[{"date_updated":"2023-11-29T10:00:18Z","author":[{"id":"93930","full_name":"Vertovec, Nikolaus","last_name":"Vertovec","first_name":"Nikolaus"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"first_name":"Kostas","last_name":"Margellos","full_name":"Margellos, Kostas"}],"date_created":"2022-03-31T11:14:13Z","title":"Verification of safety critical control policies using kernel methods","conference":{"location":"London","end_date":"2022-07-15","start_date":"2022-07-12","name":"2022 European Control Conference (ECC)"},"has_accepted_license":"1","year":"2022","citation":{"chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.","ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 2022, pp. 1870–1875.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control policies using kernel methods. In: ; 2022:1870-1875.","bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875} }","mla":"Vertovec, Nikolaus, et al. <i>Verification of Safety Critical Control Policies Using Kernel Methods</i>. 2022, pp. 1870–75.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (2022). <i>Verification of safety critical control policies using kernel methods</i>. 1870–1875."},"page":"1870-1875","_id":"30733","user_id":"15694","department":[{"_id":"636"}],"ddc":["510"],"language":[{"iso":"eng"}],"type":"conference","abstract":[{"lang":"eng","text":"Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example."}],"status":"public"},{"year":"2021","citation":{"mla":"Vertovec, Nikolaus, et al. <i>Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design</i>. pp. 1975–80.","bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos, title={Multi-objective minimum time optimal control for low-thrust trajectory design}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, pages={1975–1980} }","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: n.d., pp. 1975–1980.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (n.d.). <i>Multi-objective minimum time optimal control for low-thrust trajectory design</i>. 1975–1980.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Multi-objective minimum time optimal control for low-thrust trajectory design. In: ; :1975-1980.","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.","ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Multi-objective minimum time optimal control for low-thrust trajectory design,” Rotterdam, the Netherlands, pp. 1975–1980."},"page":"1975-1980","publication_status":"accepted","title":"Multi-objective minimum time optimal control for low-thrust trajectory design","conference":{"name":"2021 European Control Conference (ECC)","start_date":"2021-06-29","end_date":"2021-07-02","location":"Rotterdam, the Netherlands"},"date_updated":"2023-11-29T10:26:49Z","date_created":"2021-04-03T03:00:35Z","author":[{"first_name":"Nikolaus","last_name":"Vertovec","full_name":"Vertovec, Nikolaus","id":"87056"},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"first_name":"Kostas","full_name":"Margellos, Kostas","last_name":"Margellos"}],"abstract":[{"lang":"eng","text":"We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design."}],"status":"public","type":"conference","language":[{"iso":"eng"}],"_id":"21592","external_id":{"arxiv":["2103.08813"]},"user_id":"15694","department":[{"_id":"636"}]},{"type":"dissertation","status":"public","file":[{"file_name":"Dissertation_Peitz.pdf","access_level":"closed","file_id":"16298","file_size":16636801,"creator":"speitz","date_created":"2020-03-13T12:52:50Z","date_updated":"2020-03-13T12:52:50Z","relation":"main_file","success":1,"content_type":"application/pdf"}],"abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute\r\nthe set of optimal compromises (the Pareto set) between the conflicting objectives.\r\n\r\nSince – in contrast to the solution of a single objective optimization problem – the\r\nPareto set generally consists of an infinite number of solutions, the computational\r\neffort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives\r\nare costly to evaluate. Consequently, this thesis is devoted to the identification and\r\nexploitation of structure both in the Pareto set and the dynamics of the underlying\r\nmodel as well as to the development of efficient algorithms for solving problems with\r\nadditional parameters, with a high number of objectives or with PDE-constraints.\r\nThese three challenges are addressed in three respective parts.\r\n\r\nIn the first part, predictor-corrector methods are extended to entire Pareto sets.\r\nWhen certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent\r\nspace can be approximated numerically which yields a direction for the predictor\r\nstep. In the corrector step, the predicted set converges to the Pareto set at a new\r\nparameter value. The resulting algorithm is applied to an example from autonomous\r\ndriving.\r\n\r\nIn the second part, the hierarchical structure of Pareto sets is investigated. When\r\nconsidering a subset of the objectives, the resulting solution is a subset of the Pareto\r\nset of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This\r\nway, the “skeleton” of a Pareto set can be computed and due to the exponential\r\nincrease in computing time with the number of objectives, the computations of\r\nthese subsets are significantly faster which is demonstrated using an example from\r\nindustrial laundries.\r\n\r\nIn the third part, PDE-constrained multiobjective optimal control problems are\r\naddressed by reduced order modeling methods. Reduced order models exploit the\r\nstructure in the system dynamics, for example by describing the dynamics of only the\r\nmost energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of\r\nalgorithms. Both scalarization and set-oriented approaches are coupled with reduced\r\norder modeling. Convergence results are presented and the numerical benefit is\r\ninvestigated. The algorithms are applied to semi-linear heat flow problems as well\r\nas to the Navier-Stokes equations.\r\n"}],"department":[{"_id":"101"}],"user_id":"47427","_id":"10594","project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"file_date_updated":"2020-03-13T12:52:50Z","language":[{"iso":"eng"}],"ddc":["510"],"has_accepted_license":"1","publication_status":"published","citation":{"bibtex":"@book{Peitz_2017, title={  Exploiting structure in multiobjective optimization and optimal control}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>}, author={Peitz, Sebastian}, year={2017} }","mla":"Peitz, Sebastian. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>. 2017, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>.","short":"S. Peitz,   Exploiting Structure in Multiobjective Optimization and Optimal Control, 2017.","apa":"Peitz, S. (2017). <i>  Exploiting structure in multiobjective optimization and optimal control</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-176\">https://doi.org/10.17619/UNIPB/1-176</a>","ama":"Peitz S. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>.; 2017. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>","ieee":"S. Peitz, <i>  Exploiting structure in multiobjective optimization and optimal control</i>. 2017.","chicago":"Peitz, Sebastian. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>, 2017. <a href=\"https://doi.org/10.17619/UNIPB/1-176\">https://doi.org/10.17619/UNIPB/1-176</a>."},"year":"2017","date_created":"2019-07-10T08:12:22Z","author":[{"full_name":"Peitz, Sebastian","id":"47427","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"}],"oa":"1","date_updated":"2022-01-06T06:50:46Z","doi":"10.17619/UNIPB/1-176","main_file_link":[{"url":"https://d-nb.info/1139356542/34","open_access":"1"}],"title":" \tExploiting structure in multiobjective optimization and optimal control"}]