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## Grüne, Lars

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 Author ID: grune.lars Published as: Gruene, Lars; Grüne, L.; Grüne, Lars Homepage: http://num.math.uni-bayreuth.de/de/team/Gruene_Lars/ External Links: MGP
 Documents Indexed: 119 Publications since 1996, including 7 Books
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#### Co-Authors

 23 single-authored 15 Wirth, Fabian Roger 11 Worthmann, Karl 9 Semmler, Willi 7 Junge, Oliver 7 Kloeden, Peter Eris 6 Camilli, Fabio 6 Kellett, Christopher M. 6 Pannek, Jürgen 5 Nešić, Dragan 4 Stieler, Marleen 4 Weller, Steven R. 3 Allgower, Frank 3 Baier, Robert 3 Braun, Philipp 3 Falcone, Maurizio 3 Müller, Matthias A. 3 Zidani, Hasnaa 2 Diehl, Moritz Mathias 2 Ferretti, Roberto Giorgio 2 Gaitsgory, Vladimir A. 2 Geiselhart, Roman 2 Guglielmi, Roberto 2 Hafstein, Sigurður Freyr 2 Karafyllis, Iasson 2 Li, Huijuan 2 Lunze, Jan 2 Margaliot, Michael 2 Noroozi, Navid 2 Pirkelmann, Simon 2 Reble, Marcus 2 Schaller, Manuel 2 Schiela, Anton 2 Sigurani, Manuela 2 Sontag, Eduardo D. 1 Altmüller, Nils 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 Colonius, Fritz 1 Coron, Jean-Michel 1 Cyganowski, Sasha 1 Damm, Tobias 1 Findeisen, Rolf 1 Fischer, J. H. 1 Fleig, Arthur 1 Fujiwara, Yoshi 1 Groß, Dominic 1 Hanebeck, Uwe D. 1 Hirche, Sandra 1 Höger, Matthias 1 Kalise, Dante 1 Kern, Benjamin 1 Koltai, Péter 1 Kriecherbauer, Thomas 1 Le, Thuy T. T. 1 Lehmann, Daniel J. 1 McEneaney, William 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 13 Systems & Control Letters 7 IEEE Transactions on Automatic Control 5 Automatica 5 Discrete and Continuous Dynamical Systems. Series B 4 Discrete and Continuous Dynamical Systems 3 Numerische Mathematik 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 Stochastics and Dynamics 2 GAMM-Mitteilungen 2 Mathematical Control and Related Fields 2 Communications and Control Engineering 1 IMA Journal of Numerical Analysis 1 International Journal of Control 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 BIT 1 Optimal Control Applications & Methods 1 Journal of Dynamics and Differential Equations 1 Economic Theory 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Difference Equations and Applications 1 Computing and Visualization in Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 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 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Advances in Operations Research 1 Springer INdAM Series 1 Journal of Computational Dynamics 1 Springer Studium Mathematik – Bachelor
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#### Fields

 86 Systems theory; control (93-XX) 44 Calculus of variations and optimal control; optimization (49-XX) 22 Numerical analysis (65-XX) 15 Ordinary differential equations (34-XX) 14 Operations research, mathematical programming (90-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Partial differential equations (35-XX) 10 Dynamical systems and ergodic theory (37-XX) 5 Probability theory and stochastic processes (60-XX) 4 General and overarching topics; collections (00-XX) 3 Computer science (68-XX) 2 History and biography (01-XX) 2 Difference and functional equations (39-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

