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Item type:Publication, Access status: without files , Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal controlWe investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. We show that from this time-varying dissipativity notion, we can conclude turnpike behaviors concerning different objects like distributions, moments, or sample paths of the stochastic system and that the distributions of the stationary pair can be characterized by a stationary optimization problem. The analytical findings are illustrated by numerical simulations.Publicationtype: Journal Article17 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Observability for non-autonomous systems(Society for Industrial & Applied Mathematics (SIAM), 2023); ; ; We study non-autonomous observation systems align* ẋ(t) = A(t) x(t), y(t) = C(t) x(t), x(0) = x₀∈ X, align* where (A(t)) is a strongly measurable family of closed operators on a Banach space X and (C(t)) is a family of bounded observation operators from X to a Banach space Y. Based on an abstract uncertainty principle and a dissipation estimate, we prove that the observation system satisfies a final-state observability estimate in Lʳ(E; Y) for measurable subsets E ⊆ [0,T], T > 0. An application of the above result to families of uniformly strongly elliptic differential operators A(t) on Lᵖ(ℝᵈ) and observation operators C(t)u = 𝟏Ω₍t₎ u is presented. In this setting, we give sufficient and necessary geometric conditions on the family of sets (Ω(t)) such that the corresponding observation system satisfies a final-state observability estimate.Publicationtype: Journal Article147 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Optimal control of port-hamiltonian descriptor systems with minimal energy supply(Society for Industrial & Applied Mathematics (SIAM), 2022); ; ; ; 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.Publicationtype: Journal Article15 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Sufficient criteria and sharp geometric conditions for observability in banach spacesLet X, Y be Banach spaces, (St)t≥ 0 a C0-semigroup on X, A the corresponding infinitesimal generator on X, C a bounded linear operator from X to Y , and T 0. We consider the system x(̇t) = Ax(t), y(t) = Cx(t), t ∈ (0, T], x(0) = x0 ∈ X. We provide sufficient conditions such that this system satisfies a final state observability estimate in Lr((0, T); Y ), r ∈ [1,∞ ]. These sufficient conditions are given by an uncertainty relation and a dissipation estimate. Our approach unifies and generalizes the respective advantages from earlier results obtained in the context of Hilbert spaces. As an application we consider the example where A is an elliptic operator in Lp(Rd) for 1 p ∞ and where C = 1E is the restriction onto a thick set E ⊂ Rd. In this case, we show that the above system satisfies a final state observability estimate if and only if E ⊂ Rd is a thick set. Finally, we make use of the well-known relation between observability and null-controllability of the predual system and investigate bounds on the corresponding control costs.Publicationtype: Journal Article84