## Grüne, Lars

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 Author ID: grune.lars Published as: Grüne, Lars; Grüne, L.; Gruene, Lars more...less Homepage: http://num.math.uni-bayreuth.de/de/team/Gruene_Lars/ External Links: MGP
 Documents Indexed: 129 Publications since 1996, including 6 Books 3 Contributions as Editor · 1 Further Contribution Co-Authors: 94 Co-Authors with 108 Joint Publications 2,336 Co-Co-Authors
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### Co-Authors

 25 single-authored 15 Wirth, Fabian Roger 11 Worthmann, Karl 9 Semmler, Willi 8 Kellett, Christopher M. 7 Junge, Oliver 7 Kloeden, Peter Eris 6 Camilli, Fabio 6 Pannek, Jürgen 5 Nešić, Dragan 5 Weller, Steven R. 4 Braun, Philipp 4 Müller, Matthias A. 4 Pirkelmann, Simon 4 Schaller, Manuel 4 Schiela, Anton 4 Stieler, Marleen 3 Allgower, Frank 3 Baier, Robert 3 Falcone, Maurizio 3 Zidani, Hasnaa 2 Colonius, Fritz 2 Diehl, Moritz Mathias 2 Dower, Peter M. 2 Ferretti, Roberto Giorgio 2 Fleig, Arthur 2 Gaitsgory, Vladimir G. 2 Geiselhart, Roman 2 Guglielmi, Roberto 2 Hafstein, Sigurður Freyr 2 Karafyllis, Iasson 2 Li, Huijuan 2 Lunze, Jan 2 Margaliot, Michael 2 Mechelli, Luca 2 Meurer, Thomas 2 Noroozi, Navid 2 Reble, Marcus 2 Sigurani, Manuela 2 Sontag, Eduardo D. 2 Volkwein, Stefan 2 Yegorov, Ivan V. 1 Altmüller, Nils 1 Andrej, Julian 1 Aoyama, Hideaki 1 Bauer, Florian 1 Baumann, Michael Heinrich 1 Becker, Stephanie 1 Boccia, Andrea 1 Bock, Hans Georg 1 Bokanowski, Olivier 1 Botner, Meir 1 Caillau, Jean-Baptiste 1 Caraballo Garrido, Tomás 1 Cesaroni, Annalisa 1 Coron, Jean-Michel 1 Cyganowski, Sasha 1 Damm, Tobias 1 Findeisen, Rolf 1 Fujiwara, Yoshi 1 Groß, Dominic 1 Hanebeck, Uwe D. 1 Hirche, Sandra 1 Höger, Matthias 1 Kalise, Dante 1 Kern, Benjamin 1 Kliemann, Wolfgang H. 1 Koltai, Péter 1 Kriecherbauer, Thomas 1 Krügel, Lisa 1 Le, Thuy T. T. 1 Lehmann, Daniel J. 1 McEneaney, William “Mac” M. 1 Metscher, M. 1 Molin, Adam 1 Ohlberger, Mario 1 Palma, Vryan Gil S. 1 Picarelli, Athena 1 Pinho, Maria Norberta 1 Rantzer, Anders 1 Rüffer, Björn Sebastian 1 Sager, Sebastian 1 Sailer, Rudolf 1 Saint-Pierre, Patrick 1 Seehafer, Martin 1 Serea, Oana-Silvia 1 Siegmund, Stefan 1 Sieveking, Malte 1 Souma, Wataru 1 Stöcker, Christian 1 Stursberg, Olaf 1 Thatcher, Neil 1 Trélat, Emmanuel 1 Varutti, P. 1 Zanon, Mario 1 Zarai, Yoram
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### Serials

 14 SIAM Journal on Control and Optimization 14 Systems & Control Letters 7 IEEE Transactions on Automatic Control 5 Automatica 5 Discrete and Continuous Dynamical Systems. Series B 5 Mathematical Control and Related Fields 4 Discrete and Continuous Dynamical Systems 3 Numerische Mathematik 3 Optimal Control Applications & Methods 3 Journal of Economic Dynamics & Control 2 Journal of Mathematical Analysis and Applications 2 Journal of Differential Equations 2 Journal of Optimization Theory and Applications 2 SIAM Journal on Numerical Analysis 2 Applied Numerical Mathematics 2 Computational Economics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Stochastics and Dynamics 2 GAMM-Mitteilungen 2 Journal of Computational Dynamics 2 Communications and Control Engineering 1 Computers & Mathematics with Applications 1 IMA Journal of Numerical Analysis 1 International Journal of Control 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Applied Mathematics and Optimization 1 BIT 1 SIAM Review 1 Journal of Dynamics and Differential Equations 1 SIAM Journal on Scientific Computing 1 Economic Theory 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Difference Equations and Applications 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Nonlinear Analysis. Real World Applications 1 SIAM Journal on Applied Dynamical Systems 1 Lecture Notes in Control and Information Sciences 1 Lecture Notes in Mathematics 1 Systems & Control: Foundations & Applications 1 Vieweg Studium 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Operations Research 1 Springer INdAM Series 1 SpringerBriefs in Mathematics 1 Springer Studium Mathematik – Bachelor
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### Fields

