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Schättler, Heinz Michael

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Author ID: schattler.heinz-m Recent zbMATH articles by "Schättler, Heinz Michael"
Published as: Schättler, Heinz; Schättler, H.; Schaettler, Heinz; Schaettler, H.; Schaettler, Heinz M.; Schättler, Heinz M.
External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 118 Publications since 1987, including 5 Books
Biographic References: 1 Publication
all top 5

Serials

12 Mathematical Biosciences and Engineering
10 Discrete and Continuous Dynamical Systems. Series B
9 Journal of Optimization Theory and Applications
9 SIAM Journal on Control and Optimization
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 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 Nonlinear Studies
1 Optimization Methods & Software
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

Publications by Year

Citations contained in zbMATH Open

87 Publications have been cited 846 times in 484 Documents Cited by Year
Local bifurcations and feasibility regions in differential-algebraic systems. Zbl 0843.34045
Venkatasubramanian, Vaithianathan; Schättler, Heinz; Zaborszky, John
55
1995
Geometric optimal control. Theory, methods and examples. Zbl 1276.49002
Schättler, Heinz; Ledzewicz, Urszula
48
2012
Antiangiogenic therapy in cancer treatment as an optimal control problem. Zbl 1357.49086
Ledzewicz, Urszula; Schättler, Heinz
46
2007
The first-order approach to the continuous-time principal-agent problem with exponential utility. Zbl 0790.90015
Schättler, Heinz; Sung, Jaeyoung
44
1993
On optimal delivery of combination therapy for tumors. Zbl 1176.92033
d’Onofrio, Alberto; Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz
43
2009
Optimal control for mathematical models of cancer therapies. An application of geometric methods. Zbl 1331.92008
Schättler, Heinz; Ledzewicz, Urszula
42
2015
Optimal bang-bang controls for a two-compartment model in cancer chemotherapy. Zbl 1035.49020
Ledzewicz, U.; Schättler, H.
41
2002
Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments. Zbl 1237.49046
Ledzewicz, U.; Schättler, H.
30
2012
Optimal control for a class of compartmental models in cancer chemotherapy. Zbl 1052.92032
Świerniak, Andrzej; Ledzewicz, Urszula; Schättler, Heinz
25
2003
Analysis of a cell-cycle specific model for cancer chemotherapy. Zbl 1099.92035
Ledzewicz, Urszula; Schättler, Heinz
23
2002
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
21
2011
The structure of small-time reachable sets in low dimensions. Zbl 0669.49020
Krener, Arthur J.; Schättler, Heinz
21
1989
Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics. Zbl 1284.92042
Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz
19
2012
High-order approximations and generalized necessary conditions for optimality. Zbl 0941.49016
Ledzewicz, Urszula; Schättler, Heinz
18
1999
Drug resistance in cancer chemotherapy as an optimal control problem. Zbl 1088.92040
Ledzewicz, Urszula; Schättler, Heinz
17
2006
On optimal singular controls for a general SIR-model with vaccination and treatment. Zbl 1306.49056
Ledzewicz, Urszula; Schättler, Heinz
16
2011
Sufficient conditions for relative minima of broken extremals in optimal control theory. Zbl 1012.49023
Noble, John; Schättler, Heinz
15
2002
Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. Zbl 1398.92120
Ledzewicz, Urszula; Schättler, Heinz
14
2008
Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy. Zbl 1114.92042
Ledzewicz, Urszula; Schättler, Heinz
13
2007
On optimal sharing rules in discrete- and continuous-time principal-agent problems with exponential utility. Zbl 0879.90045
Schättler, Heinz; Sung, Jaeyoung
13
1997
Second-order conditions for extremum problems with nonregular equality constraints. Zbl 0835.49016
Ledzewicz, U.; Schaettler, H.
12
1995
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
Optimal control systems governed by second-order ODEs with Dirichlet boundary data and variable parameters. Zbl 1031.49002
Ledzewicz, Urszula; Schättler, Heinz; Walczak, Stanislaw
11
2003
The influence of PK/PD on the structure of optimal controls in cancer chemotherapy models. Zbl 1079.92041
Ledzewicz, Urszula; Schättler, Heinz
10
2005
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
10
2014
Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Zbl 1170.49003
Ledzewicz, Urszula; Munden, James; Schättler, Heinz
10
2009
