Büskens, Christof
Overview
Works:  67 works in 80 publications in 2 languages and 465 library holdings 

Roles:  Other, dgs, Author, Contributor 
Publication Timeline
.
Most widely held works by
Christof Büskens
Optimierungsmethoden und Sensitivitätsanalyse für optimale Steuerprozesse mit Steuer und ZustandsBeschränkungen by
Christof Büskens(
Book
)
3 editions published in 1998 in Undetermined and German and held by 21 WorldCat member libraries worldwide
3 editions published in 1998 in Undetermined and German and held by 21 WorldCat member libraries worldwide
Schlussbericht an das DLR für BlackBox Optimierer, Teilprojekt "Erweiterungen auf NLPEbene" by
Christof Büskens(
)
2 editions published in 2010 in German and held by 19 WorldCat member libraries worldwide
2 editions published in 2010 in German and held by 19 WorldCat member libraries worldwide
Abschlussbericht an das DLR über Sparse NLP Solver by
Christof Büskens(
)
2 editions published in 2007 in German and held by 19 WorldCat member libraries worldwide
2 editions published in 2007 in German and held by 19 WorldCat member libraries worldwide
WORHP : development and documentation of the SQP part by
Christof Büskens(
)
2 editions published in 2007 in German and English and held by 19 WorldCat member libraries worldwide
2 editions published in 2007 in German and English and held by 19 WorldCat member libraries worldwide
Nonlinear optimization in space applications with WORHP by Tim Nikolayzik(
)
1 edition published in 2011 in English and held by 18 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 18 WorldCat member libraries worldwide
Modellbasierte optimale Mehrgrößenregelung und optimale Reglerparametrisierung für Luftsysteme von PkwDieselmotoren by
Anna Elise Kemper(
)
1 edition published in 2015 in German and held by 17 WorldCat member libraries worldwide
1 edition published in 2015 in German and held by 17 WorldCat member libraries worldwide
PDErestringierte Optimierung in Anwendungen der spanenden Trockenbearbeitung by Heinrich Wernsing(
)
1 edition published in 2018 in German and held by 17 WorldCat member libraries worldwide
Optimization, NLP, PDE, SAND, dry milling, dry drilling, machining
1 edition published in 2018 in German and held by 17 WorldCat member libraries worldwide
Optimization, NLP, PDE, SAND, dry milling, dry drilling, machining
Effizienzsteigerung numerischer Verfahren der nichtlinearen Optimierung by Sören Geffken(
)
1 edition published in 2017 in German and held by 17 WorldCat member libraries worldwide
Nonlinear Optimization, Parametric Sensitivity Analysis, Parallel Algorithms, Efficient Algorithms, Parallelization.  This thesis focuses on the development of multiple different techniques to improve the efficiency of nonlinear optimization algorithms. The contribution of this work can be divided in three main parts. Having a closer look on an Sequential Quadratic Programming (SQP) algorithm (namely the solver WORHP) theoretical results about the inertia of the system matrix in the case of SQP with interiorpointmethod for the solution of the subproblems are given and an adaptive relaxation scheme to handle inconsistent constraints is developed. Using parametric sensitivity analysis multiple algorithms to improve the SQP method are presented. These focus mainly on the handling of nonlinear constraints, but a new strategy to improve the necessary regularization of the Hessian of the Lagrangian is shown as well. In addition to these algorithmic advancements a technical discussion about parallelism for nonlinear programming is given and used to develop a new multicore capable interface
1 edition published in 2017 in German and held by 17 WorldCat member libraries worldwide
Nonlinear Optimization, Parametric Sensitivity Analysis, Parallel Algorithms, Efficient Algorithms, Parallelization.  This thesis focuses on the development of multiple different techniques to improve the efficiency of nonlinear optimization algorithms. The contribution of this work can be divided in three main parts. Having a closer look on an Sequential Quadratic Programming (SQP) algorithm (namely the solver WORHP) theoretical results about the inertia of the system matrix in the case of SQP with interiorpointmethod for the solution of the subproblems are given and an adaptive relaxation scheme to handle inconsistent constraints is developed. Using parametric sensitivity analysis multiple algorithms to improve the SQP method are presented. These focus mainly on the handling of nonlinear constraints, but a new strategy to improve the necessary regularization of the Hessian of the Lagrangian is shown as well. In addition to these algorithmic advancements a technical discussion about parallelism for nonlinear programming is given and used to develop a new multicore capable interface
A PrimalDual Augmented Lagrangian PenaltyInteriorPoint Algorithm for Nonlinear Programming by
Renke Kuhlmann(
)
1 edition published in 2018 in English and held by 17 WorldCat member libraries worldwide
