@misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Weak and strong optimality conditions for constrained control problems with discontinuous control}, series = {Journal of Optimization Theory and Applications}, volume = {2}, journal = {Journal of Optimization Theory and Applications}, number = {110}, issn = {0022-3239}, pages = {361 -- 387}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Structural properties and approximation of optimal controls}, volume = {47}, number = {3}, issn = {0362-546X}, pages = {1869 -- 1880}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {On smoothness properties and approximability of optimal control functions}, series = {Annals of Operations Research}, volume = {101}, journal = {Annals of Operations Research}, number = {1}, issn = {0254-5330}, pages = {23 -- 42}, language = {en} } @misc{FelgenhauerWagner, author = {Felgenhauer, Ursula and Wagner, Marcus}, title = {Essential properties of L∞-functions}, series = {Zeitschrift f{\"u}r Analysis und ihre Anwendungen}, volume = {17}, journal = {Zeitschrift f{\"u}r Analysis und ihre Anwendungen}, number = {1}, issn = {0232-2064}, pages = {229 -- 242}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Regularity properties of optimal controls with application to discrete approximation}, series = {Journal of Optimization Theory and Applications}, volume = {102}, journal = {Journal of Optimization Theory and Applications}, number = {1}, issn = {0022-3239}, pages = {97 -- 110}, language = {en} } @misc{FelgenhauerPoggioliniStefani, author = {Felgenhauer, Ursula and Poggiolini, Laura and Stefani, Gianna}, title = {Optimality and stability result for bang-bang optimal controls with simple and double switch behaviour}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {The shooting approach in analyzing bang-bang extremals with simultaneous control switches}, series = {Control and Cybernetics}, volume = {37}, journal = {Control and Cybernetics}, number = {2}, issn = {0324-8569}, pages = {307 -- 327}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Optimality properties of controls with bang-bang components in problems with semilinear state equation}, series = {Control and Cybernetics}, volume = {34}, journal = {Control and Cybernetics}, number = {3}, issn = {0324-8569}, pages = {763 -- 785}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Optimality and sensitivity for semilinear bang-bang type optimal control problems}, series = {International Journal of Applied Mathematics and Computer Science}, volume = {14}, journal = {International Journal of Applied Mathematics and Computer Science}, number = {4}, issn = {0867-857X}, pages = {447 -- 454}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Stability analysis of variational inequalities for bang-singular-bang controls}, series = {Control and Cybernetics}, volume = {42}, journal = {Control and Cybernetics}, number = {3}, issn = {0324-8569}, pages = {557 -- 592}, abstract = {The paper is related to parameter dependent optimal control problems for control-affine systems. The case of scalar reference control with bang-singular-bang structure is considered. The analysis starts from a variational inequality (VI) formulation of Pontryagin's Maximum Principle. In a first step, under appropriate higher-order sufficient optimality conditions, the existence of solutions for the linearized problem (LVI) is proven. In a second step, for a certain class of right-hand side perturbation, it is shown that the controls from LVI have bang-singular-bang structure and, in L_1 topology, depend Lipschitz continuously on the data. Applying finally a common fixed-point approach to VI, the results are brought together to obtain existence and structural stability results for extremals of the original control problem under parameter perturbation.}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Note on local quadratic growth estimates in bang-bang optimal control problems}, series = {Optimization : a Journal of Mathematical Programming and Operations Research}, volume = {64}, journal = {Optimization : a Journal of Mathematical Programming and Operations Research}, number = {3}, issn = {1029-4945}, doi = {10.1080/02331934.2013.773000}, pages = {521 -- 537}, abstract = {Strong second-order conditions in mathematical programming play an important role not only as optimality tests but also as an intrinsic feature in stability and convergence theory of related numerical methods. Besides of appropriate firstorder regularity conditions, the crucial point consists in local growth estimation for the objective which yields inverse stability information on the solution. In optimal control, similar results are known in case of continuous control functions, and for bang-bang optimal controls when the state system is linear. The paper provides a generalization of the latter result to bang-bang optimal control problems for systems which are affine-linear w.r.t. the control but depend nonlinearly on the state. Local quadratic growth in terms of L1 norms of the control variation are obtained under appropriate structural and second-order sufficient optimality conditions.