 98 Systems theory; control (93-XX) 53 Calculus of variations and optimal control; optimization (49-XX) 23 Numerical analysis (65-XX) 19 Ordinary differential equations (34-XX) 14 Operations research, mathematical programming (90-XX) 13 Partial differential equations (35-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Dynamical systems and ergodic theory (37-XX) 6 Probability theory and stochastic processes (60-XX) 5 General and overarching topics; collections (00-XX) 4 Computer science (68-XX) 2 History and biography (01-XX) 2 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

93 Publications have been cited 1,152 times in 612 Documents Cited by Year
Nonlinear model predictive control. Theory and algorithms. Zbl 1220.93001
Grüne, Lars; Pannek, Jürgen
2011
Economic receding horizon control without terminal constraints. Zbl 1267.93052
Grüne, Lars
2013
Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003
Grüne, Lars; Pannek, Jürgen
2017
The dynamics of control. With an appendix by Lars Grüne. Zbl 1020.93500
Colonius, Fritz; Kliemann, Wolfgang
2000
Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045
Grüne, Lars
2009
Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001
Grüne, Lars
2002
An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013
Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl
2014
Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064
Nešić, Dragan; Grüne, Lars
2005
On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109
Grüne, Lars; Rantzer, Anders
2008
An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Zbl 0880.65045
Grüne, Lars
1997
Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077
Grüne, Lars
2000
Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026
Grüne, Lars; Semmler, Willi
2004
Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046
Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl
2010
A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2001
Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053
Grüne, Lars; Nesić, Dragan
2003
Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567
Grüne, Lars
2002
On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117
Grüne, Lars; Müller, Matthias A.
2016
Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222
Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr
2012
Pathwise approximation of random ordinary differential equations. Zbl 0998.65010
Grüne, L.; Kloeden, P. E.
2001
Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075
Grüne, L.; Kloeden, P. E.
2001
On the relation between discounted and average optimal value functions. Zbl 0918.49002
Grüne, Lars
1998
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068
Boccia, Andrea; Grüne, Lars; Worthmann, Karl
2014
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2020
Asymptotic stability equals exponential stability, and ISS equals finite energy gain – if you twist your eyes. Zbl 1043.93549
Grüne, Lars; Sontag, Eduardo D.; Wirth, Fabian R.
1999
Asymptotic controllability and exponential stabilization of nonlinear control systems at singular points. Zbl 0910.93063
Grüne, Lars
1998
Periodic optimal control, dissipativity and MPC. Zbl 1369.93356
Zanon, Mario; Grüne, Lars; Diehl, Moritz
2017
Control Lyapunov functions and Zubov’s method. Zbl 1157.93028
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2008
Global optimal control of perturbed systems. Zbl 1147.49019
Grüne, L.; Junge, O.
2008
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027
Grüne, Lars; Guglielmi, Roberto
2018
Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. Zbl 1420.49025
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2019
Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051
Müller, Matthias A.; Grüne, Lars
2016
Asset pricing with loss aversion. Zbl 1181.91072
Grüne, Lars; Semmler, Willi
2008
A receding horizon control approach to sampled-data implementation of continuous-time controllers. Zbl 1100.93042
Nešić, Dragan; Grüne, Lars
2006
ISS-Lyapunov functions for discontinuous discrete-time systems. Zbl 1360.93497
Grüne, Lars; Kellett, Christopher M.