This thesis treats a new numerical solution method for largescale nonlinear optimization problems. Nonlinear programs occur in a wide range of engineering and academic applications like discretized optimal control processes and parameter identification of physical systems. The most efficient and robust solution approaches for this problem class have been shown to be sequential quadratic programming and primaldual interiorpoint methods. The proposed algorithm combines a variant of the latter with a special penalty function to increase its robustness due to an automatic regularization of the nonlinear constraints caused by the penalty term. In detail, a modified barrier function and a primaldual augmented Lagrangian approach with an exact l2penalty is used. Both share the property that for certain Lagrangian multiplier estimates the barrier and penalty parameter do not have to converge to zero or diverge, respectively. This improves the conditioning of the internal linear equation systems near the optimal solution, handles rankdeficiency of the constraint derivatives for all nonfeasible iterates and helps with identifying infeasible problem formulations. Although the resulting merit function is nonsmooth, a certain step direction is a guaranteed descent. The algorithm includes an adaptive update strategy for the barrier and penalty parameters as well as the Lagrangian multiplier estimates based on a sensitivity analysis. Global convergence is proven to yield a firstorder optimal solution, a certificate of infeasibility or a FritzJohn point and is maintained by combining the merit function with a filter or piecewise linear penalty function. Unlike the majority of filter methods, no separate feasibility restoration phase is required. For a fixed barrier parameter the method has a quadratic order of convergence. Furthermore, a sensitivity based iterative refinement strategy is developed to approximate the optimal solution of a parameter dependent nonlinear program under parameter changes. It exploits special sensitivity derivative approximations and converges locally with a linear convergence order to a feasible point that further satisfies the perturbed complementarity condition of the modified barrier method. Thereby, activeset changes from active to inactive can be handled. Due to a certain update of the Lagrangian multiplier estimate, the refinement is suitable in the context of warmstarting the penaltyinteriorpoint approach. A special focus of the thesis is the development of an algorithm with excellent performance in practice. Details on an implementation of the proposed primaldual penaltyinteriorpoint algorithm in the nonlinear programming solver WORHP and a numerical study based on the CUTEst test collection is provided. The efficiency and robustness of the algorithm is further compared to stateoftheart nonlinear programming solvers, in particular the interiorpoint solvers IPOPT and KNITRO as well as the sequential quadratic programming solvers SNOPT and WORHP
1 edition published in 2018 in English and held by 17 WorldCat member libraries worldwide
This thesis treats a new numerical solution method for largescale nonlinear optimization problems. Nonlinear programs occur in a wide range of engineering and academic applications like discretized optimal control processes and parameter identification of physical systems. The most efficient and robust solution approaches for this problem class have been shown to be sequential quadratic programming and primaldual interiorpoint methods. The proposed algorithm combines a variant of the latter with a special penalty function to increase its robustness due to an automatic regularization of the nonlinear constraints caused by the penalty term. In detail, a modified barrier function and a primaldual augmented Lagrangian approach with an exact l2penalty is used. Both share the property that for certain Lagrangian multiplier estimates the barrier and penalty parameter do not have to converge to zero or diverge, respectively. This improves the conditioning of the internal linear equation systems near the optimal solution, handles rankdeficiency of the constraint derivatives for all nonfeasible iterates and helps with identifying infeasible problem formulations. Although the resulting merit function is nonsmooth, a certain step direction is a guaranteed descent. The algorithm includes an adaptive update strategy for the barrier and penalty parameters as well as the Lagrangian multiplier estimates based on a sensitivity analysis. Global convergence is proven to yield a firstorder optimal solution, a certificate of infeasibility or a FritzJohn point and is maintained by combining the merit function with a filter or piecewise linear penalty function. Unlike the majority of filter methods, no separate feasibility restoration phase is required. For a fixed barrier parameter the method has a quadratic order of convergence. Furthermore, a sensitivity based iterative refinement strategy is developed to approximate the optimal solution of a parameter dependent nonlinear program under parameter changes. It exploits special sensitivity derivative approximations and converges locally with a linear convergence order to a feasible point that further satisfies the perturbed complementarity condition of the modified barrier method. Thereby, activeset changes from active to inactive can be handled. Due to a certain update of the Lagrangian multiplier estimate, the refinement is suitable in the context of warmstarting the penaltyinteriorpoint approach. A special focus of the thesis is the development of an algorithm with excellent performance in practice. Details on an implementation of the proposed primaldual penaltyinteriorpoint algorithm in the nonlinear programming solver WORHP and a numerical study based on the CUTEst test collection is provided. The efficiency and robustness of the algorithm is further compared to stateoftheart nonlinear programming solvers, in particular the interiorpoint solvers IPOPT and KNITRO as well as the sequential quadratic programming solvers SNOPT and WORHP
