Edit Profile (opens in new tab) Schättler, Heinz Michael Co-Author Distance Author ID: schattler.heinz-m Published as: Schättler, Heinz; Schättler, H.; Schaettler, Heinz; Schaettler, H.; Schaettler, Heinz M.; Schättler, Heinz M. more...less External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr Documents Indexed: 121 Publications since 1987, including 2 Books and 1 Additional arXiv Preprint 4 Contributions as Editor Biographic References: 1 Publication Co-Authors: 58 Co-Authors with 113 Joint Publications 973 Co-Co-Authors all top 5 Co-Authors 12 single-authored 84 Ledzewicz, Urszula 6 Maurer, Helmut 5 Venkatasubramanian, Vaithianathan 5 Zaborszky, John 4 Leszczynski, Maciej 4 Wang, Shuo 3 d’Onofrio, Alberto 3 Kashdan, Eugene 3 Kiefer, Matthew 3 Naghnaeian, Mohammad 3 Noble, John M. 3 Ratajczyk, Elzbieta 3 Walczak, Stanislaw 2 Amini, Behrooz 2 Ching, Shinung 2 Friedman, Avner 2 Katz, I. Norman 2 Li, Jr-Shin 2 Mukai, Hiro 2 Munden, James 2 Nandi, Anirban 2 Nowakowski, Andrzej 2 Rinaldi, Paolo 2 Stefanatos, Dionisis 2 Sung, Jaeyoung 1 André, Nicolas 1 Banasiak, Jacek 1 Bhan, Sankalp 1 Bratton, Kenneth 1 Brown, Tim W. C. 1 Cardwell, Benjamin 1 de Pinho, Maria do Rosário 1 Dehkordi, Siamak Mahmoudian 1 Duncan, Dominique 1 Ferreira, Maria Margarida Amorim 1 Gahrooi, Mostafa Reisi 1 Heng, Marie Amélie 1 Hyslop, Gregory L. 1 Jankovic, Miroslava 1 Krener, Arthur James 1 Lungu, Edward M. 1 Marriott, John M. 1 Mosalman, Mozhdeh Sadat Faraji 1 Olumoye, Omeiza 1 Özcan, Alpay 1 Ozcan, İ. A. 1 Parnell, Andrew C. 1 Pasquier, Eddy 1 Ritt, Jason T. 1 Sawada, Yuichi 1 Sochen, Nir 1 Sussmann, Hector J. 1 Świerniak, Andrzej P. 1 Tanikawa, Akio 1 Tarn, Tzyh-Jong 1 Tunay, İlker 1 Yang, L. 1 Zhang, M. all top 5 Serials 12 Discrete and Continuous Dynamical Systems. Series B 12 Mathematical Biosciences and Engineering 10 SIAM Journal on Control and Optimization 9 Journal of Optimization Theory and Applications 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Discrete and Continuous Dynamical Systems 4 IEEE Transactions on Automatic Control 4 Nonlinear Analysis. Theory, Methods & Applications 2 Journal of Mathematical Biology 2 Mathematical Biosciences 2 Applicationes Mathematicae 2 Journal of Biological Systems 2 International Journal of Pure and Applied Mathematics 2 Interdisciplinary Applied Mathematics 2 Mathematical Modelling of Natural Phenomena 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Control and Cybernetics 1 Illinois Journal of Mathematics 1 Journal of Economic Theory 1 Acta Applicandae Mathematicae 1 Journal of Economic Dynamics & Control 1 MCSS. Mathematics of Control, Signals, and Systems 1 Forum Mathematicum 1 Bulletin of the American Mathematical Society. New Series 1 Computational Optimization and Applications 1 Opuscula Mathematica 1 Revista Investigación Operacional 1 Nonlinear Studies 1 Optimization Methods & Software 1 Communications in Nonlinear Science and Numerical Simulation 1 International Journal of Applied Mathematics and Computer Science 1 Journal of Dynamical and Control Systems 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Mathematical Medicine and Biology 1 Networks and Heterogeneous Media 1 Set-Valued and Variational Analysis 1 The Journal of Mathematical Neuroscience 1 Numerical Algebra, Control and Optimization 1 Journal of Theoretical Biology 1 IEEE Transactions on Circuits and Systems I: Regular Papers 1 Lecture Notes on Mathematical Modelling in the Life Sciences all top 5 Fields 104 Calculus of variations and optimal control; optimization (49-XX) 62 Biology and other natural sciences (92-XX) 46 Systems theory; control (93-XX) 7 Ordinary differential equations (34-XX) 5 Partial differential equations (35-XX) 4 General and overarching topics; collections (00-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Operator theory (47-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 1 Nonassociative rings and algebras (17-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-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 98 Publications have been cited 1,153 times in 641 Documents Cited by ▼ Year ▼ Geometric optimal control. Theory, methods and examples. Zbl 1276.49002 Schättler, Heinz; Ledzewicz, Urszula 78 2012 Optimal control for mathematical models of cancer therapies. An application of geometric methods. Zbl 1331.92008 Schättler, Heinz; Ledzewicz, Urszula 72 2015 Local bifurcations and feasibility regions in differential-algebraic systems. Zbl 0843.34045 Venkatasubramanian, Vaithianathan; Schättler, Heinz; Zaborszky, John 66 1995 Antiangiogenic therapy in cancer treatment as an optimal control problem. Zbl 1357.49086 Ledzewicz, Urszula; Schättler, Heinz 59 2007 On optimal delivery of combination therapy for tumors. Zbl 1176.92033 d’Onofrio, Alberto; Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz 58 2009 Optimal bang-bang controls for a two-compartment model in cancer chemotherapy. Zbl 