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Numerical procedure for optimal control of higher index DAEs
1.  Institute of Automatic Control and Robotics, Warsaw University of Technology, 02525 Warsaw, Poland 
References:
[1] 
K. Balla, Linear subspaces for linear DAE's of index 1,, Comput. Math. Appl., 32 (1996), 81. Google Scholar 
[2] 
K. Balla, Boundary conditions and their transfer for differential algebraic equations of index 1,, Comput. Math. Appl., 31 (1996), 1. Google Scholar 
[3] 
K. Balla and R. März, Transfer of boundary conditions for DAE's of index 1,, SIAM J. Numer. Anal., 33 (1996), 2318. Google Scholar 
[4] 
K. Balla and R. März, "An Unified Approach to Linear Differential Algebraic Equations and Their Adjoint Equations,", Institute of Mathematics Technical Report, (2000). Google Scholar 
[5] 
K. Balla, K. and R. März, Linear differential algebraic equations and their adjoint equations,, Results in Mathematica, 37 (2000), 13. Google Scholar 
[6] 
K. E. Brenan, S. L. Campbell and L. R. Petzold, "Numerical Solution of InitialValue Problems in DifferentialAlgebraic Equations,", NorthHolland, (1989). Google Scholar 
[7] 
Y. Cao, S. Li, L. Petzold and R. Serben, Adjoint sensitivity analysis for differentialalgebraic equations: Part I, The adjoint DAE system and its numerical solution,, SIAM J. Sci. Comp., 24 (2000), 1076. Google Scholar 
[8] 
Y. Cao, S. Li and L. Petzold, Adjoint sensitivity analysis for differentialalgebraic equations: Algorithms and software,, J. Comput. Appl. Math., 149 (2002), 171. Google Scholar 
[9] 
W. F. Frenery, J. E. Tolsma and P. I. Barton, Efficient sensitivity analysis of largescale differentialalgebraic systems,, Appl. Numer. Math., 25 (1997), 41. Google Scholar 
[10] 
C. W. Gear, Differentialalgebraic equation index transformations,, SIAM J. Sci. Stat. Comput., 9 (1988), 39. Google Scholar 
[11] 
C. W. Gear, Differential algebraic equations, indices and integral algebraic equations,, SIAM J. Numer. Anal., 27 (1990), 1527. Google Scholar 
[12] 
D. R. A. Giles, "A Comparison of Three ProblemOriented Simulation Programs for Dynamic Mechanical Systems,", Thesis, (1978). Google Scholar 
[13] 
E. Hairer, Ch. Lubich and M. Roche, "The Numerical Solution of DifferentialAlgebraic Equations by RungeKutta Methods,", Lecture Notes in Mathematics, 1409 (1989). Google Scholar 
[14] 
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II,", SpringerVerlag, (1996). Google Scholar 
[15] 
A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker and C. S. Woodward, "SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers,", preprint, (2004). Google Scholar 
[16] 
L. Kershenbaum, D. Q. Mayne, R. Pytlak and R. B. Vinter, Receding horizon control,, in, (1993), 20. Google Scholar 
[17] 
S. Li and L. R. Petzold, Software and algorithms for sensitivity analysis of largescale differentialalgebraic systems,, J. Comput. Appl. Math., 125 (2000), 131. Google Scholar 
[18] 
S. Li, L. R. Petzold and W. Zhu, Sensitivity analysis of differentialalgebraic equations: A comparison of methods on a special problem,, Appl. Numer. Math., 32 (2000), 161. Google Scholar 
[19] 
T. Maly, and L. R. Petzold, Numerical methods and software for sensitivity analysis of differentialalgebraic systems,, Appl. Numer. Math., 20 (1997), 57. Google Scholar 
[20] 
D. W. Manning, "A Computer Technique for Simulating Dynamic Multibody Systems Based on Dynamic Formalizm,", Thesis, (1981). Google Scholar 
[21] 
R. März, Differential algebraic systems anew,, Applied Numetical Mathematics, 42 (2002), 315. Google Scholar 
[22] 
R. März, Characterizing differential algebraic equations without the use of derivative arrays,, Int. J. Comp. & Mathem. with Appl., 50 (2005), 1141. Google Scholar 
[23] 
M. D. R. de Pinho and R. Vinter, Necessary conditions for optimal control problems involving nonlinear differential algebraic equations,, J. Math. Anal. Appl., 212 (1997), 493. Google Scholar 
[24] 
R. Pytlak, Optimal control of differentialalgebraic equations,, Proceed. of the 33rd IEEE CDC, (1994), 951. Google Scholar 
[25] 
R. Pytlak, "Numerical Methods for Optimal Control Problem With State Constraints,", Lecture Notes in Mathematics, 1707 (1999). Google Scholar 
[26] 
R. Pytlak, Optimal control of differentialalgebraic equations of higher index, Part 1: First order approximations,, J. Optimization Theory and Applications, 134 (2007), 61. Google Scholar 
[27] 
R. Pytlak, Optimal control of differentialalgebraic equations of higher index, Part 2: Necessary optimality conditions,, J. Optimization Theory and Applications, 134 (2007), 77. Google Scholar 
[28] 
R. Pytlak and R. B. Vinter, A feasible directions algorithm for optimal control problems with state and control constraints: Convergence analysis,, SIAM J. Control and Optimization, 36 (1998), 1999. Google Scholar 
[29] 
R. Pytlak and R. B. Vinter, A feasible directions type algorithm for optimal control problems with state and control constraints: Implementation,, J. Optimization Theory and Applications, 101 (1999), 623. Google Scholar 
[30] 