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
10
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
10
2013
On the local structure of time-optimal bang-bang trajectories in \({\mathbb{R}}^ 3\). Zbl 0644.49020
Schättler, Heinz
9
1988
A review of optimal chemotherapy protocols: from MTD towards metronomic therapy. Zbl 1321.92057
Ledzewicz, U.; Schättler, H.
8
2014
The local structure of time-optimal trajectories in dimension three under generic conditions. Zbl 0656.49007
Schättler, Heinz
8
1988
Local fields of extremals for optimal control problems with state constraints of relative degree 1. Zbl 1123.49031
Schättler, H.
7
2006
A model for cancer chemotherapy with state-space constraints. Zbl 1222.92050
de Pinho, Maria do Rosario; Ferreira, Maria Margarida; Ledzewicz, Urszula; Schaettler, Heinz
7
2005
Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load. Zbl 0800.94316
Venkatasubramanian, V.; Schättler, H.; Zaborszky, J.
7
1992
On optimal chemotherapy for heterogeneous tumors. Zbl 1343.92232
Ledzewicz, Urszula; Schättler, Heinz
7
2014
Singular controls and chattering arcs in optimal control problems arising in biomedicine. Zbl 1236.49054
Ledzewicz, U.; Schaettler, H.
7
2009
A high-order generalization of the Lyusternik theorem. Zbl 0954.49014
Ledzewicz, Urszula; Schättler, Heinz
6
1998
Parametrized families of extremals and singularities in solutions to the Hamilton-Jacobi-Bellman equation. Zbl 0939.49018
Kiefer, Matthew; Schättler, Heinz
6
1999
Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1259.92053
Schättler, Heinz; Ledzewicz, Urszula; Cardwell, Benjamin
6
2011
An optimal control approach to cancer treatment under immunological activity. Zbl 1215.49030
Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz
6
2011
Controlling a model for bone marrow dynamics in cancer chemotherapy. Zbl 1135.92309
Ledzewicz, Urszula; Schättler, Heinz
5
2004
Dynamics and control of a mathematical model for metronomic chemotherapy. Zbl 1326.92038
Ledzewicz, Urszula; Amini, Behrooz; Schättler, Heinz
4
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
4
2017
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
4
2004
A high-order generalized local maximum principle. Zbl 0954.49015
Ledzewicz, Urszula; Schättler, Heinz
4
2000
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
4
2018
On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1161.49037
Ledzewicz, Urszula; Schättler, Heinz
4
2009
Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Zbl 1350.49058
Wang, Shuo; Schättler, Heinz
4
2016
Mathematical methods and models in biomedicine. Zbl 1254.92046
Ledzewicz, Urszula (ed.); Schättler, Heinz (ed.); Friedman, Avner (ed.); Kashdan, Eugene (ed.)
4
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
4
2013
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
Stability regions for differential-algebraic systems. Zbl 0781.93072
Venkatasubramanian, V.; Schättler, H.; Zaborszky, J.
3
1992
A synthesis of time-optimal controls in the presence of saturated singular arcs. Zbl 0780.49017
Schättler, Heinz; Jankovic, Miroslava
3
1993
On the time-optimality of bang-bang trajectories in \(R^ 3\). Zbl 0608.49016
Schaettler, Heinz M.
3
1987
Regularity properties of optimal trajectories: Recently developed techniques. Zbl 0702.49033
Schättler, Heinz
3
1990
On the regularity of optimal controls. Zbl 0636.49009
Schättler, Heinz M.; Sussmann, Héctor J.
3
1987
Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Zbl 1418.92058
Leszczyński, Maciej; Ledzewicz, Urszula; Schättler, Heinz
3
2019
A 3-compartment model for chemotherapy of heterogeneous tumor populations. Zbl 1326.92039
Ledzewicz, Urszula; Bratton, Kenneth; Schättler, Heinz
3
2015
Minimum-time frictionless atom cooling in harmonic traps. Zbl 1237.49050
Stefanatos, Dionisis; Schaettler, Heinz; Li, Jr-Shin
3
2011
Perturbation feedback control: A geometric interpretation. Zbl 1253.49013
Schättler, Heinz; Ledzewicz, Urszula
3
2012
On the dynamics of tumor-immune system interactions and combined chemo- and immunotherapy. Zbl 1316.92020
D’Onofrio, Alberto; Ledzewicz, Urszula; Schättler, Heinz
2
2012
Pareto optimality conditions for abnormal optimization and optimal control problems. Zbl 0811.49018
Ledzewicz, Urszula; Schaettler, Heinz
2
1994
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
Small-time reachable sets and time-optimal feedback control. Zbl 0863.93005
Schättler, Heinz
2
1996
On the optimality of parametrized families of bang-bang trajectories. Zbl 1042.49533
