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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), 8186. Google Scholar 
[2] 
K. Balla, Boundary conditions and their transfer for differential algebraic equations of index 1, Comput. Math. Appl., 31 (1996), 15. Google Scholar 
[3] 
K. Balla and R. März, Transfer of boundary conditions for DAE's of index 1, SIAM J. Numer. Anal., 33 (1996), 23182332. 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, Humboldt University, Berlin, 2000. Google Scholar 
[5] 
K. Balla, K. and R. März, Linear differential algebraic equations and their adjoint equations, Results in Mathematica, 37 (2000), 1335. Google Scholar 
[6] 
K. E. Brenan, S. L. Campbell and L. R. Petzold, "Numerical Solution of InitialValue Problems in DifferentialAlgebraic Equations," NorthHolland, New York, 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), 10761089. 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), 171191. 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), 4154. Google Scholar 
[10] 
C. W. Gear, Differentialalgebraic equation index transformations, SIAM J. Sci. Stat. Comput., 9 (1988), 3947. Google Scholar 
[11] 
C. W. Gear, Differential algebraic equations, indices and integral algebraic equations, SIAM J. Numer. Anal., 27 (1990), 15271534. Google Scholar 
[12] 
D. R. A. Giles, "A Comparison of Three ProblemOriented Simulation Programs for Dynamic Mechanical Systems," Thesis, Univ. Waterloo, Ontario, 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, SpringerVerlag, Berlin, Heidelberg, 1989. Google Scholar 
[14] 
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II," SpringerVerlag, Berlin Heidelberg New York, 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, UCRLJRNL200037, 2004. Google Scholar 
[16] 
L. Kershenbaum, D. Q. Mayne, R. Pytlak and R. B. Vinter, Receding horizon control, in "Advances in ModelBased Predictive Control, Oxford, September 2021, Conference Proceedings," 1993. 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), 131145. 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), 161174. Google Scholar 
[19] 
T. Maly, and L. R. Petzold, Numerical methods and software for sensitivity analysis of differentialalgebraic systems, Appl. Numer. Math., 20 (1997), 5779. Google Scholar 
[20] 
D. W. Manning, "A Computer Technique for Simulating Dynamic Multibody Systems Based on Dynamic Formalizm," Thesis, Univ. Waterloo, Ontario, 1981. Google Scholar 
[21] 
R. März, Differential algebraic systems anew, Applied Numetical Mathematics, 42 (2002), 315335. Google Scholar 
[22] 
R. März, Characterizing differential algebraic equations without the use of derivative arrays, Int. J. Comp. & Mathem. with Appl., 50 (2005), 11411156. 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), 493516. Google Scholar 
[24] 
R. Pytlak, Optimal control of differentialalgebraic equations, Proceed. of the 33rd IEEE CDC, Orlando, Florida, (1994), 951956. Google Scholar 
[25] 
R. Pytlak, "Numerical Methods for Optimal Control Problem With State Constraints," Lecture Notes in Mathematics, 1707, SpringerVerlag, 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), 6175. 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), 7790. 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), 19992019. 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), 623649. Google Scholar 
[30] 
W. Schiehlen (ed.), "Mulitbody Systems Handbook," SpringerVerlag, Berlin, 1990. Google Scholar 
show all references
References:
[1] 
K. Balla, Linear subspaces for linear DAE's of index 1, Comput. Math. Appl., 32 (1996), 8186. Google Scholar 
[2] 
K. Balla, Boundary conditions and their transfer for differential algebraic equations of index 1, Comput. Math. Appl., 31 (1996), 15. Google Scholar 
[3] 
K. Balla and R. März, Transfer of boundary conditions for DAE's of index 1, SIAM J. Numer. Anal., 33 (1996), 23182332. 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, Humboldt University, Berlin, 2000. Google Scholar 
[5] 
K. Balla, K. and R. März, Linear differential algebraic equations and their adjoint equations, Results in Mathematica, 37 (2000), 1335. Google Scholar 
[6] 
K. E. Brenan, S. L. Campbell and L. R. Petzold, "Numerical Solution of InitialValue Problems in DifferentialAlgebraic Equations," NorthHolland, New York, 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), 10761089. 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), 171191. 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), 4154. Google Scholar 
[10] 
C. W. Gear, Differentialalgebraic equation index transformations, SIAM J. Sci. Stat. Comput., 9 (1988), 3947. Google Scholar 
[11] 
C. W. Gear, Differential algebraic equations, indices and integral algebraic equations, SIAM J. Numer. Anal., 27 (1990), 15271534. Google Scholar 
[12] 
D. R. A. Giles, "A Comparison of Three ProblemOriented Simulation Programs for Dynamic Mechanical Systems," Thesis, Univ. Waterloo, Ontario, 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, SpringerVerlag, Berlin, Heidelberg, 1989. Google Scholar 
[14] 
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations II," SpringerVerlag, Berlin Heidelberg New York, 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, UCRLJRNL200037, 2004. Google Scholar 
[16] 
L. Kershenbaum, D. Q. Mayne, R. Pytlak and R. B. Vinter, Receding horizon control, in "Advances in ModelBased Predictive Control, Oxford, September 2021, Conference Proceedings," 1993. 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), 131145. 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), 161174. Google Scholar 
[19] 
T. Maly, and L. R. Petzold, Numerical methods and software for sensitivity analysis of differentialalgebraic systems, Appl. Numer. Math., 20 (1997), 5779. Google Scholar 
[20] 
D. W. Manning, "A Computer Technique for Simulating Dynamic Multibody Systems Based on Dynamic Formalizm," Thesis, Univ. Waterloo, Ontario, 1981. Google Scholar 
[21] 
R. März, Differential algebraic systems anew, Applied Numetical Mathematics, 42 (2002), 315335. Google Scholar 
[22] 
R. März, Characterizing differential algebraic equations without the use of derivative arrays, Int. J. Comp. & Mathem. with Appl., 50 (2005), 11411156. 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), 493516. Google Scholar 
[24] 
R. Pytlak, Optimal control of differentialalgebraic equations, Proceed. of the 33rd IEEE CDC, Orlando, Florida, (1994), 951956. Google Scholar 
[25] 
R. Pytlak, "Numerical Methods for Optimal Control Problem With State Constraints," Lecture Notes in Mathematics, 1707, SpringerVerlag, 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), 6175. 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), 7790. 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), 19992019. 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), 623649. Google Scholar 
[30] 
W. Schiehlen (ed.), "Mulitbody Systems Handbook," SpringerVerlag, Berlin, 1990. Google Scholar 
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