Onboard Trajectory Computation for Mars Atmospheric Entry Based on Parametric Sensitivity Analysis of Optimal Control Problems by David Seelbinder(
)
1 edition published in 2017 in English and held by 17 WorldCat member libraries worldwide
This thesis develops a precision guidance algorithm for the entry of a small capsule into the atmosphere of Mars. The entry problem is treated as nonlinear optimal control problem and the thesis focuses on developing a suboptimal feedback law. Therefore parametric sensitivity analysis of optimal control problems is combined with dynamic programming. This approach enables a realtime capable, locally suboptimal feedback scheme. The optimal control problem is initially considered in open loop fashion. To synthesize the feedback law, the optimal control problem is embedded into a family of neighboring problems, which are described by a parameter vector. The optimal solution for a nominal set of parameters is determined using direct optimization methods. In addition the directional derivatives (sensitivities) of the optimal solution with respect to the parameters are computed. Knowledge of the nominal solution and the sensitivities allows, under certain conditions, to apply Taylor series expansion to approximate the optimal solution for disturbed parameters almost instantly. Additional correction steps can be applied to improve the optimality of the solution and to eliminate errors in the constraints. To transfer this strategy to the closed loop system, the computation of the sensitivities is performed with respect to different initial conditions. Determining the perturbation direction and interpolating between sensitivities of neighboring initial conditions allows the approximation of the extremal field in a neighborhood of the nominal trajectory. This constitutes a locally suboptimal feedback law. The proposed strategy is applied to the atmospheric entry problem. The developed algorithm is part of the main control loop, i.e. optimal controls and trajectories are computed at a fixed rate, taking into account the current state and parameters. This approach is combined with a trajectory tracking controller based on the aerodynamic drag. The performance and the strengthsa and weaknesses of this two degree of freedom guidance system are analyzed using Monte Carlo simulation. Finally the realtime capability of the proposed algorithm is demonstrated in a flight representative processorintheloop environment
1 edition published in 2017 in English and held by 17 WorldCat member libraries worldwide
This thesis develops a precision guidance algorithm for the entry of a small capsule into the atmosphere of Mars. The entry problem is treated as nonlinear optimal control problem and the thesis focuses on developing a suboptimal feedback law. Therefore parametric sensitivity analysis of optimal control problems is combined with dynamic programming. This approach enables a realtime capable, locally suboptimal feedback scheme. The optimal control problem is initially considered in open loop fashion. To synthesize the feedback law, the optimal control problem is embedded into a family of neighboring problems, which are described by a parameter vector. The optimal solution for a nominal set of parameters is determined using direct optimization methods. In addition the directional derivatives (sensitivities) of the optimal solution with respect to the parameters are computed. Knowledge of the nominal solution and the sensitivities allows, under certain conditions, to apply Taylor series expansion to approximate the optimal solution for disturbed parameters almost instantly. Additional correction steps can be applied to improve the optimality of the solution and to eliminate errors in the constraints. To transfer this strategy to the closed loop system, the computation of the sensitivities is performed with respect to different initial conditions. Determining the perturbation direction and interpolating between sensitivities of neighboring initial conditions allows the approximation of the extremal field in a neighborhood of the nominal trajectory. This constitutes a locally suboptimal feedback law. The proposed strategy is applied to the atmospheric entry problem. The developed algorithm is part of the main control loop, i.e. optimal controls and trajectories are computed at a fixed rate, taking into account the current state and parameters. This approach is combined with a trajectory tracking controller based on the aerodynamic drag. The performance and the strengthsa and weaknesses of this two degree of freedom guidance system are analyzed using Monte Carlo simulation. Finally the realtime capability of the proposed algorithm is demonstrated in a flight representative processorintheloop environment