Noble, John; Schaettler, Heinz
2
2001
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
High-order tangent cones and their application in optimization. Zbl 0909.90241
Ledzewicz, Urszula; Schättler, Heinz
2
1997
Time-optimal feedback control for nonlinear systems: A geometric approach. Zbl 0925.93137
Schättler, Heinz
2
1998
Optimal combined radio- and anti-angiogenic cancer therapy. Zbl 1409.49036
Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz
2
2019
Dynamics of tumor-immune interaction under treatment as an optimal control problem. Zbl 1306.49055
Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz
2
2011
Tumor development under combination treatments with anti-angiogenic therapies. Zbl 1345.92078
Ledzewicz, Urszula; d’Onofrio, Alberto; Schättler, Heinz
2
2013
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
2
2017
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
2
2009
Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy. Zbl 1337.92117
Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz
2
2016
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.
1
2005
A theory of first and second order conditions for nonregular extremum problems. Zbl 0811.49019
Ledzewicz, Urszula; Schaettler, Heinz
1
1994
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
Stratifiable families of extremals and sufficient conditions for optimality in optimal control problems. Zbl 1092.49019
Ledzewicz, U.; Nowakowski, A.; Schättler, H.
1
2004
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
Regularity properties of time-optimal trajectories of an analytic single- input control-linear system in dimension three. Zbl 0631.49006
Schättler, H.
1
1988
Synthesis of optimal controlled trajectories with chattering arcs. Zbl 1270.49035
Schättler, Heinz; Ledzewicz, Urszula
1
2012
Optimal control of cancer treatments: mathematical models for the tumor microenvironment. Zbl 1329.49078
Schättler, Heinz; Ledzewicz, Urszula
1
2015
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
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
1
2018
Optimal control for a mathematical model for anti-angiogenic treatment with Michaelis-Menten pharmacodynamics. Zbl 1418.92058
Leszczyński, Maciej; Ledzewicz, Urszula; Schättler, Heinz
3
2019
Optimal combined radio- and anti-angiogenic cancer therapy. Zbl 1409.49036
Ledzewicz, Urszula; Maurer, Helmut; Schättler, Heinz
2
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
4
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
1
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
4
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
2
2017
Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity. Zbl 1350.49058
Wang, Shuo; Schättler, Heinz
4
2016
Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy. Zbl 1337.92117
Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz
2
2016
Optimal control for mathematical models of cancer therapies. An application of geometric methods. Zbl 1331.92008
Schättler, Heinz; Ledzewicz, Urszula
42
2015
Dynamics and control of a mathematical model for metronomic chemotherapy. Zbl 1326.92038
Ledzewicz, Urszula; Amini, Behrooz; Schättler, Heinz
4
2015
A 3-compartment model for chemotherapy of heterogeneous tumor populations. Zbl 1326.92039
Ledzewicz, Urszula; Bratton, Kenneth; Schättler, Heinz
3
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
10
2014
A review of optimal chemotherapy protocols: from MTD towards metronomic therapy. Zbl 1321.92057
Ledzewicz, U.; Schättler, H.
8
2014
On optimal chemotherapy for heterogeneous tumors. Zbl 1343.92232
Ledzewicz, Urszula; Schättler, Heinz
7
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
10
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
10
2013
Mathematical methods and models in biomedicine. Zbl 1254.92046
Ledzewicz, Urszula; Schättler, Heinz; Friedman, Avner; Kashdan, Eugene
4
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
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
48
2012
Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments. Zbl 1237.49046
Ledzewicz, U.; Schättler, H.
30
2012
Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics. Zbl 1284.92042
Ledzewicz, Urszula; Naghnaeian, Mohammad; Schättler, Heinz
19
2012
Perturbation feedback control: A geometric interpretation. Zbl 1253.49013
Schättler, Heinz; Ledzewicz, Urszula
3
2012
On the dynamics of tumor-immune system interactions and combined chemo- and immunotherapy. Zbl 1316.92020
