Edit Profile (opens in new tab) Grüne, Lars Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1220.93001Grüne, Lars; Pannek, Jürgen 79 2011 Economic receding horizon control without terminal constraints. Zbl 1267.93052Grüne, Lars 52 2013 Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003Grüne, Lars; Pannek, Jürgen 46 2017 The dynamics of control. With an appendix by Lars Grüne. Zbl 1020.93500Colonius, Fritz; Kliemann, Wolfgang 44 2000 Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045Grüne, Lars 40 2009 Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001Grüne, Lars 39 2002 An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl 39 2014 Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064Nešić, Dragan; Grüne, Lars 35 2005 On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109Grüne, Lars; Rantzer, Anders 35 2008 An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Zbl 0880.65045Grüne, Lars 34 1997 Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077Grüne, Lars 29 2000 Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026Grüne, Lars; Semmler, Willi 29 2004 Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl 28 2010 A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061Camilli, Fabio; Grüne, Lars; Wirth, Fabian 27 2001 Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053Grüne, Lars; Nesić, Dragan 26 2003 Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567Grüne, Lars 25 2002 On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117Grüne, Lars; Müller, Matthias A. 25 2016 Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr 20 2012 Pathwise approximation of random ordinary differential equations. Zbl 0998.65010Grüne, L.; Kloeden, P. E. 19 2001 Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075Grüne, L.; Kloeden, P. E. 18 2001 On the relation between discounted and average optimal value functions. Zbl 0918.49002Grüne, Lars 17 1998 Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068Boccia, Andrea; Grüne, Lars; Worthmann, Karl 17 2014 Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044Grüne, Lars; Schaller, Manuel; Schiela, Anton 15 2020 Asymptotic stability equals exponential stability, and ISS equals finite energy gain – if you twist your eyes. Zbl 1043.93549Grüne, Lars; Sontag, Eduardo D.; Wirth, Fabian R. 14 1999 Asymptotic controllability and exponential stabilization of nonlinear control systems at singular points. Zbl 0910.93063Grüne, Lars 14 1998 Periodic optimal control, dissipativity and MPC. Zbl 1369.93356Zanon, Mario; Grüne, Lars; Diehl, Moritz 14 2017 Control Lyapunov functions and Zubov’s method. Zbl 1157.93028Camilli, Fabio; Grüne, Lars; Wirth, Fabian 12 2008 Global optimal control of perturbed systems. Zbl 1147.49019Grüne, L.; Junge, O. 12 2008 Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027Grüne, Lars; Guglielmi, Roberto 12 2018 Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. Zbl 1420.49025Grüne, Lars; Schaller, Manuel; Schiela, Anton 12 2019 Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051Müller, Matthias A.; Grüne, Lars 11 2016 Asset pricing with loss aversion. Zbl 1181.91072Grüne, Lars; Semmler, Willi 10 2008 A receding horizon control approach to sampled-data implementation of continuous-time controllers. Zbl 1100.93042Nešić, Dragan; Grüne, Lars 10 2006 ISS-Lyapunov functions for discontinuous discrete-time systems. Zbl 1360.93497Grüne, Lars; Kellett, Christopher M. 10 2014 Value iteration convergence of \(\varepsilon\)-monotone schemes for stationary Hamilton-Jacobi equations. Zbl 1334.65180Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Grüne, Lars; Kalise, Dante; Zidani, Hasnaa 10 2015 Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. Zbl 0988.65077Camilli, Fabio; Grüne, Lars 9 2000 Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081Grüne, Lars 9 2003 Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094Grüne, Lars; Semmler, Willi; Stieler, Marleen 9 2015 A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103Grüne, Lars; Worthmann, Karl 9 2012 Stabilization with discounted optimal control. Zbl 1327.93324Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil 9 2015 A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048Camilli, Fabio; Grüne, Lars; Wirth, Fabian 9 2001 Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350Grüne, Lars; Worthmann, Karl; Nešić, Dragan 9 2008 Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R. 8 2007 Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085Karafyllis, Iasson; Grüne, Lars 8 2011 Numerical stabilization of bilinear control systems. Zbl 0876.93032Grüne, Lars 8 1996 A set oriented approach to optimal feedback stabilization. Zbl 1129.93500Grüne, Lars; Junge, Oliver 8 2005 Approximation properties of receding horizon optimal control. Zbl 1336.93060Grüne, Lars 8 2016 The role of sampling for stability and performance in unconstrained nonlinear model predictive control. Zbl 1292.93061Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank 8 2014 A uniform exponential spectrum for linear flows on vector bundles. Zbl 0983.37032Grüne, Lars 7 2000 Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311Camilli, Fabio; Grüne, Lars 7 2003 Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009Grüne, Lars 7 2004 Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209Becker, Stephanie; Grüne, Lars; Semmler, Willi 6 2007 Discrete feedback stabilization of semilinear control systems. Zbl 0867.93071Grüne, Lars 6 1996 Higher order numerical approximation of switching systems. Zbl 1100.93022Grüne, L.; Kloeden, P. E. 6 2006 A distributed optimization algorithm for the predictive control of smart grids. Zbl 1359.93270Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl 6 2016 Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033Altmüller, Nils; Grüne, Lars 6 2012 Nonconservative discrete-time ISS small-gain conditions for closed sets. Zbl 1395.93506Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R. 5 2018 Stabilization of strictly dissipative discrete time systems with discounted optimal control. Zbl 1400.93267Gaitsgory, Vladimir; Grüne, Lars; Höger, Matthias; Kellett, Christopher M.; Weller, Steven R. 5 2018 Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen 5 2018 Discretization, inflation and perturbation of attractors. Zbl 0996.37013Grüne, L.; Kloeden, P. E. 5 2001 Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058Grüne, Lars; Wirth, Fabian 5 1999 Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604Grüne, Lars 5 1999 On the relation between turnpike properties for finite and infinite horizon optimal control problems. Zbl 1380.49055Grüne, Lars; Kellett, Christopher M.; Weller, Steven R. 5 2017 Computation of local ISS Lyapunov functions with low gains via linear programming. Zbl 1366.37146Li, Huijuan; Baier, Robert; Grüne, Lars; Hafstein, Sigurdur F.; Wirth, Fabian R. 5 2015 On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073Grüne, L.; Metscher, M.; Ohlberger, M. 4 1999 Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081Grüne, L.; Nešić, D.; Pannek, J. 4 2007 Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013Grüne, L.; Pannek, J. 4 2009 Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian 4 2006 Differential games and Zubov’s method. Zbl 1237.49054Grüne, Lars; Serea, Oana Silvia 4 2011 Economic model predictive control for time-varying system: performance and stability results. Zbl 1451.93095Grüne, Lars; Pirkelmann, Simon 4 2020 Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056Bauer, Florian; Grüne, Lars; Semmler, Willi 3 2006 Maple for stochastic differential equations. Zbl 0991.65006Cyganowski, S.; Grüne, L.; Kloeden, P. E. 3 2001 Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361Grüne, Lars; Semmler, Willi; Sieveking, Malte 3 2005 Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099Grüne, Lars; Palma, Vryan Gil 3 2015 Model predictive control, cost controllability, and homogeneity. Zbl 1453.93083Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl 3 2020 On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Zbl 1462.49058Grüne, Lars; Guglielmi, Roberto 3 2021 Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036 2 2002 Asset pricing with dynamic programming. Zbl 1161.91447Grüne, Lars; Semmler, Willi 2 2007 Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088Grüne, Lars 2 2001 Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068Grüne, Lars 2 2008 On approximating contractive systems. Zbl 1390.93186Botner, Meir; Zarai, Yoram; Margaliot, Michael; Grüne, Lars 2 2017 Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051Grüne, Lars 2 1999 Simultaneously long short trading in discrete and continuous time. Zbl 1353.93116Baumann, Michael Heinrich; Grüne, Lars 2 2017 Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080Grüne, Lars; Zidani, Hasnaa 2 2015 Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019Grüne, Lars; Picarelli, Athena 2 2015 Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328Li, Huijuan; Grüne, Lars 2 2016 Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. Zbl 1467.49037Grüne, Lars; Schaller, Manuel; Schiela, Anton 2 2021 Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan 2 2021 On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002Grüne, Lars; Wirth, Fabian 1 2000 An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044Grüne, Lars; Saint-Pierre, Patrick 1 2006 Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M. 1 2018 A double-sided dynamic programming approach to the minimum time problem and its numerical approximation. Zbl 1372.65193Grüne, Lars; Le, Thuy T. T. 1 2017 \(L^2\)-tracking of Gaussian distributions via model predictive control for the Fokker-Planck equation. Zbl 1406.35411Fleig, Arthur; Grüne, Lars 1 2018 On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Zbl 1462.49058Grüne, Lars; Guglielmi, Roberto 3 2021 Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. Zbl 1467.49037Grüne, Lars; Schaller, Manuel; Schiela, Anton 2 2021 Performance estimates for economic model predictive control and their application in proper orthogonal decomposition-based implementations. Zbl 1471.93084Grüne, Lars; Mechelli, Luca; Pirkelmann, Simon; Volkwein, Stefan 2 2021 Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. Zbl 1436.49044Grüne, Lars; Schaller, Manuel; Schiela, Anton 15 2020 Economic model predictive control for time-varying system: performance and stability results. Zbl 1451.93095Grüne, Lars; Pirkelmann, Simon 4 2020 Model predictive control, cost controllability, and homogeneity. Zbl 1453.93083Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl 3 2020 Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. Zbl 1420.49025Grüne, Lars; Schaller, Manuel; Schiela, Anton 12 2019 Turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems. Zbl 1387.49027Grüne, Lars; Guglielmi, Roberto 12 2018 Nonconservative discrete-time ISS small-gain conditions for closed sets. Zbl 1395.93506Noroozi, Navid; Geiselhart, Roman; Grüne, Lars; Rüffer, Björn S.; Wirth, Fabian R. 5 2018 Stabilization of strictly dissipative discrete time systems with discounted optimal control. Zbl 1400.93267Gaitsgory, Vladimir; Grüne, Lars; Höger, Matthias; Kellett, Christopher M.; Weller, Steven R. 5 2018 Strict dissipativity implies turnpike behavior for time-varying discrete time optimal control problems. Zbl 1401.49035Grüne, Lars; Pirkelmann, Simon; Stieler, Marleen 5 2018 Numerical construction of nonsmooth control Lyapunov functions. Zbl 1414.93168Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M. 1 2018 \(L^2\)-tracking of Gaussian distributions via model predictive control for the Fokker-Planck equation. Zbl 1406.35411Fleig, Arthur; Grüne, Lars 1 2018 Nonlinear model predictive control. Theory and algorithms. 2nd edition. Zbl 1429.93003Grüne, Lars; Pannek, Jürgen 46 2017 Periodic optimal control, dissipativity and MPC. Zbl 1369.93356Zanon, Mario; Grüne, Lars; Diehl, Moritz 14 2017 On the relation between turnpike properties for finite and infinite horizon optimal control problems. Zbl 1380.49055Grüne, Lars; Kellett, Christopher M.; Weller, Steven R. 5 2017 On approximating contractive systems. Zbl 1390.93186Botner, Meir; Zarai, Yoram; Margaliot, Michael; Grüne, Lars 2 2017 Simultaneously long short trading in discrete and continuous time. Zbl 1353.93116Baumann, Michael Heinrich; Grüne, Lars 2 2017 A double-sided dynamic programming approach to the minimum time problem and its numerical approximation. Zbl 1372.65193Grüne, Lars; Le, Thuy T. T. 1 2017 On the relation between strict dissipativity and turnpike properties. Zbl 1335.93117Grüne, Lars; Müller, Matthias A. 25 2016 Economic model predictive control without terminal constraints for optimal periodic behavior. Zbl 1339.93051Müller, Matthias A.; Grüne, Lars 11 2016 Approximation properties of receding horizon optimal control. Zbl 1336.93060Grüne, Lars 8 2016 A distributed optimization algorithm for the predictive control of smart grids. Zbl 1359.93270Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl 6 2016 Computation of local ISS Lyapunov functions for discrete-time systems via linear programming. Zbl 1332.93328Li, Huijuan; Grüne, Lars 2 2016 Value iteration convergence of \(\varepsilon\)-monotone schemes for stationary Hamilton-Jacobi equations. Zbl 