1035.49020 Ledzewicz, U.; Schättler, H. 57 2002 The first-order approach to the continuous-time principal-agent problem with exponential utility. Zbl 0790.90015 Schättler, Heinz; Sung, Jaeyoung 52 1993 Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments. Zbl 1237.49046 Ledzewicz, U.; Schättler, H. 39 2012 Optimal control for a class of compartmental models in cancer chemotherapy. Zbl 1052.92032 Świerniak, Andrzej; Ledzewicz, Urszula; Schättler, Heinz 36 2003 Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics. Zbl 1284.92042 Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz 33 2012 On optimal singular controls for a general SIR-model with vaccination and treatment. Zbl 1306.49056 Ledzewicz, Urszula; Schättler, Heinz 29 2011 Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy. Zbl 1259.92048 Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz 27 2011 Analysis of a cell-cycle specific model for cancer chemotherapy. Zbl 1099.92035 Ledzewicz, Urszula; Schättler, Heinz 25 2002 The structure of small-time reachable sets in low dimensions. Zbl 0669.49020 Krener, Arthur J.; Schättler, Heinz 23 1989 Drug resistance in cancer chemotherapy as an optimal control problem. Zbl 1088.92040 Ledzewicz, Urszula; Schättler, Heinz 23 2006 High-order approximations and generalized necessary conditions for optimality. Zbl 0941.49016 Ledzewicz, Urszula; Schättler, Heinz 22 1999 Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. Zbl 1398.92120 Ledzewicz, Urszula; Schättler, Heinz 19 2008 Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy. Zbl 1114.92042 Ledzewicz, Urszula; Schättler, Heinz 17 2007 Sufficient conditions for relative minima of broken extremals in optimal control theory. Zbl 1012.49023 Noble, John; Schättler, Heinz 16 2002 Second-order conditions for extremum problems with nonregular equality constraints. Zbl 0835.49016 Ledzewicz, U.; Schaettler, H. 15 1995 On optimal sharing rules in discrete- and continuous-time principal-agent problems with exponential utility. Zbl 0879.90045 Schättler, Heinz; Sung, Jaeyoung 15 1997 Sufficient conditions for strong local optimality in optimal control problems with \(L_{2}\)-type objectives and control constraints. Zbl 1304.49043 Schättler, Heinz; Ledzewicz, Urszula; Maurer, Helmut 14 2014 Optimal control systems governed by second-order ODEs with Dirichlet boundary data and variable parameters. Zbl 1031.49002 Ledzewicz, Urszula; Schättler, Heinz; Walczak, Stanislaw 13 2003 On the MTD paradigm and optimal control for multi-drug cancer chemotherapy. Zbl 1268.92065 Ledzewicz, Urszula; Schättler, Heinz; Gahrooi, Mostafa Reisi; Dehkordi, Siamak Mahmoudian 13 2013 A review of optimal chemotherapy protocols: from MTD towards metronomic therapy. Zbl 1321.92057 Ledzewicz, U.; Schättler, H. 12 2014 Optimal controls for a mathematical model of tumor-immune interactions under targeted chemotherapy with immune boost. Zbl 1275.49036 Ledzewicz, Urszula; Mosalman, Mozhdeh Sadat Faraji; Schättler, Heinz 12 2013 Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment. Zbl 1190.92015 Ledzewicz, Urszula; Marriott, John; Maurer, Helmut; Schättler, Heinz 12 2010 The influence of PK/PD on the structure of optimal controls in cancer chemotherapy models. Zbl 1079.92041 Ledzewicz, Urszula; Schättler, Heinz 11 2005 The local structure of time-optimal trajectories in dimension three under generic conditions. Zbl 0656.49007 Schättler, Heinz 10 1988 Singular controls and chattering arcs in optimal control problems arising in biomedicine. Zbl 1236.49054 Ledzewicz, U.; Schaettler, H. 10 2009 Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Zbl 1170.49003 Ledzewicz, Urszula; Munden, James; Schättler, Heinz 10 2009 Local fields of extremals for optimal control problems with state constraints of relative degree 1. Zbl 1123.49031 Schättler, H. 10 2006 On optimal chemotherapy for heterogeneous tumors. Zbl 1343.92232 Ledzewicz, Urszula; Schättler, Heinz 10 2014 On the local structure of time-optimal bang-bang trajectories in \({\mathbb{R}}^ 3\). Zbl 0644.49020 Schättler, Heinz 9 1988 A model for cancer chemotherapy with state-space constraints. Zbl 1222.92050 de Pinho, Maria do Rosario; Ferreira, Maria Margarida; Ledzewicz, Urszula; Schaettler, Heinz 9 2005 Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load. Zbl 0800.94316 Venkatasubramanian, V.; Schättler, H.; Zaborszky, J. 9 1992 A high-order generalization of the Lyusternik theorem. Zbl 0954.49014 Ledzewicz, Urszula; Schättler, Heinz 8 1998 Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Zbl 1350.49058 Wang, Shuo; Schättler, Heinz 8 2016 Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1259.92053 Schättler, Heinz; Ledzewicz, Urszula; Cardwell, Benjamin 8 2011 Regularity properties of optimal trajectories: Recently developed techniques. Zbl 0702.49033 Schättler, Heinz 7 1990 Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy. Zbl 1337.92117 Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz 7 2016 An optimal control approach to cancer treatment under immunological activity. Zbl 1215.49030 Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz 6 2011 Parametrized families of extremals and singularities in solutions to the Hamilton-Jacobi-Bellman equation. Zbl 0939.49018 Kiefer, Matthew; Schättler, Heinz 6 1999 Optimal control for a mathematical model of glioma treatment with oncolytic therapy and TNF-\(\alpha \) inhibitors. Zbl 1390.49019 Ratajczyk, Elzbieta; Ledzewicz, Urszula; Schättler, Heinz 6 2018 Comparison of optimal controls for a model in cancer chemotherapy with \(L_1\)- and \(L_2\)-type objectives. Zbl 1056.92033 Ledzewicz, Urszula; Brown, Tim; Schättler, Heinz 6 2004 Controlling a model for bone marrow dynamics in cancer chemotherapy. Zbl 1135.92309 Ledzewicz, Urszula; Schättler, Heinz 6 2004 A 3-compartment model for chemotherapy of heterogeneous tumor populations. Zbl 1326.92039 Ledzewicz, Urszula; Bratton, Kenneth; Schättler, Heinz 6 2015 Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics. Zbl 1367.49015 Leszczyński, Maciej; Ratajczyk, Elżbieta; Ledzewicz, Urszula; Schättler, Heinz 6 2017 On the dynamics of tumor-immune system interactions and combined chemo- and immunotherapy. Zbl 1316.92020 D’Onofrio, Alberto; Ledzewicz, Urszula; Schättler, Heinz 6 2012 Optimal combined radio- and anti-angiogenic cancer therapy. Zbl 1409.49036 Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz 6 2019 On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1161.49037 Ledzewicz, Urszula; Schättler, Heinz 5 2009 Dynamics and control of a mathematical model for metronomic chemotherapy. Zbl 1326.92038 Ledzewicz, Urszula; Amini, Behrooz; Schättler, Heinz 5 2015 On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth. Zbl 1268.92064 Ledzewicz, Urszula; Olumoye, Omeiza; Schättler, Heinz 5 2013 Optimal control for a mathematical model for chemotherapy with pharmacometrics. Zbl 1467.92094 Leszczyński, Maciej; Ledzewicz, Urszula; Schättler, Heinz 5 2020 Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Zbl 1418.92058 Leszczyński, Maciej; Ledzewicz, Urszula; Schättler, Heinz 5 2019 A synthesis of time-optimal controls in the presence of saturated singular arcs. Zbl 0780.49017 Schättler, Heinz; Jankovic, Miroslava 4 1993 A high-order generalized local maximum principle. Zbl 0954.49015 Ledzewicz, Urszula; Schättler, Heinz 4 2000 Mathematical methods and models in biomedicine. Zbl 1254.92046 4 2013 On the role of the objective in the optimization of compartmental models for biomedical therapies. Zbl 1462.49078 Ledzewicz, Urszula; Schättler, Heinz 4 2020 On the role of pharmacometrics in mathematical models for cancer treatments. Zbl 1466.92077 Ledzewicz, Urszula; Schättler, Heinz 4 2021 On the regularity of optimal controls. Zbl 0636.49009 Schättler, Heinz M.; Sussmann, Héctor J. 3 1987 Fast time-varying phasor analysis in the balanced three-phase large electric power system. Zbl 0850.93067 Venkatasubramanian, Vaithianathan; Schättler, Heinz; Zaborszky, John 3 1995 Minimum-time frictionless atom cooling in harmonic traps. Zbl 1237.49050 Stefanatos, Dionisis; Schaettler, Heinz; Li, Jr-Shin 3 2011 Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment. Zbl 1173.49004 Ledzewicz, Urszula; Oussa, Vignon; Schättler, Heinz 3 2009 On the time-optimality of bang-bang trajectories in \(R^ 3\). Zbl 0608.49016 Schaettler, Heinz M. 3 1987 Stability regions for differential-algebraic systems. Zbl 0781.93072 Venkatasubramanian, V.; Schättler, H.; Zaborszky, J. 3 1992 Small-time reachable sets and time-optimal feedback control. Zbl 0863.93005 Schättler, Heinz 3 1996 On drug resistance and metronomic chemotherapy: a mathematical modeling and optimal control approach. Zbl 1351.49049 Ledzewicz, Urszula; Wang, Shuo; Schättler, Heinz; André, Nicolas; Heng, Marie Amélie; Pasquier, Eddy 3 2017 Dynamics of tumor-immune interaction under treatment as an optimal control problem. Zbl 1306.49055 Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz 3 2011 Perturbation feedback control: A geometric interpretation. Zbl 1253.49013 Schättler, Heinz; Ledzewicz, Urszula 3 2012 Lyapunov-Schmidt reduction for optimal control problems. Zbl 1246.49018 Schättler, Heinz; Ledzewicz, Urszula 2 2012 Time-optimal feedback control for nonlinear systems: A geometric approach. Zbl 0925.93137 Schättler, Heinz 2 1998 High-order tangent cones and their application in optimization. Zbl 0909.90241 Ledzewicz, Urszula; Schättler, Heinz 2 1997 On the optimality of parametrized families of bang-bang trajectories. Zbl 1042.49533 Noble, John; Schaettler, Heinz 2 2001 Solution of a differential game formulation of military air operations by the method of characteristics. Zbl 1097.91017 Katz, I. N.; Mukai, H.; Schättler, H.; Zhang, M.; Xu, M. 2 2005 Extremal trajectories, small-time reachable sets and local feedback synthesis: A synopsis of