Calculus of Variations and Optimal Control Theory
A Concise Introduction
Daniel Liberzon
University of Illinois at Urbana-Champaign
Bibliography
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Contents
Index
AF66
M. Athans and P. L. Falb.
Optimal Control .
McGraw Hill, New York, 1966.
Reprinted by Dover in 2006.
AM90
B. D. O. Anderson and J. B. Moore.
Optimal Control: Linear Quadratic Methods .
Prentice Hall, New Jersey, 1990.
Reprinted by Dover in 2007.
Arn89
V. I. Arnold.
Mathematical Methods of Classical Mechanics .
Springer, New York, 2nd edition, 1989.
Arn92
V. I. Arnold.
Ordinary Differential Equations .
Springer, Berlin, 3rd edition, 1992.
AS04
A. A. Agrachev and Yu. L. Sachkov.
Control Theory from the Geometric Viewpoint .
Springer, Berlin, 2004.
BCD97
M. Bardi and I. Capuzzo-Dolcetta.
Optimal Control and Viscosity Solutions of
Hamilton-Jacobi-Bellman Equations .
Birkhäuser, Boston, 1997.
Bel57
R. Bellman.
Dynamic Programming .
Princeton University Press, 1957.
Ber99
D. P. Bertsekas.
Nonlinear Programming .
Athena Scientific, Belmont, MA, 2nd edition, 1999.
BGFB94
S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan.
Linear Matrix Inequalities in System and Control Theory ,
volume 15 of SIAM Studies in Applied Mathematics .
SIAM, Philadelphia, 1994.
Bli30
G. A. Bliss.
On the problem of Lagrange in the calculus of variations.
Amer. J. Math. , 52:673-744, 1930.
Blo03
A. M. Bloch.
Nonholonomic Mechanics and Control .
Springer, New York, 2003.
BM91
U. Brechtken-Manderscheid.
Introduction to the Calculus of Variations .
Chapman & Hall, London, 1991.
Boo86
W. M. Boothby.
An Introduction to Differentiable Manifolds and Riemannian
Geometry .
Academic Press, Orlando, 1986.
BP04
U. Boscain and B. Piccoli.
Optimal Syntheses for Control Systems on 2-D Manifolds .
Springer, New York, 2004.
BP07
A. Bressan and B. Piccoli.
Introduction to the Mathematical Theory of Control .
American Institute of Mathematical Sciences, 2007.
Bre85
A. Bressan.
A high order test for optimality of bang-bang controls.
SIAM J. Control Optim. , 23:38-48, 1985.
Bro70
R. W. Brockett.
Finite Dimensional Linear Systems .
Wiley, New York, 1970.
Bry96
A. E. Bryson Jr.
Optimal control--1950 to 1985.
IEEE Control Systems Magazine , 16:26-33, 1996.
BV04
S. Boyd and L. Vandenberghe.
Convex Optimization .
Cambridge University Press, 2004.
BWEV05
M. Boccadoro, Y. Wardi, M. Egerstedt, and E. Verriest.
Optimal control of switching surfaces in hybrid dynamical systems.
Discrete Event Dyn. Syst. , 15:433-448, 2005.
CEHS87
G. S. Christensen, M. E. El-Hawary, and S. A. Soliman.
Optimal Control Applications in Electric Power Systems .
Plenum Press, New York, 1987.
Ces83
L. Cesari.
Optimization--Theory and Applications .
Springer, New York, 1983.
CL83
M. G. Crandall and P. L. Lions.
Viscosity solutions of Hamilton-Jacobi equations.
Trans. Amer. Math. Soc. , 277:1-42, 1983.
Cla89
F. H. Clarke.
Methods of Dynamic and Nonsmooth Optimization .
SIAM, Philadelphia, 1989.
DGKF89
J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis.
State-space solutions to standard
and
control problems.
IEEE Trans. Automat. Control , 34:831-847, 1989.
DK08
A. V. Dmitruk and A. M. Kaganovich.
The Hybrid Maximum Principle is a consequence of Pontryagin
Maximum Principle.
Systems Control Lett. , 57:964-970, 2008.
dlF00
A. de la Fuente.
Mathematical Methods and Models for Economists .