2014
Value iteration convergence of $$\varepsilon$$-monotone schemes for stationary Hamilton-Jacobi equations. Zbl 1334.65180
Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Grüne, Lars; Kalise, Dante; Zidani, Hasnaa
2015
Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. Zbl 0988.65077
Camilli, Fabio; Grüne, Lars
2000
Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081
Grüne, Lars
2003
Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094
Grüne, Lars; Semmler, Willi; Stieler, Marleen
2015
A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103
Grüne, Lars; Worthmann, Karl
2012
Stabilization with discounted optimal control. Zbl 1327.93324
Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil
2015
A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2001
Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350
Grüne, Lars; Worthmann, Karl; Nešić, Dragan
2008
Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010
Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R.
2007
Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085
Karafyllis, Iasson; Grüne, Lars
2011
Numerical stabilization of bilinear control systems. Zbl 0876.93032
Grüne, Lars
1996
A set oriented approach to optimal feedback stabilization. Zbl 1129.93500
Grüne, Lars; Junge, Oliver
2005
Approximation properties of receding horizon optimal control. Zbl 1336.93060
Grüne, Lars
2016
The role of sampling for stability and performance in unconstrained nonlinear model predictive control. Zbl 1292.93061
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
2014
A uniform exponential spectrum for linear flows on vector bundles. Zbl 0983.37032
Grüne, Lars
2000
Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311
Camilli, Fabio; Grüne, Lars
2003
Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009
Grüne, Lars
2004
Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209
Becker, Stephanie; Grüne, Lars; Semmler, Willi
2007
Discrete feedback stabilization of semilinear control systems. Zbl 0867.93071
Grüne, Lars
1996
Higher order numerical approximation of switching systems. Zbl 1100.93022
Grüne, L.; Kloeden, P. E.
2006
A distributed optimization algorithm for the predictive control of smart grids. Zbl 1359.93270
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
2016
Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033
Altmüller, Nils; Grüne, Lars
2012
Nonconservative discrete-time ISS small-gain conditions for closed sets. Zbl 1395.93506
Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R.
2018
Stabilization of strictly dissipative discrete time systems with discounted optimal control. Zbl 1400.93267
Gaitsgory, Vladimir; Grüne, Lars; Höger, Matthias; Kellett, Christopher M.; Weller, Steven R.
2018
Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035
Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen
2018
Discretization, inflation and perturbation of attractors. Zbl 0996.37013
Grüne, L.; Kloeden, P. E.
2001
Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058
Grüne, Lars; Wirth, Fabian
1999
Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604
Grüne, Lars
1999
On the relation between turnpike properties for finite and infinite horizon optimal control problems. Zbl 1380.49055
Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.
2017
Computation of local ISS Lyapunov functions with low gains via linear programming. Zbl 1366.37146
Li, Huijuan; Baier, Robert; Grüne, Lars; Hafstein, Sigurdur F.; Wirth, Fabian R.
2015
On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073
Grüne, L.; Metscher, M.; Ohlberger, M.
1999
Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081
Grüne, L.; Nešić, D.; Pannek, J.
2007
Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013
Grüne, L.; Pannek, J.
2009
Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033
Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian
2006
Differential games and Zubov’s method. Zbl 1237.49054
Grüne, Lars; Serea, Oana Silvia
2011
Economic model predictive control for time-varying system: performance and stability results. Zbl 1451.93095
Grüne, Lars; Pirkelmann, Simon
2020
Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056
Bauer, Florian; Grüne, Lars; Semmler, Willi
2006
Maple for stochastic differential equations. Zbl 0991.65006
Cyganowski, S.; Grüne, L.; Kloeden, P. E.