the three-dimensional case. Zbl 0745.49017 Schättler, Heinz 2 1991 Descent algorithms for optimal periodic output feedback control. Zbl 0783.93042 Hyslop, Gregory L.; Schättler, Heinz; Tarn, Tzyh-Jong 2 1992 Pareto optimality conditions for abnormal optimization and optimal control problems. Zbl 0811.49018 Ledzewicz, Urszula; Schaettler, Heinz 2 1994 Treatment of glioma with virotherapy and TNF-\(\alpha\) inhibitors: analysis as a dynamical system. Zbl 1376.92027 Ratajczyk, Elzbieta; Ledzewicz, Urszula; Leszczyński, Maciej; Schättler, Heinz 2 2018 Sequential linear-quadratic method for differential games with air combat applications. Zbl 1048.91016 Mukai, H.; Tanikawa, A.; Tunay, İ.; Ozcan, İ. A.; Katz, I. N.; Schättler, H.; Rinaldi, P.; Wang, G. J.; Yang, L.; Sawada, Y. 2 2003 Tumor development under combination treatments with anti-angiogenic therapies. Zbl 1345.92078 Ledzewicz, Urszula; d’Onofrio, Alberto; Schättler, Heinz 2 2013 Synthesis of optimal controlled trajectories with chattering arcs. Zbl 1270.49035 Schättler, Heinz; Ledzewicz, Urszula 2 2012 Fundamental limits of forced asynchronous spiking with integrate and fire dynamics. Zbl 1397.92118 Nandi, Anirban; Schättler, Heinz; Ritt, Jason T.; Ching, ShiNung 2 2017 Regularity properties of time-optimal trajectories of an analytic single- input control-linear system in dimension three. Zbl 0631.49006 Schättler, H. 1 1988 Stability of elliptic optimal control problems. Zbl 0985.49015 Walczak, S.; Ledzewicz, U.; Schättler, H. 1 2001 Optimal controls for a 3-compartment model for cancer chemotherapy with quadratic objective. Zbl 1062.49032 Ledzewicz, Urszula; Schättler, Heinz 1 2003 Bang-bang controls for anti-angiogenesis under logistic growth of the tumor. Zbl 1165.49004 Ledzewicz, Urszula; Munden, James; Schättler, Heinz 1 2008 Stratifiable families of extremals and sufficient conditions for optimality in optimal control problems. Zbl 1092.49019 Ledzewicz, U.; Nowakowski, A.; Schättler, H. 1 2004 Controlling the bone marrow dynamics in cancer chemotherapy. Zbl 1076.49019 Ledzewicz, Urszula; Schättler, Heinz 1 2004 A local feedback synthesis of time-optimal stabilizing controls in dimension three. Zbl 0762.93026 Schättler, Heinz 1 1991 An extended maximum principle. Zbl 0879.49019 Ledzewicz, Urszula; Schättler, Heinz 1 1997 A theory of first and second order conditions for nonregular extremum problems. Zbl 0811.49019 Ledzewicz, Urszula; Schaettler, Heinz 1 1994 A computational method for the calculation of the feasibility boundary and clustering in differential-algebraic systems. Zbl 1374.93114 Özcan, Alpay; Schättler, Heinz 1 2005 Optimal control of cancer treatments: mathematical models for the tumor microenvironment. Zbl 1329.49078 Schättler, Heinz; Ledzewicz, Urszula 1 2015 On the role of pharmacometrics and the objective in optimizing cancer therapies. Zbl 1478.92083 Ledzewicz, Urszula; Schaettler, Heinz 1 2019 On the role of tumor heterogeneity for optimal cancer chemotherapy. Zbl 1425.92113 Ledzewicz, Urszula; Schättler, Heinz; Wang, Shuo 1 2019 On modeling the synergy of cancer immunotherapy with radiotherapy. Zbl 1507.92043 Ledzewicz, Urszula; Schättler, Heinz 1 2023 A variational approach to perturbation feedback control for optimal control problems with terminal constraints and free terminal time. Zbl 1419.49043 Bhan, Sankalp; Schättler, Heinz 1 2019 On modeling the synergy of cancer immunotherapy with radiotherapy. Zbl 1507.92043 Ledzewicz, Urszula; Schättler, Heinz 1 2023 On the role of pharmacometrics in mathematical models for cancer treatments. Zbl 1466.92077 Ledzewicz, Urszula; Schättler, Heinz 4 2021 Optimal control for a mathematical model for chemotherapy with pharmacometrics. Zbl 1467.92094 Leszczyński, Maciej; Ledzewicz, Urszula; Schättler, Heinz 5 2020 On the role of the objective in the optimization of compartmental models for biomedical therapies. Zbl 1462.49078 Ledzewicz, Urszula; Schättler, Heinz 4 2020 Optimal combined radio- and anti-angiogenic cancer therapy. Zbl 1409.49036 Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz 6 2019 Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Zbl 1418.92058 Leszczyński, Maciej; Ledzewicz, Urszula; Schättler, Heinz 5 2019 On the role of pharmacometrics and the objective in optimizing cancer therapies. Zbl 1478.92083 Ledzewicz, Urszula; Schaettler, Heinz 1 2019 On the role of tumor heterogeneity for optimal cancer chemotherapy. Zbl 1425.92113 Ledzewicz, Urszula; Schättler, Heinz; Wang, Shuo 1 2019 A variational approach to perturbation feedback control for optimal control problems with terminal constraints and free terminal time. Zbl 1419.49043 Bhan, Sankalp; Schättler, Heinz 1 2019 Optimal control for a mathematical model of glioma treatment with oncolytic therapy and TNF-\(\alpha \) inhibitors. Zbl 1390.49019 Ratajczyk, Elzbieta; Ledzewicz, Urszula; Schättler, Heinz 6 2018 Treatment of glioma with virotherapy and