Cambridge University Press, 2000.
Fil88
A. F. Filippov.
Differential Equations with Discontinuous Righthand Sides .
Kluwer, Dordrecht, 1988.
FLS63
R. P. Feynman, R. B. Leighton, and M. Sands.
The Feynman Lectures on Physics .
Addison-Wesley, Reading, MA, 1963.
Ful85
A. T. Fuller.
Minimization of various performance indices for a system with bounded
control.
Int. J. Control , 41:1-37, 1985.
Gar86
P. R. Garabedian.
Partial Differential Equations .
Chelsea Pub. Co., New York, 2nd edition, 1986.
GF63
I. M. Gelfand and S. V. Fomin.
Calculus of Variations .
Prentice Hall, New Jersey, 1963.
Reprinted by Dover in 2000.
Gol80
H. H. Goldstine.
A History of the Calculus of Variations from the 17th through
the 19th Century .
Springer, New York, 1980.
GP05
M. Garavello and B. Piccoli.
Hybrid necessary principle.
SIAM J. Control Optim. , 43:1867-1887, 2005.
GS07
R. Goebel and M. Subbotin.
Continuous time linear quadratic regulator with control constraints
via convex duality.
IEEE Trans. Automat. Control , 52:886-892, 2007.
HJ85
R. A. Horn and C. R. Johnson.
Matrix Analysis .
Cambridge University Press, 1985.
Isi95
A. Isidori.
Nonlinear Control Systems .
Springer, Berlin, 3rd edition, 1995.
Jur96
V. Jurdjevic.
Geometric Control Theory .
Cambridge University Press, 1996.
Kal60
R. E. Kalman.
Contributions to the theory of optimal control.
Bol. Soc. Mat. Mexicana , 5:102-119, 1960.
Reprinted in Control Theory: Twenty-Five Seminal Papers
(1931-1981) , T. Basar, editor, IEEE Press, New York, 2001, pages 149-166.
Kha02
H. K. Khalil.
Nonlinear Systems .
Prentice Hall, New Jersey, 3rd edition, 2002.
Kno81
G. Knowles.
An Introduction to Applied Optimal Control .
Academic Press, New York, 1981.
Kre77
A. J. Krener.
The high order maximal principle and its applications to singular
extremals.
SIAM J. Control Optim. , 15:256-293, 1977.
KS72
H. Kwakernaak and R. Sivan.
Linear Optimal Control Systems .
Wiley, New York, 1972.
Lei81
G. Leitmann.
The Calculus of Variations and Optimal Control: An
Introduction .
Plenum Press, New York, 1981.
LL50
M. A. Lavrentiev and L. A. Lusternik.
A Course in the Calculus of Variations .
Moscow, 2nd edition, 1950.
In Russian.
LM67
E. B. Lee and L. Markus.
Foundations of Optimal Control Theory .
Wiley, New York, 1967.
LSW96
Y. Lin, E. D. Sontag, and Y. Wang.
A smooth converse Lyapunov theorem for robust stability.
SIAM J. Control Optim. , 34:124-160, 1996.
Lue69
D. G. Luenberger.
Optimization by Vector Space Methods .
Wiley, New York, 1969.
Lue84
D. G. Luenberger.
Linear and Nonlinear Programming .
Addison-Wesley, Reading, MA, 2nd edition, 1984.
Mac05
C. R. MacCluer.
Calculus of Variations .
Prentice Hall, New Jersey, 2005.
McS39
E. J. McShane.
On multipliers for Lagrange problems.
Amer. J. Math. , 61:809-819, 1939.
MO98
A. A. Milyutin and N. P. Osmolovskii.
Calculus of Variations and Optimal Control .
American Mathematical Society, Providence, RI, 1998.
NRV84
Z. Nahorski, H. F. Ravn, and R. V. V. Vidal.
The discrete-time maximum principle: a survey and some new results.
Int. J. Control , 40:533-554, 1984.
PB94
H. J. Pesch and R. Bulirsch.
The maximum principle, Bellman's equation, and Carathéodory's
work.
J. Optim. Theory Appl. , 80:199-225, 1994.
PBGM62
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko.