1334.65180Bokanowski, Olivier; Falcone, Maurizio; Ferretti, Roberto; Grüne, Lars; Kalise, Dante; Zidani, Hasnaa 10 2015 Using nonlinear model predictive control for dynamic decision problems in economics. Zbl 1401.93094Grüne, Lars; Semmler, Willi; Stieler, Marleen 9 2015 Stabilization with discounted optimal control. Zbl 1327.93324Gaitsgory, Vladimir; Grüne, Lars; Thatcher, Neil 9 2015 Computation of local ISS Lyapunov functions with low gains via linear programming. Zbl 1366.37146Li, Huijuan; Baier, Robert; Grüne, Lars; Hafstein, Sigurdur F.; Wirth, Fabian R. 5 2015 Robustness of performance and stability for multistep and updated multistep MPC schemes. Zbl 1334.49099Grüne, Lars; Palma, Vryan Gil 3 2015 Zubov’s equation for state-constrained perturbed nonlinear systems. Zbl 1322.93080Grüne, Lars; Zidani, Hasnaa 2 2015 Zubov’s method for controlled diffusions with state constraints. Zbl 1323.93019Grüne, Lars; Picarelli, Athena 2 2015 An exponential turnpike theorem for dissipative discrete time optimal control problems. Zbl 1303.49013Damm, Tobias; Grüne, Lars; Stieler, Marleen; Worthmann, Karl 39 2014 Stability and feasibility of state constrained MPC without stabilizing terminal constraints. Zbl 1297.93068Boccia, Andrea; Grüne, Lars; Worthmann, Karl 17 2014 ISS-Lyapunov functions for discontinuous discrete-time systems. Zbl 1360.93497Grüne, Lars; Kellett, Christopher M. 10 2014 The role of sampling for stability and performance in unconstrained nonlinear model predictive control. Zbl 1292.93061Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank 8 2014 Economic receding horizon control without terminal constraints. Zbl 1267.93052Grüne, Lars 52 2013 Linear programming based Lyapunov function computation for differential inclusions. Zbl 1235.93222Baier, Robert; Grüne, Lars; Hafstein, Sigurður Freyr 20 2012 A distributed NMPC scheme without stabilizing terminal constraints. Zbl 1328.93103Grüne, Lars; Worthmann, Karl 9 2012 Distributed and boundary model predictive control for the heat equation. Zbl 1256.49033Altmüller, Nils; Grüne, Lars 6 2012 Nonlinear model predictive control. Theory and algorithms. Zbl 1220.93001Grüne, Lars; Pannek, Jürgen 79 2011 Feedback stabilization methods for the numerical solution of ordinary differential equations. Zbl 1237.65085Karafyllis, Iasson; Grüne, Lars 8 2011 Differential games and Zubov’s method. Zbl 1237.49054Grüne, Lars; Serea, Oana Silvia 4 2011 Analysis of unconstrained nonlinear MPC schemes with time varying control horizon. Zbl 1208.49046Grüne, Lars; Pannek, Jürgen; Seehafer, Martin; Worthmann, Karl 28 2010 Analysis and design of unconstrained nonlinear MPC schemes for finite and infinite dimensional systems. Zbl 1194.49045Grüne, Lars 40 2009 Practical NMPC suboptimality estimates along trajectories. Zbl 1159.93013Grüne, L.; Pannek, J. 4 2009 On the infinite horizon performance of receding horizon controllers. Zbl 1367.90109Grüne, Lars; Rantzer, Anders 35 2008 Control Lyapunov functions and Zubov’s method. Zbl 1157.93028Camilli, Fabio; Grüne, Lars; Wirth, Fabian 12 2008 Global optimal control of perturbed systems. Zbl 1147.49019Grüne, L.; Junge, O. 12 2008 Asset pricing with loss aversion. Zbl 1181.91072Grüne, Lars; Semmler, Willi 10 2008 Continuous-time controller redesign for digital implementation: a trajectory based approach. Zbl 1138.93350Grüne, Lars; Worthmann, Karl; Nešić, Dragan 9 2008 Input-to-state stability, numerical dynamics and sampled-data control. Zbl 1196.93068Grüne, Lars 2 2008 Lyapunov’s second method for nonautonomous differential equations. Zbl 1128.37010Grüne, Lars; Kloeden, Peter E.; Siegmund, Stefan; Wirth, Fabian R. 8 2007 Comparing accuracy of second-order approximation and dynamic programming. Zbl 1282.91209Becker, Stephanie; Grüne, Lars; Semmler, Willi 6 2007 Model predictive control for nonlinear sampled-data systems. Zbl 1223.93081Grüne, L.; Nešić, D.; Pannek, J. 4 2007 Asset pricing with dynamic programming. Zbl 1161.91447Grüne, Lars; Semmler, Willi 2 2007 A receding horizon control approach to sampled-data implementation of continuous-time controllers. Zbl 1100.93042Nešić, Dragan; Grüne, Lars 10 2006 Higher order numerical approximation of switching systems. Zbl 1100.93022Grüne, L.; Kloeden, P. E. 6 2006 Stabilization of controlled diffusions and Zubov’s method. Zbl 1135.93033Camilli, Fabio; Cesaroni, Annalisa; Grüne, Lars; Wirth, Fabian 4 2006 Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations. Zbl 