2001
Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361
Grüne, Lars; Semmler, Willi; Sieveking, Malte
2005
Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099
Grüne, Lars; Palma, Vryan Gil
2015
Model predictive control, cost controllability, and homogeneity. Zbl 1453.93083
Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl
2020
On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Zbl 1462.49058
Grüne, Lars; Guglielmi, Roberto
2021
Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036
2002
Asset pricing with dynamic programming. Zbl 1161.91447
Grüne, Lars; Semmler, Willi
2007
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088
Grüne, Lars
2001
Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068
Grüne, Lars
2008
On approximating contractive systems. Zbl 1390.93186
Botner, Meir; Zarai, Yoram; Margaliot, Michael; Grüne, Lars
2017
Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051
Grüne, Lars
1999
Simultaneously long short trading in discrete and continuous time. Zbl 1353.93116
Baumann, Michael Heinrich; Grüne, Lars
2017
Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080
Grüne, Lars; Zidani, Hasnaa
2015
Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019
Grüne, Lars; Picarelli, Athena
2015
Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328
Li, Huijuan; Grüne, Lars
2016
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. Zbl 1467.49037
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2021
Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084
Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan
2021
On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002
Grüne, Lars; Wirth, Fabian
2000
An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044
Grüne, Lars; Saint-Pierre, Patrick
2006
Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168
Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M.
2018
A double-sided dynamic programming approach to the minimum time problem and its numerical approximation. Zbl 1372.65193
Grüne, Lars; Le, Thuy T. T.
2017
$$L^2$$-tracking of Gaussian distributions via model predictive control for the Fokker-Planck equation. Zbl 1406.35411
Fleig, Arthur; Grüne, Lars
2018
On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Zbl 1462.49058
Grüne, Lars; Guglielmi, Roberto
2021
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. Zbl 1467.49037
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2021
Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084
Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan
2021
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2020
Economic model predictive control for time-varying system: performance and stability results. Zbl 1451.93095
Grüne, Lars; Pirkelmann, Simon
2020
Model predictive control, cost controllability, and homogeneity. Zbl 1453.93083
Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl
2020
Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. Zbl 1420.49025
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2019
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027
Grüne, Lars; Guglielmi, Roberto
2018
Nonconservative discrete-time ISS small-gain conditions for closed sets. Zbl 1395.93506
Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R.
2018
Stabilization of strictly dissipative discrete time systems with discounted optimal control. Zbl 1400.93267
Gaitsgory, Vladimir; Grüne, Lars; Höger, Matthias; Kellett, Christopher M.; Weller, Steven R.
2018
Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035
Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen
2018
Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168
Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M.
2018
$$L^2$$-tracking of Gaussian distributions via model predictive control for the Fokker-Planck equation. Zbl 1406.35411
Fleig, Arthur; Grüne, Lars
2018
Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003
Grüne, Lars; Pannek, Jürgen
2017
Periodic optimal control, dissipativity and MPC. Zbl 1369.93356
Zanon, Mario; Grüne, Lars; Diehl, Moritz
2017
On the relation between turnpike properties for finite and infinite horizon optimal control problems. Zbl 1380.49055
Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.
2017
On approximating contractive systems. Zbl 1390.93186
Botner, Meir; Zarai, Yoram; Margaliot, Michael; Grüne, Lars
2017
Simultaneously long short trading in discrete and continuous time. Zbl 1353.93116
Baumann, Michael Heinrich; Grüne, Lars
2017
A double-sided dynamic programming approach to the minimum time problem and its numerical approximation. Zbl 1372.65193
Grüne, Lars; Le, Thuy T. T.
2017
On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117
Grüne, Lars; Müller, Matthias A.
2016
Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051
Müller, Matthias A.; Grüne, Lars
2016
Approximation properties of receding horizon optimal control. Zbl 1336.93060
Grüne, Lars
2016
A distributed optimization algorithm for the predictive control of smart grids. Zbl 1359.93270
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
2016
Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328
Li, Huijuan; Grüne, Lars
2016
Value iteration convergence of $$\varepsilon$$-monotone schemes for stationary Hamilton-Jacobi equations. Zbl 1334.65180
Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Grüne, Lars; Kalise, Dante; Zidani, Hasnaa
2015
Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094
Grüne, Lars; Semmler, Willi; Stieler, Marleen
2015
Stabilization with discounted optimal control. Zbl 1327.93324
Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil
2015
Computation of local ISS Lyapunov functions with low gains via linear programming. Zbl 1366.37146
Li, Huijuan; Baier, Robert; Grüne, Lars; Hafstein, Sigurdur F.; Wirth, Fabian R.
