Techniques in computational stochastic dynamic programming

Control and Dynamic Systems

Volumn 76, Issue C, 1996, Pages 103-162

  Hanson, Floyd B ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000740418     PISSN: 00905267     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0090-5267(96)80017-X     Document Type: Chapter

References (121)

1. Akian M., Chancelier J.P., and Quadrat J.P. Dynamic Programming Complexity and Applications. Proceedings of 27th IEEE Conference on Decision and Control 2 (1988) 1551-1558
2. Anderson B.D.O., and Moore J.B. Optimal Control: Linear Quadratic Methods (1990), Prentice Hall, Englewood Cliffs, NJ
3. Arnold L. Stochastic Equations: Theory and Applications (1974), Wiley, New York, NY
4. Ascher U., Christiansen J., and Russell R.D. A Collocation Solver for Mixed Order Systems of Boundary Value Problems. Mathematics of Computation 33 (1979) 659-679
5. Ascher U., Christiansen J., and Russell R.D. Collocation Software for Boundary-Value ODEs. ACM Transactions on Mathematical Software 7 (1981) 209-222
6. Athans M., Castanon D., Dunn K.P., Greene C.S., Lee W.H., Sandell Jr. N.R., and Willsky A.S. The Stochastic Control of the F-8c Aircraft Using a Multiple Model Adaptive Control (MMAC) Method-Part I: Equilibrium Flight. IEEE Transactions on Automatic Control AC-22 (1977) 768-780
7. Bell G. Ultracomputers: A Teraflop Before Its Time. Communications of ACM 35 8 (1992) 26-47
8. Bellman R.E. Dynamic Programming (1957), Princeton University Press, Princeton, NJ
9. Bellman R.E. Adaptive Control Processes: A Guided Tour (1961), Princeton University Press, Princeton, NJ
10. Brandt A. Multilevel Computations: Review and Recent Developments. In: McCormick S.F. (Ed). Multigrid Methods: Theory, Applications, and Supercomputing (1988), Marcel Dekker, New York 35-62
11. Briggs W.L. Multigrid Tutorial (1987), Society for Industrial and Applied Mathematics, Philadelphia, PA
12. Bryson A.E., and Ho Y. Applied Optimal Control (1969), Ginn, Waltham, MA
13. Calvet J.L., Dantas de Melo J., and Garcia J.M. A Fast Parallel Dynamic Programming Algorithm for Optimal Control. Proceedings of 1990 American Control Conference (1990) 3
14. Casti J., Richardson M., and Larson R. Dynamic Programming and Parallel Computers. Journal of Optimization Theory and Applications 12 4 (1973) 423-786
15. Caffey H., Liao L.-Z., and Shoemaker C.A. Parallel Processing of Large Scale Discrete-Time Unconstrained Differential Dynamic Programming. Parallel Computing 19 (1993) 1003-1017
16. Chang L.-C., Shoemaker C.A., and Liu P.L.-F. Optimal Time-Varying Pumping Rates for Groundwater Remediation: Application of a Constrained Optimal Control Algorithm. Water Resources Research 28 12 (1992) 3157-3173
17. Chung S.-L., and Hanson F.B. Parallel Optimizations for Computational Stochastic Dynamic Programming. In: Yew P.-C. (Ed). Proceedings of 1990 International Conference on Parallel Processing 3: Algorithms and Applications (1990) 254-260
18. Chung S.-L., and Hanson F.B. Optimization Techniques for Stochastic Dynamic Programming. Proceedings of 29th IEEE Conference on Decision and Control 4 (1990) 2450-2455
19. Chung S.-L., Hanson F.B., and Xu H. Supercomputer Optimizations for Stochastic Optimal Control Applications. In: Taylor L.W. (Ed). Proceedings of 4th NASA Workshop on Computational Control of Flexible Aerospace Systems, NASA Conf. Publ. 10065, Part 1. NASA Langley Research Center (March 1991) 57-70
20. Chung S.-L., Hanson F.B., and Xu H.H. Parallel Stochastic Dynamic Programming: Finite Element Methods. Linear Algebra and Applications 172 (1992) 197-218
21. Crandall M.G., and Lions P.L. Two Approximations of Solutions of Hamilton Jacobi Equations. Mathematics of Computation 43 (1984) 1-19
22. Crandall M.G., Ishii H., and Lions P.L. User's Guide to Viscosity Solutions of Second Order Partial Differential Equations. Bulletin of the AMS 27 1 (1992) 1-67