1100.65056Bauer, Florian; Grüne, Lars; Semmler, Willi 3 2006 An invariance kernel representation of ISDS Lyapunov functions. Zbl 1100.93044Grüne, Lars; Saint-Pierre, Patrick 1 2006 Lyapunov-based continuous-time nonlinear controller redesign for sampled-data implementation. Zbl 1115.93064Nešić, Dragan; Grüne, Lars 35 2005 A set oriented approach to optimal feedback stabilization. Zbl 1129.93500Grüne, Lars; Junge, Oliver 8 2005 Creditworthiness and thresholds in a credit market model with multiple equilibria. Zbl 1107.91361Grüne, Lars; Semmler, Willi; Sieveking, Malte 3 2005 Using dynamic programming with adaptive grid scheme for optimal control problems in economics. Zbl 1202.49026Grüne, Lars; Semmler, Willi 29 2004 Error estimation and adaptive discretization for the discrete stochastic Hamilton-Jacobi-Bellman equation. Zbl 1074.65009Grüne, Lars 7 2004 Optimization-based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. Zbl 1044.93053Grüne, Lars; Nesić, Dragan 26 2003 Attraction rates, robustness, and discretization of attractors. Zbl 1058.65081Grüne, Lars 9 2003 Characterizing attraction probabilities via the stochastic Zubov equation. Zbl 1123.60311Camilli, Fabio; Grüne, Lars 7 2003 Asymptotic behavior of dynamical and control systems under perturbation and discretization. Zbl 0991.37001Grüne, Lars 39 2002 Input-to-state dynamical stability and its Lyapunov function characterization. Zbl 1364.93567Grüne, Lars 25 2002 Dynamics, bifurcations, and control. 3rd nonlinear control workshop, Kloster Irsee, Germany, April 1–3, 2001. Zbl 0994.00036 2 2002 A generalization of Zubov’s method to perturbed systems. Zbl 1006.93061Camilli, Fabio; Grüne, Lars; Wirth, Fabian 27 2001 Pathwise approximation of random ordinary differential equations. Zbl 0998.65010Grüne, L.; Kloeden, P. E. 19 2001 Higher order numerical schemes for affinely controlled nonlinear systems. Zbl 0992.65075Grüne, L.; Kloeden, P. E. 18 2001 A regularization of Zubov’s equation for robust domains of attraction. Zbl 1239.93048Camilli, Fabio; Grüne, Lars; Wirth, Fabian 9 2001 Discretization, inflation and perturbation of attractors. Zbl 0996.37013Grüne, L.; Kloeden, P. E. 5 2001 Maple for stochastic differential equations. Zbl 0991.65006Cyganowski, S.; Grüne, L.; Kloeden, P. E. 3 2001 Adaptive grid generation for evolutive Hamilton-Jacobi-Bellman equations. Zbl 0988.65088Grüne, Lars 2 2001 The dynamics of control. With an appendix by Lars Grüne. Zbl 1020.93500Colonius, Fritz; Kliemann, Wolfgang 44 2000 Homogeneous state feedback stabilization of homogeneous systems. Zbl 0958.93077Grüne, Lars 29 2000 Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. Zbl 0988.65077Camilli, Fabio; Grüne, Lars 9 2000 A uniform exponential spectrum for linear flows on vector bundles. Zbl 0983.37032Grüne, Lars 7 2000 On the rate of convergence of infinite horizon discounted optimal value functions. Zbl 0974.49002Grüne, Lars; Wirth, Fabian 1 2000 Asymptotic stability equals exponential stability, and ISS equals finite energy gain – if you twist your eyes. Zbl 1043.93549Grüne, Lars; Sontag, Eduardo D.; Wirth, Fabian R. 14 1999 Feedback stabilization of discrete-time homogeneous semi-linear systems. Zbl 0917.93058Grüne, Lars; Wirth, Fabian 5 1999 Stabilization by sampled and discrete feedback with positive sampling rate. Zbl 0945.93604Grüne, Lars 5 1999 On numerical algorithm and interactive visualization for optimal control problems. Zbl 0970.65073Grüne, L.; Metscher, M.; Ohlberger, M. 4 1999 Input-to-state stability of exponentially stabilized semilinear control systems with inhomogeneous perturbations. Zbl 0948.93051Grüne, Lars 2 1999 On the relation between discounted and average optimal value functions. Zbl 0918.49002Grüne, Lars 17 1998 Asymptotic controllability and exponential stabilization of nonlinear control systems at singular points. Zbl 0910.93063Grüne, Lars 14 1998 An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation. Zbl 0880.65045Grüne, Lars 34 1997 Numerical stabilization of bilinear control systems. Zbl 0876.93032Grüne, Lars 8 1996 Discrete feedback stabilization of semilinear control systems. Zbl 0867.93071Grüne, Lars 6 1996 all cited Publications top 5 cited Publications all top 5 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 all top 5 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 all top 5 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) Citations by Year