TNF-\(\alpha\) inhibitors: analysis as a dynamical system. Zbl 1376.92027 Ratajczyk, Elzbieta; Ledzewicz, Urszula; Leszczyński, Maciej; Schättler, Heinz 2 2018 Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics. Zbl 1367.49015 Leszczyński, Maciej; Ratajczyk, Elżbieta; Ledzewicz, Urszula; Schättler, Heinz 6 2017 On drug resistance and metronomic chemotherapy: a mathematical modeling and optimal control approach. Zbl 1351.49049 Ledzewicz, Urszula; Wang, Shuo; Schättler, Heinz; André, Nicolas; Heng, Marie Amélie; Pasquier, Eddy 3 2017 Fundamental limits of forced asynchronous spiking with integrate and fire dynamics. Zbl 1397.92118 Nandi, Anirban; Schättler, Heinz; Ritt, Jason T.; Ching, ShiNung 2 2017 Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Zbl 1350.49058 Wang, Shuo; Schättler, Heinz 8 2016 Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy. Zbl 1337.92117 Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz 7 2016 Optimal control for mathematical models of cancer therapies. An application of geometric methods. Zbl 1331.92008 Schättler, Heinz; Ledzewicz, Urszula 72 2015 A 3-compartment model for chemotherapy of heterogeneous tumor populations. Zbl 1326.92039 Ledzewicz, Urszula; Bratton, Kenneth; Schättler, Heinz 6 2015 Dynamics and control of a mathematical model for metronomic chemotherapy. Zbl 1326.92038 Ledzewicz, Urszula; Amini, Behrooz; Schättler, Heinz 5 2015 Optimal control of cancer treatments: mathematical models for the tumor microenvironment. Zbl 1329.49078 Schättler, Heinz; Ledzewicz, Urszula 1 2015 Sufficient conditions for strong local optimality in optimal control problems with \(L_{2}\)-type objectives and control constraints. Zbl 1304.49043 Schättler, Heinz; Ledzewicz, Urszula; Maurer, Helmut 14 2014 A review of optimal chemotherapy protocols: from MTD towards metronomic therapy. Zbl 1321.92057 Ledzewicz, U.; Schättler, H. 12 2014 On optimal chemotherapy for heterogeneous tumors. Zbl 1343.92232 Ledzewicz, Urszula; Schättler, Heinz 10 2014 On the MTD paradigm and optimal control for multi-drug cancer chemotherapy. Zbl 1268.92065 Ledzewicz, Urszula; Schättler, Heinz; Gahrooi, Mostafa Reisi; Dehkordi, Siamak Mahmoudian 13 2013 Optimal controls for a mathematical model of tumor-immune interactions under targeted chemotherapy with immune boost. Zbl 1275.49036 Ledzewicz, Urszula; Mosalman, Mozhdeh Sadat Faraji; Schättler, Heinz 12 2013 On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth. Zbl 1268.92064 Ledzewicz, Urszula; Olumoye, Omeiza; Schättler, Heinz 5 2013 Mathematical methods and models in biomedicine. Zbl 1254.92046 4 2013 Tumor development under combination treatments with anti-angiogenic therapies. Zbl 1345.92078 Ledzewicz, Urszula; d’Onofrio, Alberto; Schättler, Heinz 2 2013 Geometric optimal control. Theory, methods and examples. Zbl 1276.49002 Schättler, Heinz; Ledzewicz, Urszula 78 2012 Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments. Zbl 1237.49046 Ledzewicz, U.; Schättler, H. 39 2012 Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics. Zbl 1284.92042 Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz 33 2012 On the dynamics of tumor-immune system interactions and combined chemo- and immunotherapy. Zbl 1316.92020 D’Onofrio, Alberto; Ledzewicz, Urszula; Schättler, Heinz 6 2012 Perturbation feedback control: A geometric interpretation. Zbl 1253.49013 Schättler, Heinz; Ledzewicz, Urszula 3 2012 Lyapunov-Schmidt reduction for optimal control problems. Zbl 1246.49018 Schättler, Heinz; Ledzewicz, Urszula 2 2012 Synthesis of optimal controlled trajectories with chattering arcs. Zbl 1270.49035 Schättler, Heinz; Ledzewicz, Urszula 2 2012 On optimal singular controls for a general SIR-model with vaccination and treatment. Zbl 1306.49056 Ledzewicz, Urszula; Schättler, Heinz 29 2011 Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy. Zbl 1259.92048 Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz 27 2011 Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1259.92053 Schättler, Heinz; Ledzewicz, Urszula; Cardwell, Benjamin 8 2011 An optimal control approach to cancer treatment under immunological activity. Zbl 1215.49030 Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz 6 2011 Minimum-time frictionless atom cooling in harmonic traps. Zbl 1237.49050 Stefanatos, Dionisis; Schaettler, Heinz; Li, Jr-Shin 3 2011 Dynamics of tumor-immune interaction under treatment as an optimal control problem. Zbl 1306.49055 Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz 3 2011 Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment. Zbl 1190.92015 Ledzewicz, Urszula; Marriott, John; Maurer, Helmut; Schättler, Heinz 12 2010 On optimal delivery of combination therapy for tumors. Zbl 1176.92033 d’Onofrio, Alberto; Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz 58 2009 Singular controls and chattering arcs in optimal control problems arising in biomedicine. Zbl 1236.49054 