The Mathematical Theory of Optimal Processes .
Interscience, New York, 1962.
Pet87
I. R. Petersen.
Disturbance attenuation and
optimization: a design
method based on the algebraic Riccati equation.
IEEE Trans. Automat. Control , 32:427-429, 1987.
PS00
B. Piccoli and H. J. Sussmann.
Regular synthesis and sufficiency conditions for optimality.
SIAM J. Control Optim. , 39:359-410, 2000.
Roc74
R. T. Rockafellar.
Conjugate Duality and Optimization .
SIAM, Philadelphia, 1974.
Rud76
W. Rudin.
Principles of Mathematical Analysis .
McGraw Hill, New York, 3rd edition, 1976.
RW00
R. T. Rockafellar and P. R. Wolenski.
Convexity in Hamilton-Jacobi theory I: dynamics and duality.
SIAM J. Control Optim. , 39:1323-1350, 2000.
Rya87
E. P. Ryan.
Feedback solution of a class of optimal bilinear control problems.
Int. J. Control , 45:1035-1041, 1987.
Son98
E. D. Sontag.
Mathematical Control Theory: Deterministic Finite Dimensional
Systems .
Springer, New York, 2nd edition, 1998.
ST05
S. P. Sethi and G. L. Thompson.
Optimal Control Theory: Applications to Management Science and
Economics .
Springer, New York, 2nd edition, 2005.
Sus79
H. J. Sussmann.
A bang-bang theorem with bounds on the number of switchings.
SIAM J. Control Optim. , 17:629-651, 1979.
Sus83
H. J. Sussmann.
Lie brackets, real analyticity and geometric control.
In R. W. Brockett, R. S. Millman, and H. J. Sussmann, editors, Differential Geometric Control Theory , pages 1-116. Birkhäuser, Boston,
1983.
Sus97
H. J. Sussmann.
An introduction to the coordinate-free maximum principle.
In B. Jakubczyk and W. Respondek, editors, Geometry of Feedback
and Optimal Control , pages 463-557. Marcel Dekker, New York, 1997.
Sus99
H. J. Sussmann.
A maximum principle for hybrid optimal control problems.
In Proc. 38th IEEE Conf. on Decision and Control , pages
425-430, 1999.
Sus00
H. J. Sussmann.
Handouts for the course taught at the Weizmann Institute, 2000.
Available at http://www.math.rutgers.edu/
sussmann.
Sus07
H. J. Sussmann.
Set separation, approximating multicones, and the Lipschitz maximum
principle.
J. Differential Equations , 243:448-488, 2007.
Sut75
W. A. Sutherland.
Introduction to Metric and Topological Spaces .
Oxford University Press, 1975.
SW77
A. P. Sage and C. C. White.
Optimum Systems Control .
Prentice Hall, New Jersey, 2nd edition, 1977.
SW97
H. J. Sussmann and J. C. Willems.
300 years of optimal control: from the brachystochrone to the maximum
principle.
IEEE Control Systems Magazine , 17:32-44, 1997.
Swa84
G. W. Swan.
Applications of Optimal Control Theory in Biomedicine .
Marcel Dekker, New York, 1984.
vdS96
A. van der Schaft.
-Gain and Passivity Techniques in Nonlinear Control .
Springer, London, 1996.
vdSS00
A. van der Schaft and H. Schumacher.
An Introduction to Hybrid Dynamical Systems .
Springer, London, 2000.
Vin00
R. Vinter.
Optimal Control .
Birkhäuser, Boston, 2000.
War83
F. W. Warner.
Foundations of Differentiable Manifolds and Lie Groups .
Springer, New York, 1983.
You80
L. C. Young.
Lectures on the Calculus of Variations and Optimal Control
Theory .
Chelsea Pub. Co., New York, 2nd edition, 1980.
YZ99
J. Yong and X. Y. Zhou.
Stochastic Controls: Hamiltonian Systems and HJB Equations .
Springer, New York, 1999.
ZDG96
K. Zhou, J. C. Doyle, and K. Glover.
Robust and Optimal Control .
Prentice Hall, New Jersey, 1996.
Daniel
2010-12-20