89 Publications have been cited 936 times in 530 Documents Cited by Year
Nonlinear model predictive control. Theory and algorithms. Zbl 1220.93001
Grüne, Lars; Pannek, Jürgen
2011
Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001
Grüne, Lars
2002
Economic receding horizon control without terminal constraints. Zbl 1267.93052
Grüne, Lars
2013
Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045
Grüne, Lars
2009
Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064
Nešić, Dragan; Grüne, Lars
2005
An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Zbl 0880.65045
Grüne, Lars
1997
On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109
Grüne, Lars; Rantzer, Anders
2008
An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013
Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl
2014
A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2001
Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046
Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl
2010
Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026
Grüne, Lars; Semmler, Willi
2004
Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567
Grüne, Lars
2002
Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077
Grüne, Lars
2000
Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053
Grüne, Lars; Nesić, Dragan
2003
Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003
Grüne, Lars; Pannek, Jürgen
2017
Pathwise approximation of random ordinary differential equations. Zbl 0998.65010
Grüne, L.; Kloeden, P. E.
2001
Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222
Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr
2012
Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075
Grüne, L.; Kloeden, P. E.
2001
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068
Boccia, Andrea; Grüne, Lars; Worthmann, Karl
2014
On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117
Grüne, Lars; Müller, Matthias A.
2016
Global optimal control of perturbed systems. Zbl 1147.49019
Grüne, L.; Junge, O.
2008
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
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
Control Lyapunov functions and Zubov’s method. Zbl 1157.93028
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2008
Periodic optimal control, dissipativity and MPC. Zbl 1369.93356
Zanon, Mario; Grüne, Lars; Diehl, Moritz
2017
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
Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350
Grüne, Lars; Worthmann, Karl; Nešić, Dragan
2008
A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103
Grüne, Lars; Worthmann, Karl
2012
Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010
Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R.
2007
A set oriented approach to optimal feedback stabilization. Zbl 1129.93500
Grüne, Lars; Junge, Oliver
2005
Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009
Grüne, Lars
2004
Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081
Grüne, Lars
2003
A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
2001
Numerical stabilization of bilinear control systems. Zbl 0876.93032
Grüne, Lars
1996
Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051
Müller, Matthias A.; 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
Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085
Karafyllis, Iasson; Grüne, Lars
2011
Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311
Camilli, Fabio; Grüne, Lars
2003
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
Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027
Grüne, Lars; Guglielmi, Roberto
2018
Approximation properties of receding horizon optimal control. Zbl 1336.93060
Grüne, Lars
2016
Stabilization with discounted optimal control. Zbl 1327.93324
Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil
2015
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
Higher order numerical approximation of switching systems. Zbl 1100.93022
Grüne, L.; Kloeden, P. E.
2006
Discrete feedback stabilization of semilinear control systems. Zbl 0867.93071
Grüne, Lars
1996
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
Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094
Grüne, Lars; Semmler, Willi; Stieler, Marleen
2015
Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209
Becker, Stephanie; Grüne, Lars; Semmler, Willi
2007
Discretization, inflation and perturbation of attractors. Zbl 0996.37013
Grüne, L.; Kloeden, P. E.
2001
Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604
Grüne, Lars
1999
Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058
Grüne, Lars; Wirth, Fabian
1999
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
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
Differential games and Zubov’s method. Zbl 1237.49054
Grüne, Lars; Serea, Oana Silvia
2011
Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081
Grüne, L.; Nešić, D.; Pannek, J.
2007
Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033
Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian
2006
Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361
Grüne, Lars; Semmler, Willi; Sieveking, Malte
2005
Maple for stochastic differential equations. Zbl 0991.65006
Cyganowski, S.; Grüne, L.; Kloeden, P. E.
2001
On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073
Grüne, L.; Metscher, M.; Ohlberger, M.
1999
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
Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099
Grüne, Lars; Palma, Vryan Gil
2015
Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033
Altmüller, Nils; Grüne, Lars
2012
Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056
Bauer, Florian; Grüne, Lars; Semmler, Willi
2006
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044
Grüne, Lars; Schaller, Manuel; Schiela, Anton
2020
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
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
Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019
Grüne, Lars; Picarelli, Athena
2015
Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080
Grüne, Lars; Zidani, Hasnaa
2015
Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013
Grüne, L.; Pannek, J.
2009
Asset pricing with dynamic programming. Zbl 1161.91447
Grüne, Lars; Semmler, Willi
2007
Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036
Colonius, Fritz (ed.); Grüne, Lars (ed.)
2002
Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088
Grüne, Lars
2001
On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002
Grüne, Lars; Wirth, Fabian
2000
Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051
Grüne, Lars
1999
Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168
Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M.
2018
Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035
Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen
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
Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328
Li, Huijuan; Grüne, Lars
2016
Numerical event-based ISS controller design via a dynamic game approach. Zbl 1327.93178
Grüne, Lars; Sigurani, Manuela
2015
Ordinary differential equations. An introduction from the dynamical systems perspective. Zbl 1175.34001
Grüne, Lars; Junge, Oliver
2009
Optimization based stabilization of nonlinear control systems. Zbl 1229.93090
Grüne, Lars
2008
Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068
Grüne, Lars
2008
An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044
Grüne, Lars; Saint-Pierre, Patrick
2006
Quantitative aspects of the input-to-state-stability property. Zbl 1078.93060
Grüne, Lars
2004
Convergence rates of perturbed attracting sets with vanishing perturbation. Zbl 0960.65137
Grüne, Lars
2000
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044
Grüne, Lars; Schaller, Manuel; Schiela, Anton
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
Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168
Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M.
2018
Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035
Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen
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
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
Stabilization with discounted optimal control. Zbl 1327.93324
Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil
2015
Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094
Grüne, Lars; Semmler, Willi; Stieler, Marleen
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 method for controlled diffusions with state constraints. Zbl 1323.93019
Grüne, Lars; Picarelli, Athena
2015
Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080
Grüne, Lars; Zidani, Hasnaa
2015
Numerical event-based ISS controller design via a dynamic game approach. Zbl 1327.93178
Grüne, Lars; Sigurani, Manuela
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
Ordinary differential equations. An introduction from the dynamical systems perspective. Zbl 1175.34001
Grüne, Lars; Junge, Oliver
2009
On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109
Grüne, Lars; Rantzer, Anders
2008
Global optimal control of perturbed systems. Zbl 1147.49019
Grüne, L.; Junge, O.
2008
Control Lyapunov functions and Zubov’s method. Zbl 1157.93028
Camilli, Fabio; Grüne, Lars; Wirth, Fabian
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
Optimization based stabilization of nonlinear control systems. Zbl 1229.93090
Grüne, Lars
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
Quantitative aspects of the input-to-state-stability property. Zbl 1078.93060
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
Colonius, Fritz (ed.); Grüne, Lars (ed.)
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
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
Convergence rates of perturbed attracting sets with vanishing perturbation. Zbl 0960.65137
Grüne, Lars
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
Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604
Grüne, Lars
1999
Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058
Grüne, Lars; Wirth, Fabian
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 822 Authors