Datenbasierte Modellierung und Optimierung von KraftWärmeKopplungsanlagen by Stephanie Qing Qing Chen(
)
1 edition published in 2017 in German and held by 17 WorldCat member libraries worldwide
Cogeneration, modelling, optimization.  The demand of energy increases steadily. However, the conventional energy resources are limited and a complete changeover to other resources like regenerative energies is not done yet. Therefore, the efficient use of the conventional energy is important. Cogeneration is a method to achieve this goal and it is already used in different plants in industry though the plants can be more efficient if a mathematical optimization is applied to plan the production of energy. In this dissertation, a new method to model cogeneration plants is introduced. The resulting models are very precise, and the evaluations times are very small, which enables the use of sequential quadratic programming (SQP)based optimization algorithms, and reduces operational costs and emission of greenhouse gases
1 edition published in 2017 in German and held by 17 WorldCat member libraries worldwide
Cogeneration, modelling, optimization.  The demand of energy increases steadily. However, the conventional energy resources are limited and a complete changeover to other resources like regenerative energies is not done yet. Therefore, the efficient use of the conventional energy is important. Cogeneration is a method to achieve this goal and it is already used in different plants in industry though the plants can be more efficient if a mathematical optimization is applied to plan the production of energy. In this dissertation, a new method to model cogeneration plants is introduced. The resulting models are very precise, and the evaluations times are very small, which enables the use of sequential quadratic programming (SQP)based optimization algorithms, and reduces operational costs and emission of greenhouse gases
Development of a Reachability Analysis Algorithm for Space Applications by Yunus Emre Arslantaş(
)
1 edition published in 2017 in English and held by 17 WorldCat member libraries worldwide
In the last decades developments in space technology paved the way to more challenging missions like asteroid mining, space tourism and human expansion into the Solar System. These missions require difficult tasks such as realtime capable guidance schemes for reentry, landing on celestial bodies and implementation of large angle maneuvers for spacecraft. There is a need for an analysis tool to increase the robustness and success of these missions. Reachability analysis contributes to this requirement by obtaining the set of all achievable states for a dynamical system starting from an initial condition with given admissible control inputs of the system. In this study, an optimal control based reachability analysis algorithm is developed for evaluating the performance of the guidance and control methods for space missions considering the desired performance index. The developed method considers a softlanding problem for a Moon mission as the case study, and attainable area of the lander as the performance index. The method computes feasible trajectories for the lunar lander between the point where the terminal landing maneuver starts and points that constitutes the candidate landing region. The candidate landing region is discretized by equidistant points on a two dimensional plane, i.e. in downrange and crossrange coordinates, and for each grid point a distance function is defined. This distance function acts as an objective function for a related optimal control problem (OCP). Each infinite dimensional OCP is transcribed into a finite dimensional Nonlinear Programming Problem (NLP) by using PseudoSpectral Methods (PSM). The NLPs are solved using available tools to obtain feasible trajectories and approximated reachable sets with information about the states of the dynamical system at the grid points. The proposed method approximates reachable sets of the lander with propellanttoreach and timetoreach cost by solution of NLPs. A polynomialbased Apollo guidance scheme is used to compare the results for the developed method. The coefficients that define the position of the lander are obtained by solving a series of explicit equations for the given initial and final states. A model inversion based PD controller is designed to track the generated trajectory. Feasible solutions that satisfy safe landing conditions are filtered and the results are compared for the two different approaches. Finally, the uncertainties which are characterized by initial state error and system parameters are also considered. A multivariate trajectory interpolation tool is used to interpolate RS with different initial states. A Riccati equationbased controller is designed to track the previously obtained reference trajectories within presence of the uncertainties. Monte Carlo (MC) simulations are carried out to obtain safe attainable landing area of the lunar lander as probability maps. The same uncertainty set is used to verify these probability maps by propagating the uncertainties using unscented transform. The developed tool analyzes the different guidance and control methods, for the attainable landing area of the lander, under various landing scenarios, with different dynamical models and controller parameters. Numerous quality metrics are used to compare the change of characteristics of the attainable landing area and performance of the guidance and control methods, and selected design parameters