2015
Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099
Grüne, Lars; Palma, Vryan Gil
2015
Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080
Grüne, Lars; Zidani, Hasnaa
2015
Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019
Grüne, Lars; Picarelli, Athena
2015
An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013
Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl
2014
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068
Boccia, Andrea; Grüne, Lars; Worthmann, Karl
2014
ISS-Lyapunov functions for discontinuous discrete-time systems. Zbl 1360.93497
Grüne, Lars; Kellett, Christopher M.
2014
The role of sampling for stability and performance in unconstrained nonlinear model predictive control. Zbl 1292.93061
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
2014
Economic receding horizon control without terminal constraints. Zbl 1267.93052
Grüne, Lars
2013
Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222
Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr
2012
A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103
Grüne, Lars; Worthmann, Karl
2012
Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033
Altmüller, Nils; Grüne, Lars
2012
Nonlinear model predictive control. Theory and algorithms. Zbl 1220.93001
Grüne, Lars; Pannek, Jürgen
2011
Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085
Karafyllis, Iasson; Grüne, Lars
2011
Differential games and Zubov’s method. Zbl 1237.49054
Grüne, Lars; Serea, Oana Silvia
2011
Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046
Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl
2010
Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045
Grüne, Lars
2009
Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013
Grüne, L.; Pannek, J.
2009
On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109
Grüne, Lars; Rantzer, Anders
2008
Control Lyapunov functions and Zubov’s method. Zbl 1157.93028
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2008
Global optimal control of perturbed systems. Zbl 1147.49019
Grüne, L.; Junge, O.
2008
Asset pricing with loss aversion. Zbl 1181.91072
Grüne, Lars; Semmler, Willi
2008
Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350
Grüne, Lars; Worthmann, Karl; Nešić, Dragan
2008
Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068
Grüne, Lars
2008
Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010
Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R.
2007
Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209
Becker, Stephanie; Grüne, Lars; Semmler, Willi
2007
Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081
Grüne, L.; Nešić, D.; Pannek, J.
2007
Asset pricing with dynamic programming. Zbl 1161.91447
Grüne, Lars; Semmler, Willi
2007
A receding horizon control approach to sampled-data implementation of continuous-time controllers. Zbl 1100.93042
Nešić, Dragan; Grüne, Lars
2006
Higher order numerical approximation of switching systems. Zbl 1100.93022
Grüne, L.; Kloeden, P. E.
2006
Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033
Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian
2006
Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056
Bauer, Florian; Grüne, Lars; Semmler, Willi
2006
An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044
Grüne, Lars; Saint-Pierre, Patrick
2006
Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064
Nešić, Dragan; Grüne, Lars
2005
A set oriented approach to optimal feedback stabilization. Zbl 1129.93500
Grüne, Lars; Junge, Oliver
2005
Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361
Grüne, Lars; Semmler, Willi; Sieveking, Malte
2005
Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026
Grüne, Lars; Semmler, Willi
2004
Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009
Grüne, Lars
2004
Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053
Grüne, Lars; Nesić, Dragan
2003
Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081
Grüne, Lars
2003
Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311
Camilli, Fabio; Grüne, Lars
2003
Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001
Grüne, Lars
2002
Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567
Grüne, Lars
2002
Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036
2002
A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2001
Pathwise approximation of random ordinary differential equations. Zbl 0998.65010
Grüne, L.; Kloeden, P. E.
2001
Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075
Grüne, L.; Kloeden, P. E.
2001
A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2001
Discretization, inflation and perturbation of attractors. Zbl 0996.37013
Grüne, L.; Kloeden, P. E.
2001
Maple for stochastic differential equations. Zbl 0991.65006
Cyganowski, S.; Grüne, L.; Kloeden, P. E.
2001
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088
Grüne, Lars
2001
The dynamics of control. With an appendix by Lars Grüne. Zbl 1020.93500
Colonius, Fritz; Kliemann, Wolfgang
2000
Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077
Grüne, Lars
2000
Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. Zbl 0988.65077
Camilli, Fabio; Grüne, Lars
2000
A uniform exponential spectrum for linear flows on vector bundles. Zbl 0983.37032
Grüne, Lars
2000
On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002
Grüne, Lars; Wirth, Fabian
2000
Asymptotic stability equals exponential stability, and ISS equals finite energy gain – if you twist your eyes. Zbl 1043.93549
Grüne, Lars; Sontag, Eduardo D.; Wirth, Fabian R.