Ledzewicz, U.; Schaettler, H. 10 2009 Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Zbl 1170.49003 Ledzewicz, Urszula; Munden, James; Schättler, Heinz 10 2009 On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1161.49037 Ledzewicz, Urszula; Schättler, Heinz 5 2009 Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment. Zbl 1173.49004 Ledzewicz, Urszula; Oussa, Vignon; Schättler, Heinz 3 2009 Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. Zbl 1398.92120 Ledzewicz, Urszula; Schättler, Heinz 19 2008 Bang-bang controls for anti-angiogenesis under logistic growth of the tumor. Zbl 1165.49004 Ledzewicz, Urszula; Munden, James; Schättler, Heinz 1 2008 Antiangiogenic therapy in cancer treatment as an optimal control problem. Zbl 1357.49086 Ledzewicz, Urszula; Schättler, Heinz 59 2007 Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy. Zbl 1114.92042 Ledzewicz, Urszula; Schättler, Heinz 17 2007 Drug resistance in cancer chemotherapy as an optimal control problem. Zbl 1088.92040 Ledzewicz, Urszula; Schättler, Heinz 23 2006 Local fields of extremals for optimal control problems with state constraints of relative degree 1. Zbl 1123.49031 Schättler, H. 10 2006 The influence of PK/PD on the structure of optimal controls in cancer chemotherapy models. Zbl 1079.92041 Ledzewicz, Urszula; Schättler, Heinz 11 2005 A model for cancer chemotherapy with state-space constraints. Zbl 1222.92050 de Pinho, Maria do Rosario; Ferreira, Maria Margarida; Ledzewicz, Urszula; Schaettler, Heinz 9 2005 Solution of a differential game formulation of military air operations by the method of characteristics. Zbl 1097.91017 Katz, I. N.; Mukai, H.; Schättler, H.; Zhang, M.; Xu, M. 2 2005 A computational method for the calculation of the feasibility boundary and clustering in differential-algebraic systems. Zbl 1374.93114 Özcan, Alpay; Schättler, Heinz 1 2005 Comparison of optimal controls for a model in cancer chemotherapy with \(L_1\)- and \(L_2\)-type objectives. Zbl 1056.92033 Ledzewicz, Urszula; Brown, Tim; Schättler, Heinz 6 2004 Controlling a model for bone marrow dynamics in cancer chemotherapy. Zbl 1135.92309 Ledzewicz, Urszula; Schättler, Heinz 6 2004 Stratifiable families of extremals and sufficient conditions for optimality in optimal control problems. Zbl 1092.49019 Ledzewicz, U.; Nowakowski, A.; Schättler, H. 1 2004 Controlling the bone marrow dynamics in cancer chemotherapy. Zbl 1076.49019 Ledzewicz, Urszula; Schättler, Heinz 1 2004 Optimal control for a class of compartmental models in cancer chemotherapy. Zbl 1052.92032 Świerniak, Andrzej; Ledzewicz, Urszula; Schättler, Heinz 36 2003 Optimal control systems governed by second-order ODEs with Dirichlet boundary data and variable parameters. Zbl 1031.49002 Ledzewicz, Urszula; Schättler, Heinz; Walczak, Stanislaw 13 2003 Sequential linear-quadratic method for differential games with air combat applications. Zbl 1048.91016 Mukai, H.; Tanikawa, A.; Tunay, İ.; Ozcan, İ. A.; Katz, I. N.; Schättler, H.; Rinaldi, P.; Wang, G. J.; Yang, L.; Sawada, Y. 2 2003 Optimal controls for a 3-compartment model for cancer chemotherapy with quadratic objective. Zbl 1062.49032 Ledzewicz, Urszula; Schättler, Heinz 1 2003 Optimal bang-bang controls for a two-compartment model in cancer chemotherapy. Zbl 1035.49020 Ledzewicz, U.; Schättler, H. 57 2002 Analysis of a cell-cycle specific model for cancer chemotherapy. Zbl 1099.92035 Ledzewicz, Urszula; Schättler, Heinz 25 2002 Sufficient conditions for relative minima of broken extremals in optimal control theory. Zbl 1012.49023 Noble, John; Schättler, Heinz 16 2002 On the optimality of parametrized families of bang-bang trajectories. Zbl 1042.49533 Noble, John; Schaettler, Heinz 2 2001 Stability of elliptic optimal control problems. Zbl 0985.49015 Walczak, S.; Ledzewicz, U.; Schättler, H. 1 2001 A high-order generalized local maximum principle. Zbl 0954.49015 Ledzewicz, Urszula; Schättler, Heinz 4 2000 High-order approximations and generalized necessary conditions for optimality. Zbl 0941.49016 Ledzewicz, Urszula; Schättler, Heinz 22 1999 Parametrized families of extremals and singularities in solutions to the Hamilton-Jacobi-Bellman equation. Zbl 0939.49018 Kiefer, Matthew; Schättler, Heinz 6 1999 A high-order generalization of the Lyusternik theorem. Zbl 0954.49014 Ledzewicz, Urszula; Schättler, Heinz 8 1998 Time-optimal feedback control for nonlinear systems: A geometric approach. Zbl 0925.93137 Schättler, Heinz 2 1998 On optimal sharing rules in discrete- and continuous-time principal-agent problems with exponential utility. Zbl 0879.90045 Schättler, Heinz; Sung, Jaeyoung 15 1997 High-order tangent cones and their application in optimization. Zbl 0909.90241 Ledzewicz, Urszula; Schättler, Heinz 2 1997 An extended maximum principle. Zbl 0879.49019 Ledzewicz, Urszula; Schättler, Heinz 1 1997 Small-time reachable sets and time-optimal feedback control. Zbl 0863.93005 