply

Optimal control of port-Hamiltonian descriptor systems with minimal energy supply

Optimal control of thermodynamic port-Hamiltonian Systems

Stage‐cost design for optimal and model predictive control of linear port‐Hamiltonian systems: Energy efficiency and robustness

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