 54 Grüne, Lars 21 Kloeden, Peter Eris 15 Giesl, Peter 15 Hafstein, Sigurður Freyr 13 Müller, Matthias A. 13 Wirth, Fabian Roger 12 Karafyllis, Iasson 12 Kellett, Christopher M. 12 Semmler, Willi 11 Allgower, Frank 9 Dashkovskiy, Sergey N. 9 Worthmann, Karl 8 Efimov, Denis V. 7 Junge, Oliver 7 Li, Huijuan 7 Mironchenko, Andrii 7 Nešić, Dragan 6 Falcone, Maurizio 6 Gaitsgory, Vladimir A. 6 Jiang, Zhong-Ping 6 Kunisch, Karl 6 Zuazua, Enrique 5 Angeli, David 5 Borzì, Alfio 5 Colonius, Fritz 5 Geiselhart, Roman 5 Houska, Boris 5 Malisoff, Michael 5 Pepe, Pierdomenico 5 Picarelli, Athena 5 Polyakov, Andrey 5 Teel, Andrew Richard 5 Trélat, Emmanuel 4 Annunziato, Mario 4 Asai, Yusuke 4 Azmi, Behzad 4 Baier, Robert 4 Bokanowski, Olivier 4 Carbonell, Felix 4 Graichen, Knut 4 Jentzen, Arnulf 4 Jimenez, Juan Carlos 4 Kawan, Christoph 4 Krstić, Miroslav 4 Lazar, Mircea 4 Naujok, Lars 4 Pannek, Jürgen 4 Perruquetti, Wilfrid 4 Rasmussen, Martin 4 Sanchez, Tonametl 4 Weller, Steven R. 4 Zidani, Hasnaa 3 Ahmed-Ali, Tarek 3 Alamir, Mazen 3 Alla, Alessandro 3 Bock, Hans Georg 3 Camilli, Fabio 3 Chatterjee, Debasish 3 Dai, Hao 3 de Queiroz, Marcio S. 3 Dower, Peter M. 3 Elaiw, Ahmed M. 3 Fečkan, Michal 3 Gerdts, Matthias 3 Goreac, Dan 3 Gray, W. Steven 3 Gugat, Martin 3 Guglielmi, Roberto 3 He, Defeng 3 Jerbi, Hamadi 3 Jia, Jinping 3 Jones, Colin Neil 3 Khlopin, Dmitriĭ Valer’evich 3 Kolmanovsky, Ilya V. 3 Lamnabhi-Lagarrigue, Françoise 3 Le, Thuy T. T. 3 Manzie, Chris 3 Mayne, David Q. 3 Monaco, Salvatore 3 Moreno, Jaime A. 3 Neuenkirch, Andreas 3 Normand-Cyrot, Dorothée 3 Noroozi, Navid 3 Peitz, Sebastian 3 Potschka, Andreas 3 Reble, Marcus 3 Rüffer, Björn Sebastian 3 Sahu, Smita 3 Schiela, Anton 3 Tozza, Silvia 3 Veliov, Vladimir M. 2 Abedi, Fakhreddin 2 Albi, Giacomo 2 Atolia, Manoj 2 Bernuau, Emmanuel 2 Biscay, Rolando J. 2 Bitmead, Robert R. 2 Boccia, Andrea 2 Bonvin, Dominique 2 Borkar, Vivek Shripad ...and 722 more Authors
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#### Cited in 124 Serials