Schättler, Heinz 3 1996 Local bifurcations and feasibility regions in differential-algebraic systems. Zbl 0843.34045 Venkatasubramanian, Vaithianathan; Schättler, Heinz; Zaborszky, John 66 1995 Second-order conditions for extremum problems with nonregular equality constraints. Zbl 0835.49016 Ledzewicz, U.; Schaettler, H. 15 1995 Fast time-varying phasor analysis in the balanced three-phase large electric power system. Zbl 0850.93067 Venkatasubramanian, Vaithianathan; Schättler, Heinz; Zaborszky, John 3 1995 Pareto optimality conditions for abnormal optimization and optimal control problems. Zbl 0811.49018 Ledzewicz, Urszula; Schaettler, Heinz 2 1994 A theory of first and second order conditions for nonregular extremum problems. Zbl 0811.49019 Ledzewicz, Urszula; Schaettler, Heinz 1 1994 The first-order approach to the continuous-time principal-agent problem with exponential utility. Zbl 0790.90015 Schättler, Heinz; Sung, Jaeyoung 52 1993 A synthesis of time-optimal controls in the presence of saturated singular arcs. Zbl 0780.49017 Schättler, Heinz; Jankovic, Miroslava 4 1993 Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load. Zbl 0800.94316 Venkatasubramanian, V.; Schättler, H.; Zaborszky, J. 9 1992 Stability regions for differential-algebraic systems. Zbl 0781.93072 Venkatasubramanian, V.; Schättler, H.; Zaborszky, J. 3 1992 Descent algorithms for optimal periodic output feedback control. Zbl 0783.93042 Hyslop, Gregory L.; Schättler, Heinz; Tarn, Tzyh-Jong 2 1992 Extremal trajectories, small-time reachable sets and local feedback synthesis: A synopsis of the three-dimensional case. Zbl 0745.49017 Schättler, Heinz 2 1991 A local feedback synthesis of time-optimal stabilizing controls in dimension three. Zbl 0762.93026 Schättler, Heinz 1 1991 Regularity properties of optimal trajectories: Recently developed techniques. Zbl 0702.49033 Schättler, Heinz 7 1990 The structure of small-time reachable sets in low dimensions. Zbl 0669.49020 Krener, Arthur J.; Schättler, Heinz 23 1989 The local structure of time-optimal trajectories in dimension three under generic conditions. Zbl 0656.49007 Schättler, Heinz 10 1988 On the local structure of time-optimal bang-bang trajectories in \({\mathbb{R}}^ 3\). Zbl 0644.49020 Schättler, Heinz 9 1988 Regularity properties of time-optimal trajectories of an analytic single- input control-linear system in dimension three. Zbl 0631.49006 Schättler, H. 1 1988 On the regularity of optimal controls. Zbl 0636.49009 Schättler, Heinz M.; Sussmann, Héctor J. 3 1987 On the time-optimality of bang-bang trajectories in \(R^ 3\). Zbl 0608.49016 Schaettler, Heinz M. 3 1987 all cited Publications top 5 cited Publications all top 5 Cited by 1,063 Authors 46 Schättler, Heinz Michael 39 Ledzewicz, Urszula 14 Zhang, Qingling 13 Khailov, Evgenii N. 13 Maurer, Helmut 11 Trélat, Emmanuel 10 Galewski, Marek 10 Tret’yakov, Alexey A. 9 Liu, Chao 8 Bonnard, Bernard 8 Bratus, Alexander S. 8 d’Onofrio, Alberto 7 Bayen, Térence 7 Foryś, Urszula 7 Riaza, Ricardo 7 Silva, Cristiana J. 6 Bourdin, Loïc 6 Chakraborty, Kunal 6 Cvitanić, Jakša 6 de Pinho, Maria do Rosário 6 Grigorieva, Ellina V. 6 Kar, Tapan Kumar 6 Meng, Xinyou 6 Sung, Jaeyoung 6 Torres, Delfim Fernando Marado 5 Alamir, Mazen 5 Aronna, María Soledad 5 Grigorenko, Nikolaĭ Leont’evich 5 Liu, Bin 5 Piotrowska, Monika Joanna 5 Possamaï, Dylan 5 Wang, Shuo 5 Yegorov, Ivan V. 5 Zhang, Xue 4 Agrachev, Andreĭ Aleksandrovich 4 Arutyunov, Aram Vladimirovic 4 Bednarczuk, Ewa M. 4 Belmonte-Beitia, Juan 4 Brezhneva, Olga A. 4 Buonomo, Bruno 4 Clairambault, Jean 4 Dai, Feng 4 Deng, Li 4 Felgenhauer, Ursula 4 Jiang, Yaolin 4 Korobeinikov, Andrei 4 Liu, Wei 4 Lykina, Valeriya 4 Mairet, Francis 4 Marszałek, Wiesław 4 Mastrolia, Thibaut 4 Osuna-Gómez, Rafaela 4 Rojas-Medar, Marko Antonio 4 Rouot, Jérémy 4 Shu, Yadong 4 Sigalotti, Mario 4 Wu, Yu-Qian 4 Zhang, Yi 3 Ainseba, Bedr’Eddine 3 Ayala, Victor 3 Băleanu, Dumitru I. 3 Benosman, Chahrazed 3 Biolo, Carolina 3 Boarotto, Francesco 3 Bonnans, Joseph Frédéric 3 Campbell, Stephen LaVern 3 Carrère, Cécile 3 Cerf, Max 3 Chakraborty, Milon 3 Constantin, Elena 3 Cots, Olivier 3 Duan, Xiaodong 3 Eftimie, Raluca 3 Fimmel, Elena 3 Glick, Adam E. 3 Grochowski, Marek 3 Hernández-Jiménez, Beatriz 3 Jana, Soovoojeet 3 Klimenkova, Anna D. 3 Kolobov, Andrey V. 3 Kuznetsov, Maxim B. 3 Lai, Chong 3 Lenhart, Suzanne M. 3 Leszczynski, Maciej 3 Li, Bo 3 Li, Jr-Shin 3 Margaliot, Michael 3 Martalò, Giorgio 3 Mastroberardino, Antonio 3 Moore, Helen 3 Palladino, Michele 3 Papa, Federico 3 Prusińska, Agnieszka 3 Rachik, Mostafa 3 Rampazzo, Franco 3 Ratajczyk, Elzbieta 3 Roy, Sankar Kumar 3 Sebbah, Matthieu 3 Shamsi, Mostafa 3 Sowndarrajan, Puthur Thangaraj ...and 963 more Authors all top 5 Cited in 180 Serials 30 Journal of Optimization Theory and Applications 24 Mathematical Biosciences 22 Mathematical Biosciences and Engineering 20 Applied Mathematics and Computation 