1 edition published in 2017 in English and held by 17 WorldCat member libraries worldwide
In the last decades developments in space technology paved the way to more challenging missions like asteroid mining, space tourism and human expansion into the Solar System. These missions require difficult tasks such as realtime capable guidance schemes for reentry, landing on celestial bodies and implementation of large angle maneuvers for spacecraft. There is a need for an analysis tool to increase the robustness and success of these missions. Reachability analysis contributes to this requirement by obtaining the set of all achievable states for a dynamical system starting from an initial condition with given admissible control inputs of the system. In this study, an optimal control based reachability analysis algorithm is developed for evaluating the performance of the guidance and control methods for space missions considering the desired performance index. The developed method considers a softlanding problem for a Moon mission as the case study, and attainable area of the lander as the performance index. The method computes feasible trajectories for the lunar lander between the point where the terminal landing maneuver starts and points that constitutes the candidate landing region. The candidate landing region is discretized by equidistant points on a two dimensional plane, i.e. in downrange and crossrange coordinates, and for each grid point a distance function is defined. This distance function acts as an objective function for a related optimal control problem (OCP). Each infinite dimensional OCP is transcribed into a finite dimensional Nonlinear Programming Problem (NLP) by using PseudoSpectral Methods (PSM). The NLPs are solved using available tools to obtain feasible trajectories and approximated reachable sets with information about the states of the dynamical system at the grid points. The proposed method approximates reachable sets of the lander with propellanttoreach and timetoreach cost by solution of NLPs. A polynomialbased Apollo guidance scheme is used to compare the results for the developed method. The coefficients that define the position of the lander are obtained by solving a series of explicit equations for the given initial and final states. A model inversion based PD controller is designed to track the generated trajectory. Feasible solutions that satisfy safe landing conditions are filtered and the results are compared for the two different approaches. Finally, the uncertainties which are characterized by initial state error and system parameters are also considered. A multivariate trajectory interpolation tool is used to interpolate RS with different initial states. A Riccati equationbased controller is designed to track the previously obtained reference trajectories within presence of the uncertainties. Monte Carlo (MC) simulations are carried out to obtain safe attainable landing area of the lunar lander as probability maps. The same uncertainty set is used to verify these probability maps by propagating the uncertainties using unscented transform. The developed tool analyzes the different guidance and control methods, for the attainable landing area of the lander, under various landing scenarios, with different dynamical models and controller parameters. Numerous quality metrics are used to compare the change of characteristics of the attainable landing area and performance of the guidance and control methods, and selected design parameters
Dynamic Modeling and Implementation of Trajectory Optimization, Sensitivity Analysis, and Optimal Control for Autonomous Deep
Space Navigation by Anne Sarah Schattel(
)
1 edition published in 2018 in English and held by 17 WorldCat member libraries worldwide
