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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, SpringerVerlag, 1988. 
[2] 
C. D. Aliprantis and K. C. Border, "Infinitedimensional Analysis,'' 2nd edition, SpringerVerlag, New YorkHeidelbergBerlin, 1999. 
[3] 
M. Athans and P. L. Falb, "Optimal Control. An Introduction to the Theory and its Applications,'' McGrawHill, 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), 900927. 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: Secondorder 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), 716729. 
[8] 
R. E. Kalman, Contributions to the theory of optimal control, Boletín de la Sociedad Matemática Mexicana. Segunda Serie, 5 (1960), 102119. 
[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 fizikomatematicheskoi 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, SpringerVerlag, New YorkHeidelbergBerlin, 1998. 
[13] 
H. J. Sussmann, An introduction to the coordinatefree maximum principle, in "Geometry of Feedback and Optimal Control'' (eds. B. Jakubczyk and W. Respondek), Dekker Marcel Dekker, New York, (1997), 463557. 
[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, SpringerVerlag, 1988. 
[2] 
C. D. Aliprantis and K. C. Border, "Infinitedimensional Analysis,'' 2nd edition, SpringerVerlag, New YorkHeidelbergBerlin, 1999. 
[3] 
M. Athans and P. L. Falb, "Optimal Control. An Introduction to the Theory and its Applications,'' McGrawHill, 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), 900927. 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: Secondorder 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), 716729. 
[8] 
R. E. Kalman, Contributions to the theory of optimal control, Boletín de la Sociedad Matemática Mexicana. Segunda Serie, 5 (1960), 102119. 
[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 fizikomatematicheskoi 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, SpringerVerlag, New YorkHeidelbergBerlin, 1998. 
[13] 
H. J. Sussmann, An introduction to the coordinatefree maximum principle, in "Geometry of Feedback and Optimal Control'' (eds. B. Jakubczyk and W. Respondek), Dekker Marcel Dekker, New York, (1997), 463557. 
[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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