D’Onofrio, Alberto; Ledzewicz, Urszula; Schättler, Heinz
2
2012
Synthesis of optimal controlled trajectories with chattering arcs. Zbl 1270.49035
Schättler, Heinz; Ledzewicz, Urszula
1
2012
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
21
2011
On optimal singular controls for a general SIR-model with vaccination and treatment. Zbl 1306.49056
Ledzewicz, Urszula; Schättler, Heinz
16
2011
Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1259.92053
Schättler, Heinz; Ledzewicz, Urszula; Cardwell, Benjamin
6
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
2
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
43
2009
Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Zbl 1170.49003
Ledzewicz, Urszula; Munden, James; Schättler, Heinz
10
2009
Singular controls and chattering arcs in optimal control problems arising in biomedicine. Zbl 1236.49054
Ledzewicz, U.; Schaettler, H.
7
2009
On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis. Zbl 1161.49037
Ledzewicz, Urszula; Schättler, Heinz
4
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
2
2009
Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. Zbl 1398.92120
Ledzewicz, Urszula; Schättler, Heinz
14
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
46
2007
Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy. Zbl 1114.92042
Ledzewicz, Urszula; Schättler, Heinz
13
2007
Drug resistance in cancer chemotherapy as an optimal control problem. Zbl 1088.92040
Ledzewicz, Urszula; Schättler, Heinz
17
2006
Local fields of extremals for optimal control problems with state constraints of relative degree 1. Zbl 1123.49031
Schättler, H.
7
2006
The influence of PK/PD on the structure of optimal controls in cancer chemotherapy models. Zbl 1079.92041
Ledzewicz, Urszula; Schättler, Heinz
10
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
7
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.
1
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
Controlling a model for bone marrow dynamics in cancer chemotherapy. Zbl 1135.92309
Ledzewicz, Urszula; Schättler, Heinz
5
2004
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
4
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
Optimal control for a class of compartmental models in cancer chemotherapy. Zbl 1052.92032
Świerniak, Andrzej; Ledzewicz, Urszula; Schättler, Heinz
25
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
11
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.
41
2002
Analysis of a cell-cycle specific model for cancer chemotherapy. Zbl 1099.92035
Ledzewicz, Urszula; Schättler, Heinz
23
2002
Sufficient conditions for relative minima of broken extremals in optimal control theory. Zbl 1012.49023
Noble, John; Schättler, Heinz
15
2002
On the optimality of parametrized families of bang-bang trajectories. Zbl 1042.49533
Noble, John; Schaettler, Heinz
2
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
18
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
6
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
13
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
2
1996
Local bifurcations and feasibility regions in differential-algebraic systems. Zbl 0843.34045
Venkatasubramanian, Vaithianathan; Schättler, Heinz; Zaborszky, John
55
1995
Second-order conditions for extremum problems with nonregular equality constraints. Zbl 0835.49016
Ledzewicz, U.; Schaettler, H.
12
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
44
1993
A synthesis of time-optimal controls in the presence of saturated singular arcs. Zbl 0780.49017
Schättler, Heinz; Jankovic, Miroslava
3
1993
Voltage dynamics: Study of a generator with voltage control, transmission, and matched MW load. Zbl 0800.94316
Venkatasubramanian, V.; Schättler, H.; Zaborszky, J.
7
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
3
1990
The structure of small-time reachable sets in low dimensions. Zbl 0669.49020
Krener, Arthur J.; Schättler, Heinz
21
1989
On the local structure of time-optimal bang-bang trajectories in \({\mathbb{R}}^ 3\). Zbl 0644.49020
Schättler, Heinz
9
1988
The local structure of time-optimal trajectories in dimension three under generic conditions. Zbl 0656.49007
Schättler, Heinz
8
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 time-optimality of bang-bang trajectories in \(R^ 3\). Zbl 0608.49016
Schaettler, Heinz M.
3
1987
On the regularity of optimal controls. Zbl 0636.49009
Schättler, Heinz M.; Sussmann, Héctor J.
3
1987
all top 5