W. Schiehlen (ed.), "Mulitbody Systems Handbook,", SpringerVerlag, (1990). Google Scholar 
show all references
References:
[1] 
K. Balla, Linear subspaces for linear DAE's of index 1,, Comput. Math. Appl., 32 (1996), 81. Google Scholar 
[2] 
K. Balla, Boundary conditions and their transfer for differential algebraic equations of index 1,, Comput. Math. Appl., 31 (1996), 1. Google Scholar 
[3] 
K. Balla and R. März, Transfer of boundary conditions for DAE's of index 1,, SIAM J. Numer. Anal., 33 (1996), 2318. Google Scholar 
[4] 
K. Balla and R. März, "An Unified Approach to Linear Differential Algebraic Equations and Their Adjoint Equations,", Institute of Mathematics Technical Report, (2000). Google Scholar 
[5] 
K. Balla, K. and R. März, Linear differential algebraic equations and their adjoint equations,, Results in Mathematica, 37 (2000), 13. Google Scholar 
[6] 
K. E. Brenan, S. L. Campbell and L. R. Petzold, "Numerical Solution of InitialValue Problems in DifferentialAlgebraic Equations,", NorthHolland, (1989). Google Scholar 
[7] 
Y. Cao, S. Li, L. Petzold and R. Serben, Adjoint sensitivity analysis for differentialalgebraic equations: Part I, The adjoint DAE system and its numerical solution,, SIAM J. Sci. Comp., 24 (2000), 1076. Google Scholar 
[8] 
Y. Cao, S. Li and L. Petzold, Adjoint sensitivity analysis for differentialalgebraic equations: Algorithms and software,, J. Comput. Appl. Math., 149 (2002), 171. Google Scholar 
[9] 
W. F. Frenery, J. E. Tolsma and P. I. Barton, Efficient sensitivity analysis of largescale differentialalgebraic systems,, Appl. Numer. Math., 25 (1997), 41. Google Scholar 
[10] 
C. W. Gear, Differentialalgebraic equation index transformations,, SIAM J. Sci. Stat. Comput., 9 (1988), 39. Google Scholar 
[11] 
C. W. Gear, Differential algebraic equations, indices and integral algebraic equations,, SIAM J. Numer. Anal., 27 (1990), 1527. Google Scholar 
[12] 
D. R. A. Giles, "A Comparison of Three ProblemOriented Simulation Programs for Dynamic Mechanical Systems,", Thesis, (1978). Google Scholar 
[13] 
E. Hairer, Ch. Lubich and M. Roche, "The Numerical Solution of DifferentialAlgebraic Equations by RungeKutta Methods,", Lecture Notes in Mathematics, 1409 (1989). Google Scholar 
[14] 
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II,", SpringerVerlag, (1996). Google Scholar 
[15] 
A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker and C. S. Woodward, "SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers,", preprint, (2004). Google Scholar 
[16] 
L. Kershenbaum, D. Q. Mayne, R. Pytlak and R. B. Vinter, Receding horizon control,, in, (1993), 20. Google Scholar 
[17] 
S. Li and L. R. Petzold, Software and algorithms for sensitivity analysis of largescale differentialalgebraic systems,, J. Comput. Appl. Math., 125 (2000), 131. Google Scholar 
[18] 
S. Li, L. R. Petzold and W. Zhu, Sensitivity analysis of differentialalgebraic equations: A comparison of methods on a special problem,, Appl. Numer. Math., 32 (2000), 161. Google Scholar 
[19] 
T. Maly, and L. R. Petzold, Numerical methods and software for sensitivity analysis of differentialalgebraic systems,, Appl. Numer. Math., 20 (1997), 57. Google Scholar 
[20] 
D. W. Manning, "A Computer Technique for Simulating Dynamic Multibody Systems Based on Dynamic Formalizm,", Thesis, (1981). Google Scholar 
[21] 
R. März, Differential algebraic systems anew,, Applied Numetical Mathematics, 42 (2002), 315. Google Scholar 
[22] 
R. März, Characterizing differential algebraic equations without the use of derivative arrays,, Int. J. Comp. & Mathem. with Appl., 50 (2005), 1141. Google Scholar 
[23] 
M. D. R. de Pinho and R. Vinter, Necessary conditions for optimal control problems involving nonlinear differential algebraic equations,, J. Math. Anal. Appl., 212 (1997), 493. Google Scholar 
[24] 
R. Pytlak, Optimal control of differentialalgebraic equations,, Proceed. of the 33rd IEEE CDC, (1994), 951. Google Scholar 
[25] 
R. Pytlak, "Numerical Methods for Optimal Control Problem With State Constraints,", Lecture Notes in Mathematics, 1707 (1999). Google Scholar 
[26] 
R. Pytlak, Optimal control of differentialalgebraic equations of higher index, Part 1: First order approximations,, J. Optimization Theory and Applications, 134 (2007), 61. Google Scholar 
[27] 
R. Pytlak, Optimal control of differentialalgebraic equations of higher index, Part 2: Necessary optimality conditions,, J. Optimization Theory and Applications, 134 (2007), 77. Google Scholar 
[28] 
R. Pytlak and R. B. Vinter, A feasible directions algorithm for optimal control problems with state and control constraints: Convergence analysis,, SIAM J. Control and Optimization, 36 (1998), 1999. Google Scholar 
[29] 
R. Pytlak and R. B. Vinter, A feasible directions type algorithm for optimal control problems with state and control constraints: Implementation,, J. Optimization Theory and Applications, 101 (1999), 623. Google Scholar 
[30] 
W. Schiehlen (ed.), "Mulitbody Systems Handbook,", SpringerVerlag, (1990). Google Scholar 
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