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Lagrangian and Hamiltonian formalism in Field Theory: A simple model
Geometric Jacobian linearization and LQR theory
1. | Department of Mathematics and Statistics, Queen's University, Kingston, ON K7L 3N6, Canada, Canada |
References:
[1] |
R. Abraham, J. E. Marsden and T. S. Ratiu, "Manifolds, Tensor Analysis, and Applications,'' 2nd edition, Number 75 in Applied Mathematical Sciences, Springer-Verlag, 1988. |
[2] |
C. D. Aliprantis and K. C. Border, "Infinite-dimensional Analysis,'' 2nd edition, Springer-Verlag, New York-Heidelberg-Berlin, 1999. |
[3] |
M. Athans and P. L. Falb, "Optimal Control. An Introduction to the Theory and its Applications,'' McGraw-Hill, New York, 1966. |
[4] |
R. M. Bianchini and G. Stefani, Controllability along a trajectory: A variational approach, SIAM Journal on Control and Optimization, 31 (1993), 900-927.
doi: 10.1137/0331039. |
[5] |
R. W. Brockett, "Finite Dimensional Linear Systems,'' John Wiley and Sons, New York, New York, 1970. |
[6] |
R. M. Hirschorn and A. D. Lewis, Geometric local controllability: Second-order conditions, Preprint, June 2002, available online at http://www.mast.queensu.ca/ andrew/. |
[7] |
M. Ikeda, H. Maeda and S. Kodama, Stabilization of linear systems, Journal of the Society of Industrial and Applied Mathematics, Series A Control, 10 (1972), 716-729. |
[8] |
R. E. Kalman, Contributions to the theory of optimal control, Boletín de la Sociedad Matemática Mexicana. Segunda Serie, 5 (1960), 102-119. |
[9] |
E. B. Lee and L. Markus, "Foundations of Optimal Control Theory,'' John Wiley and Sons, New York, New York, 1967. |
[10] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "Matematicheskaya Teoriya Optimal' nykh Protsessov,'' Gosudarstvennoe izdatelstvo fiziko-matematicheskoi literatury, Moscow, 1961. Reprint of translation: [11]. |
[11] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes,'' Classics of Soviet Mathematics. Gordon & Breach Science Publishers, New York, 1986. Reprint of 1962 translation from the Russian by K. N. Trirogoff. |
[12] |
E. D. Sontag, "Mathematical Control Theory: Deterministic Finite Dimensional Systems,'' 2nd edition, Number 6 in Texts in Applied Mathematics, Springer-Verlag, New York-Heidelberg-Berlin, 1998. |
[13] |
H. J. Sussmann, An introduction to the coordinate-free maximum principle, in "Geometry of Feedback and Optimal Control'' (eds. B. Jakubczyk and W. Respondek), Dekker Marcel Dekker, New York, (1997), 463-557. |
[14] |
D. R. Tyner, "Geometric Jacobian Linearisation,'' PhD thesis, Queen's University, Kingston, Kingston, ON, Canada, 2007. |
[15] |
M. Vidyasagar, "Nonlinear Systems Analysis,'' 2nd edition, Number 42 in Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 2002. Reprint of 1993 Prentice Hall second edition. |
[16] |
K. Yano and S. Ishihara, "Tangent and Cotangent Bundles,'' Number 16 in Pure and Applied Mathematics. Dekker Marcel Dekker, New York, 1973. |
show all references
References:
[1] |
R. Abraham, J. E. Marsden and T. S. Ratiu, "Manifolds, Tensor Analysis, and Applications,'' 2nd edition, Number 75 in Applied Mathematical Sciences, Springer-Verlag, 1988. |
[2] |
C. D. Aliprantis and K. C. Border, "Infinite-dimensional Analysis,'' 2nd edition, Springer-Verlag, New York-Heidelberg-Berlin, 1999. |
[3] |
M. Athans and P. L. Falb, "Optimal Control. An Introduction to the Theory and its Applications,'' McGraw-Hill, New York, 1966. |
[4] |
R. M. Bianchini and G. Stefani, Controllability along a trajectory: A variational approach, SIAM Journal on Control and Optimization, 31 (1993), 900-927.
doi: 10.1137/0331039. |
[5] |
R. W. Brockett, "Finite Dimensional Linear Systems,'' John Wiley and Sons, New York, New York, 1970. |
[6] |
R. M. Hirschorn and A. D. Lewis, Geometric local controllability: Second-order conditions, Preprint, June 2002, available online at http://www.mast.queensu.ca/ andrew/. |
[7] |
M. Ikeda, H. Maeda and S. Kodama, Stabilization of linear systems, Journal of the Society of Industrial and Applied Mathematics, Series A Control, 10 (1972), 716-729. |
[8] |
R. E. Kalman, Contributions to the theory of optimal control, Boletín de la Sociedad Matemática Mexicana. Segunda Serie, 5 (1960), 102-119. |
[9] |
E. B. Lee and L. Markus, "Foundations of Optimal Control Theory,'' John Wiley and Sons, New York, New York, 1967. |
[10] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "Matematicheskaya Teoriya Optimal' nykh Protsessov,'' Gosudarstvennoe izdatelstvo fiziko-matematicheskoi literatury, Moscow, 1961. Reprint of translation: [11]. |
[11] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes,'' Classics of Soviet Mathematics. Gordon & Breach Science Publishers, New York, 1986. Reprint of 1962 translation from the Russian by K. N. Trirogoff. |
[12] |
E. D. Sontag, "Mathematical Control Theory: Deterministic Finite Dimensional Systems,'' 2nd edition, Number 6 in Texts in Applied Mathematics, Springer-Verlag, New York-Heidelberg-Berlin, 1998. |
[13] |
H. J. Sussmann, An introduction to the coordinate-free maximum principle, in "Geometry of Feedback and Optimal Control'' (eds. B. Jakubczyk and W. Respondek), Dekker Marcel Dekker, New York, (1997), 463-557. |
[14] |
D. R. Tyner, "Geometric Jacobian Linearisation,'' PhD thesis, Queen's University, Kingston, Kingston, ON, Canada, 2007. |
[15] |
M. Vidyasagar, "Nonlinear Systems Analysis,'' 2nd edition, Number 42 in Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 2002. Reprint of 1993 Prentice Hall second edition. |
[16] |
K. Yano and S. Ishihara, "Tangent and Cotangent Bundles,'' Number 16 in Pure and Applied Mathematics. Dekker Marcel Dekker, New York, 1973. |
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