1999
Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058
Grüne, Lars; Wirth, Fabian
1999
Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604
Grüne, Lars
1999
On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073
Grüne, L.; Metscher, M.; Ohlberger, M.
1999
Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051
Grüne, Lars
1999
On the relation between discounted and average optimal value functions. Zbl 0918.49002
Grüne, Lars
1998
Asymptotic controllability and exponential stabilization of nonlinear control systems at singular points. Zbl 0910.93063
Grüne, Lars
1998
An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Zbl 0880.65045
Grüne, Lars
1997
Numerical stabilization of bilinear control systems. Zbl 0876.93032
Grüne, Lars
1996
Discrete feedback stabilization of semilinear control systems. Zbl 0867.93071
Grüne, Lars
1996
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### Cited by 915 Authors

 61 Grüne, Lars 19 Kloeden, Peter Eris 17 Worthmann, Karl 16 Giesl, Peter 16 Hafstein, Sigurður Freyr 15 Wirth, Fabian Roger 14 Kellett, Christopher M. 14 Müller, Matthias A. 13 Karafyllis, Iasson 13 Semmler, Willi 11 Allgower, Frank 10 Zuazua, Enrique 9 Efimov, Denis V. 9 Gaitsgory, Vladimir G. 8 Dashkovskiy, Sergey N. 8 Kunisch, Karl 8 Mironchenko, Andrii 8 Polyakov, Andrey 7 Borzì, Alfio 7 Faulwasser, Timm 7 Li, Huijuan 6 Falcone, Maurizio 6 Jiang, Zhong-Ping 6 Junge, Oliver 6 Picarelli, Athena 6 Schaller, Manuel 6 Teel, Andrew Richard 5 Angeli, David 5 Annunziato, Mario 5 Azmi, Behzad 5 Bokanowski, Olivier 5 Colonius, Fritz 5 Geiselhart, Roman 5 Houska, Boris 5 Kolmanovsky, Ilya V. 5 Malisoff, Michael 5 Nešić, Dragan 5 Pannek, Jürgen 5 Pepe, Pierdomenico 5 Schiela, Anton 5 Trélat, Emmanuel 5 Weller, Steven R. 4 Albi, Giacomo 4 Alla, Alessandro 4 Asai, Yusuke 4 Baier, Robert 4 Carbonell, Felix 4 Graichen, Knut 4 Gugat, Martin 4 Jentzen, Arnulf 4 Jimenez, Juan Carlos 4 Jones, Colin Neil 4 Kalise, Dante 4 Kawan, Christoph 4 Khlopin, Dmitriĭ Valer’evich 4 Krstić, Miroslav 4 Lazar, Mircea 4 Mehrez, Mohamed W. 4 Moreno, Jaime A. 4 Naujok, Lars 4 Noroozi, Navid 4 Peitz, Sebastian 4 Perruquetti, Wilfrid 4 Rasmussen, Martin 4 Sanchez, Tonametl 4 Shvartsman, Ilya A. 4 Volkwein, Stefan 4 Zidani, Hasnaa 3 Ahmed-Ali, Tarek 3 Alamir, Mazen 3 Camilli, Fabio 3 Chatterjee, Debasish 3 Dai, Hao 3 Dawid, Herbert 3 de Queiroz, Marcio S. 3 Dower, Peter M. 3 Elaiw, Ahmed M. 3 Fečkan, Michal 3 Flaßkamp, Kathrin 3 Gerdts, Matthias 3 Goreac, Dan 3 Gray, W. Steven 3 Grundel, Sara M. 3 Guglielmi, Roberto 3 He, Defeng 3 Herty, Michael Matthias 3 Jerbi, Hamadi 3 Jia, Jinping 3 Lamnabhi-Lagarrigue, Françoise 3 Le, Thuy T. T. 3 Limon, Daniel 3 Manzie, Chris 3 Monaco, Salvatore 3 Neuenkirch, Andreas 3 Normand-Cyrot, Dorothée 3 Novara, Carlo 3 Pirkelmann, Simon 3 Rawlings, James B. 3 Reble, Marcus 3 Ritschel, Tobias K. S. ...and 815 more Authors
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### Cited in 136 Serials

 107 Automatica 44 Systems & Control Letters 25 SIAM Journal on Control and Optimization 23 International Journal of Control 16 MCSS. Mathematics of Control, Signals, and Systems 16 European Journal of Control 15 Journal of Optimization Theory and Applications 14 Journal of Economic Dynamics & Control 13 Journal of the Franklin Institute 12 International Journal of Robust and Nonlinear Control 11 Journal of Mathematical Analysis and Applications 11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Discrete and Continuous Dynamical Systems. Series B 9 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 Journal of Differential Equations 7 Journal of Difference Equations and Applications 7 Discrete and Continuous Dynamical Systems 6 Journal of Computational and Applied Mathematics 6 Numerische Mathematik 6 SIAM Journal on Scientific Computing 6 Nonlinear Analysis. Hybrid Systems 6 Mathematical Control and Related