 93 Automatica 44 Systems & Control Letters 19 SIAM Journal on Control and Optimization 18 International Journal of Control 15 Journal of Optimization Theory and Applications 15 MCSS. Mathematics of Control, Signals, and Systems 14 European Journal of Control 12 Journal of the Franklin Institute 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 12 Journal of Economic Dynamics & Control 12 International Journal of Robust and Nonlinear Control 10 Journal of Mathematical Analysis and Applications 8 Journal of Differential Equations 8 Discrete and Continuous Dynamical Systems. Series B 7 Journal of Difference Equations and Applications 7 Discrete and Continuous Dynamical Systems 6 Journal of Computational and Applied Mathematics 6 Mathematical Problems in Engineering 5 Applied Mathematics and Computation 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Nonlinear Analysis. Hybrid Systems 5 Journal of Computational Dynamics 4 Computers & Mathematics with Applications 4 Numerische Mathematik 4 Optimal Control Applications & Methods 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Journal of Dynamics and Differential Equations 4 Computational Economics 4 SIAM Journal on Scientific Computing 4 Nonlinear Dynamics 4 Optimization Methods & Software 4 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 4 Communications in Nonlinear Science and Numerical Simulation 4 Stochastics and Dynamics 3 Journal of Computational Physics 3 Applied Mathematics and Optimization 3 BIT 3 Computing 3 Applied Numerical Mathematics 3 Complexity 3 Journal of Systems Science and Complexity 3 GAMM-Mitteilungen 3 Dynamic Games and Applications 3 Mathematical Control and Related Fields 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Information Sciences 2 Numerical Algorithms 2 Computational Optimization and Applications 2 Advances in Computational Mathematics 2 Differential Equations and Dynamical Systems 2 Vietnam Journal of Mathematics 2 Chaos 2 Mathematical and Computer Modelling of Dynamical Systems 2 Optimization and Engineering 2 SIAM Journal on Applied Dynamical Systems 2 Advances in Difference Equations 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Asian Journal of Control 2 Journal of Theoretical Biology 1 Journal of Mathematical Biology 1 Mathematical Biosciences 1 Ukrainian Mathematical Journal 1 Chaos, Solitons and Fractals 1 Journal of Theoretical and Applied Mechanics (Sofia) 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 Physica D 1 Queueing Systems 1 Journal of Scientific Computing 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 Applied Mathematical Modelling 1 Automation and Remote Control 1 European Journal of Operational Research 1 SIAM Review 1 Journal of Mathematical Imaging and Vision 1 NoDEA. Nonlinear Differential Equations and Applications 1 Sbornik: Mathematics 1 Computing and Visualization in Science 1 Positivity 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Natural Resource Modeling 1 LMS Journal of Computation and Mathematics 1 Macroeconomic Dynamics 1 Computational Geosciences 1 Engineering Computations 1 CEJOR. Central European Journal of Operations Research 1 Differential Equations ...and 24 more Serials
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#### Cited in 33 Fields

 355 Systems theory; control (93-XX) 122 Calculus of variations and optimal control; optimization (49-XX) 74 Numerical analysis (65-XX) 66 Ordinary differential equations (34-XX) 57 Operations research, mathematical programming (90-XX) 50 Dynamical systems and ergodic theory (37-XX) 46 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Partial differential equations (35-XX) 30 Probability theory and stochastic processes (60-XX) 19 Biology and other natural sciences (92-XX) 13 Difference and functional equations (39-XX) 7 Fluid mechanics (76-XX) 7 Information and communication theory, circuits (94-XX) 4 Statistics (62-XX) 4 Computer science (68-XX) 4 Mechanics of particles and systems (70-XX) 3 General and overarching topics; collections (00-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 Linear and multilinear algebra; matrix theory (15-XX) 2 General topology (54-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Differential geometry (53-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)