Cited by 774 Authors

39 Schättler, Heinz Michael
33 Ledzewicz, Urszula
13 Zhang, Qingling
10 Khailov, Evgenii N.
10 Maurer, Helmut
9 Liu, Chao
9 Trélat, Emmanuel
8 Bratus, Alexander S.
8 Galewski, Marek
8 Tret’yakov, Alexey A.
7 d’Onofrio, Alberto
7 Riaza, Ricardo
6 Bayen, Térence
6 Bonnard, Bernard
6 Chakraborty, Kunal
6 Cvitanić, Jakša
6 de Pinho, Maria do Rosário
6 Kar, Tapan Kumar
5 Bourdin, Loïc
5 Grigorieva, Ellina V.
5 Silva, Cristiana J.
5 Sung, Jaeyoung
5 Wang, Shuo
5 Yegorov, Ivan V.
5 Zhang, Xue
4 Aronna, María Soledad
4 Arutyunov, Aram Vladimirovic
4 Bednarczuk, Ewa M.
4 Felgenhauer, Ursula
4 Foryś, Urszula
4 Jiang, Yaolin
4 Korobeinikov, Andrei
4 Liu, Wei
4 Lykina, Valeriya
4 Marszałek, Wiesław
4 Piotrowska, Monika Joanna
4 Possamaï, Dylan
4 Sigalotti, Mario
4 Torres, Delfim Fernando Marado
4 Zhang, Yi
3 Ainseba, Bedr’Eddine
3 Ayala, Victor
3 Benosman, Chahrazed
3 Boarotto, Francesco
3 Brezhneva, Olga A.
3 Campbell, Stephen LaVern
3 Carrère, Cécile
3 Chakraborty, Milon
3 Clairambault, Jean
3 Constantin, Elena
3 Cots, Olivier
3 Deng, Li
3 Duan, Xiaodong
3 Eftimie, Raluca
3 Fimmel, Elena
3 Grochowski, Marek
3 Hernández-Jiménez, Beatriz
3 Jana, Soovoojeet
3 Leszczynski, Maciej
3 Mairet, Francis
3 Margaliot, Michael
3 Mastrolia, Thibaut
3 Meng, Xinyou
3 Moore, Helen
3 Osuna-Gómez, Rafaela
3 Prusińska, Agnieszka
3 Ratajczyk, Elzbieta
3 Sebbah, Matthieu
3 Shamsi, Mostafa
3 Tang, Yun
3 Wan, Xuhu
3 Zhang, Yue
2 Agrachev, Andreĭ Aleksandrovich
2 Al Agha, A. D.
2 Alamir, Mazen
2 Amini, Behrooz
2 Băleanu, Dumitru I.
2 Barlo, Mehmet
2 Belmiloudi, Aziz
2 Belmonte-Beitia, Juan
2 Bernard, Séverine
2 Billy, Frédérique
2 Biolo, Carolina
2 Biswas, Md. Haider Ali
2 Bloch, Anthony M.
2 Bonnans, Joseph Frédéric
2 Boscain, Ugo
2 Bramson, Jonathan L.
2 Bruni, Carlo
2 Bunimovich-Mendrazitsky, Svetlana
2 Buonomo, Bruno
2 Cacace, Filippo
2 Capponi, Agostino
2 Cerf, Max
2 Chen, Zheng
2 Chiang, Hsiao-Dong
2 Chitour, Yacine
2 Coron, Jean-Michel
2 Cui, Qing
2 Cusimano, Valerio
...and 674 more Authors
all top 5

