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Item type:Publication, Access status: with files , Optimal control of port-Hamiltonian systems: energy, entropy, and exergy(Elsevier, 2024-10-26); ; ; ; We consider irreversible and coupled reversible–irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on finite-time horizons. We analyze a class of optimal control problems, where the performance functional can be interpreted as a linear combination of energy supply, entropy generation, or exergy supply. Our results establish the integral turnpike property towards the set of thermodynamic equilibria providing a rigorous connection of optimal system trajectories to optimal steady states. Throughout the paper, we illustrate our findings by means of two examples: a network of heat exchangers and a gas-piston system.Publicationtype: Journal Article45 34 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Manifold turnpikes, trims, and symmetries(Springer, 2022-12); Scopus© Citations 7 21 48 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Control of port-Hamiltonian systems with minimal energy supply(Elsevier, 2021-11-01); ; ; ; 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.Publicationtype: Journal Article6 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systemsTurnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this paper. More concretely, we analyze symmetry-induced velocity turnpikes, i.e. controlled relative equilibria, called trim primitives, which are optimal operation points regarding the given cost criterion. We characterize velocity turnpikes by means of dissipativity inequalities. Moreover, we study the equivalence between optimal control problems and steady-state problems via the corresponding necessary optimality conditions. An academic example is given for illustration.Publicationtype: Conference Paper30 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Minimizing the energy supply of infinite-dimensional linear port-Hamiltonian systems(IFAC, 2021); ; ; ; We consider the problem of minimizing the supplied energy of infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit the turnpike phenomenon towards certain subspaces induced by the dissipation of the dynamics. The theoretical foundations are illustrated by means of numerical examples concerning a Timoshenko beam and the heat equation.Publicationtype: Conference Paper15 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Towards velocity turnpikes in optimal control of mechanical systemsThe paper proposes first steps towards the formalization and characterization of time-varying turnpikes in optimal control of mechanical systems. We propose the concepts of velocity steady states, which can be considered as partial steady states, and hyperbolic velocity turnpike properties for analysis and control. We show for a specific example that, for all finite horizons, both the (essential part of the) optimal solution and the orbit of the time-varying turnpike correspond to (optimal) trim solutions. Hereby, the present paper appears to be the first to combine the concepts of trim primitives and time-varying turnpike properties.Publicationtype: Conference Paper8