Within this thesis, methods for onboard trajectory optimization and optimal control regarding different tasks of an autonomous deep space exploration mission are investigated. These include cruise flight maneuvers towards a small celestial body, more specifically an asteroid, operations in its vicinity, and the performance of landing procedures. Therefore, dynamic models and respective optimal control problems are formulated. The former include where appropriate the gravitational influence of the Sun, of further planets, and of the asteroid, and the effects due to solar radiation pressure. Because of the high complexity and large a priori uncertainty about asteroids as well as the limited resources on a spacecraft, high precision methods of nonlinear optimization and optimal control are necessary. In this course, optimal control problems are transcribed into large sparse nonlinear optimization problems via direct transcription techniques. Conflicting mission aims, that is, short flight times and low energy consumption, are considered within the objective functions. Additionally, an onboard capable parametric sensitivity analysis is implemented, allowing for an approximation of deviations in optimal solutions in case of perturbations within model parameters. Thus, additional stability information is provided. Furthermore, the approximation of perturbed controls can be used for realtime control in time critical situations. The results strengthen the need for trajectory optimization and sensitivity analysis as a foundation for autonomous decision making and fault detection, isolation, and recovery (FDIR) techniques regarding flight maneuvers during deep space missions. However, the field of space science is just a sample application. By changing the dynamics and model properties, the developed algorithms can easily be adapted for terrestrial applications such as autonomous driving or deep sea navigation
1 edition published in 2018 in English and held by 17 WorldCat member libraries worldwide
Within this thesis, methods for onboard trajectory optimization and optimal control regarding different tasks of an autonomous deep space exploration mission are investigated. These include cruise flight maneuvers towards a small celestial body, more specifically an asteroid, operations in its vicinity, and the performance of landing procedures. Therefore, dynamic models and respective optimal control problems are formulated. The former include where appropriate the gravitational influence of the Sun, of further planets, and of the asteroid, and the effects due to solar radiation pressure. Because of the high complexity and large a priori uncertainty about asteroids as well as the limited resources on a spacecraft, high precision methods of nonlinear optimization and optimal control are necessary. In this course, optimal control problems are transcribed into large sparse nonlinear optimization problems via direct transcription techniques. Conflicting mission aims, that is, short flight times and low energy consumption, are considered within the objective functions. Additionally, an onboard capable parametric sensitivity analysis is implemented, allowing for an approximation of deviations in optimal solutions in case of perturbations within model parameters. Thus, additional stability information is provided. Furthermore, the approximation of perturbed controls can be used for realtime control in time critical situations. The results strengthen the need for trajectory optimization and sensitivity analysis as a foundation for autonomous decision making and fault detection, isolation, and recovery (FDIR) techniques regarding flight maneuvers during deep space missions. However, the field of space science is just a sample application. By changing the dynamics and model properties, the developed algorithms can easily be adapted for terrestrial applications such as autonomous driving or deep sea navigation
Hochgenaue Modellierung, Simulation und Optimierung von KWKAnlagen Schlussbericht (01.08.201231.05.2015) by
Christof Büskens(
)
1 edition published in 2015 in German and held by 16 WorldCat member libraries worldwide
1 edition published in 2015 in German and held by 16 WorldCat member libraries worldwide
Solver development strategy(
)
2 editions published in 2008 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 2008 in English and held by 14 WorldCat member libraries worldwide
Interface control document by Dennis Wassel(
)
2 editions published in 2008 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 2008 in English and held by 14 WorldCat member libraries worldwide
Higher order realtime approximations of pertubed control constrainted PDE optimal control problems by
Christof Büskens(
)
2 editions published in 2004 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 13 WorldCat member libraries worldwide
Suboptimal improvement of the classical Riccati controller(
)
1 edition published in 2006 in English and held by 12 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 12 WorldCat member libraries worldwide
Nonlinear largescale Optimization with WORHP(
)
1 edition published in 2010 in English and held by 12 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 12 WorldCat member libraries worldwide
Differentiability of consistency functions(
)
1 edition published in 2004 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 11 WorldCat member libraries worldwide
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Related Identities
 Wassel, Dennis Other Author
 Nikolayzik, Tim Author
 Gerdts, Matthias
 Universität Bremen Degree grantor
 Chen, Stephanie Contributor
 Rick, Matthias Contributor
 Schill, Kerstin 1958 Contributor
 Clemens, Joachim Author
 Echim, Mitja Author
 Kuhlmann, Renke Author
Associated Subjects