Cited in 156 Serials

27 Journal of Optimization Theory and Applications
19 Mathematical Biosciences
17 Applied Mathematics and Computation
17 Mathematical Biosciences and Engineering
13 Journal of Mathematical Biology
13 Discrete and Continuous Dynamical Systems. Series B
12 Journal of Theoretical Biology
11 SIAM Journal on Control and Optimization
10 Journal of Economic Theory
9 Journal of Mathematical Analysis and Applications
9 Bulletin of Mathematical Biology
9 Automatica
9 Discrete Dynamics in Nature and Society
8 Optimal Control Applications & Methods
8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
8 Mathematical Modelling of Natural Phenomena
7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
7 Journal of Dynamical and Control Systems
7 International Journal of Biomathematics
6 Journal of the Franklin Institute
6 Journal of Differential Equations
5 Mathematics and Computers in Simulation
5 Systems & Control Letters
5 Journal of Mathematical Sciences (New York)
5 Nonlinear Analysis. Real World Applications
5 Mathematics and Financial Economics
4 International Journal of Control
4 Chaos, Solitons and Fractals
4 Journal of Computational and Applied Mathematics
4 Acta Applicandae Mathematicae
4 Journal of Global Optimization
4 Nonlinear Analysis. Theory, Methods & Applications
3 Journal of Geometry and Physics
3 Numerical Functional Analysis and Optimization
3 Mathematical and Computer Modelling
3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
3 Applied Mathematical Modelling
3 Discrete and Continuous Dynamical Systems
3 Mathematical Finance
3 Abstract and Applied Analysis
3 Communications in Nonlinear Science and Numerical Simulation
3 Journal of Biological Systems
3 Advances in Difference Equations
3 Computational & Mathematical Methods in Medicine
3 Nonlinear Analysis. Hybrid Systems
3 SIAM Journal on Financial Mathematics
3 Set-Valued and Variational Analysis
3 Numerical Algebra, Control and Optimization
2 Applicable Analysis
2 Computers & Mathematics with Applications
2 International Journal of Systems Science
2 Journal of Mathematical Physics
2 Physica A
2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
2 Optimization
2 Journal of Economic Dynamics & Control
2 Annals of Operations Research
2 Computational Mathematics and Mathematical Physics
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 Mathematical Programming. Series A. Series B
2 SIAM Journal on Optimization
2 Computational Optimization and Applications
2 Computational and Applied Mathematics
2 Opuscula Mathematica
2 Mathematical Problems in Engineering
2 European Journal of Control
2 Nonlinear Dynamics
2 International Journal of Applied Mathematics and Computer Science
2 Journal of Applied Mathematics
2 SIAM Journal on Applied Dynamical Systems
2 Central European Journal of Mathematics
2 Proceedings of the Steklov Institute of Mathematics
2 Journal of Biological Dynamics
2 Discrete and Continuous Dynamical Systems. Series S
2 Mathematical Control and Related Fields
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Nonlinearity
1 The Mathematical Intelligencer
1 Prikladnaya Matematika i Mekhanika
1 Applied Mathematics and Optimization
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Mathematical Economics
1 Mathematics of Operations Research
1 Results in Mathematics
1 Moscow University Computational Mathematics and Cybernetics
1 Cybernetics and Systems
1 Mathematical Social Sciences
1 Statistics & Probability Letters
1 Circuits, Systems, and Signal Processing
1 Applied Numerical Mathematics
1 Algorithmica
1 Discrete & Computational Geometry
1 MCSS. Mathematics of Control, Signals, and Systems
1 Computational Mathematics and Modeling
1 Automation and Remote Control
1 Communications in Statistics. Simulation and Computation
1 European Journal of Operational Research
1 SIAM Journal on Applied Mathematics
1 Bulletin of the American Mathematical Society. New Series
...and 56 more Serials
all top 5

Cited in 36 Fields

253 Calculus of variations and optimal control; optimization (49-XX)
238 Biology and other natural sciences (92-XX)
132 Systems theory; control (93-XX)
92 Ordinary differential equations (34-XX)
68 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
45 Partial differential equations (35-XX)
39 Operations research, mathematical programming (90-XX)
37 Dynamical systems and ergodic theory (37-XX)
27 Numerical analysis (65-XX)
15 Probability theory and stochastic processes (60-XX)
15 Mechanics of particles and systems (70-XX)
10 Operator theory (47-XX)
8 Global analysis, analysis on manifolds (58-XX)
8 Computer science (68-XX)
8 Quantum theory (81-XX)
7 Difference and functional equations (39-XX)
6 Fluid mechanics (76-XX)
5 Real functions (26-XX)
5 Functional analysis (46-XX)
5 Differential geometry (53-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)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Algebraic geometry (14-XX)
1 Measure and integration (28-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Relativity and gravitational theory (83-XX)
1 Mathematics education (97-XX)

Citations by Year

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