18 SIAM Journal on Control and Optimization 17 Discrete and Continuous Dynamical Systems. Series B 17 Journal of Theoretical Biology 16 Bulletin of Mathematical Biology 14 Journal of Mathematical Biology 11 Chaos, Solitons and Fractals 11 Automatica 11 Journal of Economic Theory 11 Mathematical Modelling of Natural Phenomena 9 Journal of Mathematical Analysis and Applications 9 Optimal Control Applications & Methods 9 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 9 Discrete Dynamics in Nature and Society 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Journal of Dynamical and Control Systems 8 International Journal of Biomathematics 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Systems & Control Letters 7 Applied Mathematical Modelling 7 Communications in Nonlinear Science and Numerical Simulation 6 International Journal of Control 6 Journal of the Franklin Institute 6 Mathematical Methods in the Applied Sciences 6 Journal of Differential Equations 6 Journal of Biological Systems 5 Mathematics and Computers in Simulation 5 Acta Applicandae Mathematicae 5 Journal of Global Optimization 5 Journal of Mathematical Sciences (New York) 5 Nonlinear Analysis. Real World Applications 5 Mathematics and Financial Economics 4 Journal of Computational and Applied Mathematics 4 Numerical Functional Analysis and Optimization 4 Optimization 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Computational Optimization and Applications 4 Computational and Applied Mathematics 4 European Journal of Control 4 SIAM Journal on Applied Dynamical Systems 4 Advances in Difference Equations 4 Proceedings of the Steklov Institute of Mathematics 4 Numerical Algebra, Control and Optimization 4 Nonlinear Analysis. Theory, Methods & Applications 3 Physica A 3 Journal of Geometry and Physics 3 Mathematical and Computer Modelling 3 MCSS. Mathematics of Control, Signals, and Systems 3 International Journal of Robust and Nonlinear Control 3 Economic Theory 3 Discrete and Continuous Dynamical Systems 3 Mathematical Finance 3 Abstract and Applied Analysis 3 International Journal of Applied Mathematics and Computer Science 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Computational & Mathematical Methods in Medicine 3 Nonlinear Analysis. Hybrid Systems 3 SIAM Journal on Financial Mathematics 3 Set-Valued and Variational Analysis 3 Mathematical Control and Related Fields 3 AIMS Mathematics 2 Applicable Analysis 2 Computers & Mathematics with Applications 2 International Journal of Systems Science 2 Journal of Mathematical Physics 2 Nonlinearity 2 Applied Mathematics and Optimization 2 Journal of Mathematical Economics 2 Mathematics of Operations Research 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Journal of Economic Dynamics & Control 2 Computational Mathematics and Modeling 2 Annals of Operations Research 2 Computational Mathematics and Mathematical Physics 2 European Journal of Operational Research 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Mathematical Programming. Series A. Series B 2 SIAM Journal on Optimization 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Opuscula Mathematica 2 Revista Investigación Operacional 2 Mathematical Problems in Engineering 2 Finance and Stochastics 2 Nonlinear Dynamics 2 Journal of Applied Mathematics 2 Journal of Applied Mathematics and Computing 2 Central European Journal of Mathematics 2 Boundary Value Problems 2 Journal of Industrial and Management Optimization 2 Journal of Biological Dynamics 2 Optimization Letters 2 Journal of Physics A: Mathematical and Theoretical 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Geometric Mechanics 2 Games 2 Journal of Dynamics and Games 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences ...and 80 more Serials all top 5 Cited in 37 Fields 337 Biology and other natural sciences (92-XX) 334 Calculus of variations and optimal control; optimization (49-XX) 167 Systems theory; control (93-XX) 118 Ordinary differential equations (34-XX) 85 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 60 Partial differential equations (35-XX) 48 Dynamical systems and ergodic theory (37-XX) 48 Operations research, mathematical programming (90-XX) 34 Numerical analysis (65-XX) 23 Probability theory and stochastic processes (60-XX) 17 Mechanics of particles and systems (70-XX) 10 Operator theory (47-XX) 10 Global analysis, analysis on manifolds (58-XX) 10 Quantum theory (81-XX) 9 Computer science (68-XX) 8 Fluid mechanics (76-XX) 7 Difference and functional equations (39-XX) 6 Real functions (26-XX) 6 Differential geometry (53-XX) 5 Functional analysis (46-XX) 4 Mechanics of deformable solids (74-XX) 4 Optics, electromagnetic theory (78-XX) 4 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Integral equations (45-XX) 2 Convex and discrete geometry (52-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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