}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Discretization of semilinear bang-singular-bang control problems}, series = {Computational Optimization and Applications}, volume = {64}, journal = {Computational Optimization and Applications}, number = {1}, issn = {0926-6003}, doi = {10.1007/s10589-015-9800-2}, pages = {295 -- 326}, abstract = {Bang--singular controls may appear in optimal control problems where the control enters the system linearly. We analyze a discretization of the first-order system of necessary optimality conditions written in terms of a variational inequality (or: inclusion) under appropriate assumptions including second-order optimality conditions. For the so-called semilinear case, it is proved that the discrete control has the same principal bang-singular-bang structure as the reference control and, in L_1 topology, the convergence is of order one w.r.t. the stepsize.}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {On stability of bang-bang type controls}, series = {SIAM Journal on Control and Optimization}, volume = {41}, journal = {SIAM Journal on Control and Optimization}, number = {6}, doi = {10.1137/S0363012901399271}, pages = {1843 -- 1867}, abstract = {From the theory of nonlinear optimal control problems it is known that the solution stability w.r.t. data perturbations and conditions for strict local optimality are closely related facts. For important classes of control problems, sufficient optimality conditions can be formulated as a combination of the independence of active constraints' gradients and certain coercivity criteria. In the case of discontinuous controls, however, common pointwise coercivity approaches may fail. In the paper, we consider sufficient optimality conditions for strong local minimizers which make use of an integrated Hamilton--Jacobi inequality. In the case of linear system dynamics, we show that the solution stability (including the switching points localization) is ensured under relatively mild regularity assumptions on the switching function zeros. For the objective functional, local quadratic growth estimates in L1 sense are provided. An example illustrates stability as well as instability effects in case the regularity condition is violated.}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {Structural Stability Investigation of Bang-Singular-Bang Optimal Controls}, series = {Journal of Optimization Theory and Applications}, volume = {152}, journal = {Journal of Optimization Theory and Applications}, number = {3}, issn = {0022-3239}, pages = {605 -- 631}, abstract = {The paper is devoted to parametric optimal control problems with a scalar, partially singular optimal control function. In contrast to the case of pure bang-bang behavior, the investigation of structural stability properties for partially singular controls so far has been rarely addressed in literature. The central result of the paper deals with the case of one first order singular arc under regular concatenation to bang-arcs. Conditions will be provided which ensure the Lipschitz stability of bang-singular junction times positions with respect to small parameter changes. Three examples illustrate the main theorem.}, language = {en} } @misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {A Newton-type method and optimality test for problems with bang-singular-bang optimal control}, series = {Pure and Applied Functional Analysis}, volume = {1}, journal = {Pure and Applied Functional Analysis}, number = {2}, pages = {197 -- 215}, abstract = {In the paper, a second-order method is investigated for control problems where the control has bang-singular-bang structure. To start with, the first-order system is formulated as a variational inequality including a differential equation for the switching function. For this system, a certain inexact Josephy-Newton method is considered. Under strong second-order sufficient conditions obtained via Goh's transformation of control and state-adjoint data, the local solvability is proved for the iterative problems. For so-called semilinear problems, locally the state and adjoint iterates converge superlinearly. The paper is completed by a Riccati test approach for verifying second-order optimality.}, language = {en} } @misc{AltFelgenhauerSeydenschwanz, author = {Alt, Walter and Felgenhauer, Ursula and Seydenschwanz, Martin}, title = {Euler discretization for a class of nonlinear optimal control problems with control appearing linearly}, series = {Computational Optimization and Applications}, volume = {69}, journal = {Computational Optimization and Applications}, number = {3}, issn = {0926-6003}, doi = {10.1007/s10589-017-9969-7}, pages = {825 -- 856}, language = {en} }