Fields 5 Computers & Mathematics with Applications 5 Applied Mathematics and Computation 5 Applied Mathematics and Optimization 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Mathematical Problems in Engineering 5 Journal of Computational Dynamics 4 Optimal Control Applications & Methods 4 Journal of Dynamics and Differential Equations 4 Computational Economics 4 Nonlinear Dynamics 4 Optimization Methods & Software 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Mathematical and Computer Modelling of Dynamical Systems 4 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Systems Science and Complexity 4 Stochastics and Dynamics 3 Journal of Computational Physics 3 BIT 3 Computing 3 Physica D 3 Applied Numerical Mathematics 3 Journal of Scientific Computing 3 Numerical Algorithms 3 Complexity 3 SIAM Journal on Applied Dynamical Systems 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 GAMM-Mitteilungen 3 Dynamic Games and Applications 3 International Journal of Systems Science. Principles and Applications of Systems and Integration 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Chaos, Solitons and Fractals 2 Information Sciences 2 Applied Mathematical Modelling 2 Automation and Remote Control 2 Computational Optimization and Applications 2 Advances in Computational Mathematics 2 Differential Equations and Dynamical Systems 2 Vietnam Journal of Mathematics 2 Chaos 2 Optimization and Engineering 2 Differential Equations 2 Advances in Difference Equations 2 Asian Journal of Control 2 Journal of Theoretical Biology 1 Journal of Mathematical Biology 1 Ukrainian Mathematical Journal 1 Journal of Theoretical and Applied Mechanics (Sofia) 1 Canadian Mathematical Bulletin 1 International Journal for Numerical Methods in Engineering 1 Journal of Approximation Theory 1 Journal of Economic Theory 1 Metroeconomica 1 Naval Research Logistics 1 Operations Research 1 Proceedings of the American Mathematical Society 1 Studies in Applied Mathematics 1 Stochastic Analysis and Applications 1 Optimization 1 Queueing Systems 1 Science in China. Series A 1 Neural Networks 1 European Journal of Applied Mathematics 1 Real-Time Systems 1 Neural Computation 1 International Journal of Adaptive Control and Signal Processing 1 Computational Mathematics and Mathematical Physics 1 European Journal of Operational Research 1 SIAM Review 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Journal of Mathematical Imaging and Vision 1 Calculus of Variations and Partial Differential Equations 1 St. Petersburg Mathematical Journal 1 Computational and Applied Mathematics 1 NoDEA. Nonlinear Differential Equations and Applications 1 Sbornik: Mathematics 1 Computing and Visualization in Science 1 Positivity ...and 36 more Serials
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### Cited in 38 Fields

 408 Systems theory; control (93-XX) 152 Calculus of variations and optimal control; optimization (49-XX) 86 Numerical analysis (65-XX) 68 Ordinary differential equations (34-XX) 64 Operations research, mathematical programming (90-XX) 57 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 54 Partial differential equations (35-XX) 52 Dynamical systems and ergodic theory (37-XX) 33 Probability theory and stochastic processes (60-XX) 23 Biology and other natural sciences (92-XX) 13 Difference and functional equations (39-XX) 8 Computer science (68-XX) 7 Fluid mechanics (76-XX) 6 Information and communication theory, circuits (94-XX) 5 Mechanics of particles and systems (70-XX) 4 Statistics (62-XX) 3 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Operator theory (47-XX) 3 Mechanics of deformable solids (74-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Combinatorics (05-XX) 2 Sequences, series, summability (40-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 (04-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)