23. Crow M.L., Tylavsky D.J., and Bose A. Concurrent Processing in Power System Analysis. In: Leondes C.T. (Ed). Control and Dynamical Systems: Advances in Theory and Applications 42 (1991), Academic Press, New York, NY 1-55
24. Culver T., and Shoemaker C.A. Dynamic Optimal Control for Groundwater Remediation with Flexible Management Periods. Water Resources Research 28 3 (1992) 629-641
25. Culver T., and Shoemaker C.A. Optimal Control for Groundwater Remediation by Differential Dynamic Programming with Quasi-Newton Approximations. Water Resources Research 29 4 (1993) 823-831
26. Dantas de Melo J., Calvet J.L., and Garcia J.M. Vectorization and Multitasking of Dynamic Programming in Control: Experiments on a Cray-2. Parallel Computing 13 (1990) 261-269
27. Dyer P., and McReynolds S.R. The Computation and Theory of Optimal Control (1970), Academic Press, New York, NY
28. 8 pages. Decker N.H. On the Parallel Efficiency of the Frederickson-McBryan Multigrid Algorithm. ICASE Report No. 90-17 (February 1990), NASA Langley Research Center, Hampton, VA
29. Dongarra J.J., Duff I.S., Sorensen D.C., and van der Vorst H.A. Solving Linear Systems on Vector and Shared Memory Computers (1991), Society for Industrial and Applied Mathematics, Philadelphia, PA
30. 31 pages. Dongarra J.J., Meyer H.W., and Strohmaier E. TOP500 Supercomputer Sites (November 1994), Computer Center, University of Mannheim. http://www.unimannheim.de/info/rumdoc/top500.ps.Z
31. Douglas Jr. J., and Dupont T. Galerkin Methods of Parabolic Equations. SIAM J. Numerical Analysis 7 (1970) 575-626
32. Douglas Jr. J. Time Step Procedures of Nonlinear Parabolic PDEs. In: Whiteman J. (Ed). Mathematics of Finite Elements and Applications, MAFELAP (1979), Academic Press, London 289-304
33. Dreyfus S.E. Dynamic Programming and the Calculus of Variations (1965)
34. Dyksen W.R., Houstis E.N., Lynch R.E., and Rice J.R. The Performance of the Collocation and Galerkin Methods with Hermite Bicubics. SIAM J. Numerical Analysis 21 (1984) 695-715
35. Feiner S., and Beshers C. Visualizing n-Dimensional Virtual Worlds with n-Vision. Computer Graphics: Special Issue on 3D Interactive Graphics 24 2 (1990) 37-38
36. Feldstein A., and Neves K.W. High Order Methods for State-Dependent Delay Differential Equations with Nonsmooth Solution. SIAM J. Numerical Analysis 21 (1984) 844-863
37. Flaherty J.E., and O'Malley Jr. R.E. Numerical Methods of Stiff Systems of Two-Point Boundary Value Problems. SIAM J. Scientific and Statistical Computing 5 (1984) 865-886
38. Fleming W.H., and Rishel R.W. Deterministic and Stochastic Optimal Control (1975), Springer-Verlag, New York, NY
39. (J. Basic Engr. 2). Florentin J.J. Optimal Control of Systems with Generalized Poisson Inputs. ASME Trans. 85D (1963) 217-221
40. Frederickson P.O., and McBryan O.A. Parallel Superconvergent Multigrid. In: McCormick S.F. (Ed). Multigrid Methods: Theory, Applications, and Supercomputing (1988), Marcel Dekker, New York 195-210
41. In: Boyle A., Caviness B.F., Hearn A.C., and Chairperson W. (Eds). Future Directions for Research in Symbolic Computations: Report of Workshop on Symbolic and Algebraic Computing (1990), Society for Industrial and Applied Mathematics, Philadelphia, PA
42. In: Fleming, and Chairman W.H. (Ed). Future Directions in Control Theory: A Mathematical Perspective (1988), Society for Industrial and Applied Mathematics, Philadelphia, PA
43. Gihman I.I., and Skorohod A.V. Stochastic Differential Equations (1972), Springer-Verlag, New York, NY
44. Gihman I.I., and Skorohod A.V. Controlled Stochastic Processes (1979), Springer-Verlag, New York, NY
45. Grand Challenges: High Performance Computing and Communications: The FY 1993 U.S Research and Development Program (1993), Federal Coordinating Council for Science, Engineering, and Technology, Committee on Physical, Mathematical, and Engineering Sciences, c/o National Science Foundation (CISE), Washington, DC
46. High Performance Computing and Communications: Technology and Communications for the National Information Infrastructure: The 1995 Blue Book (1995), National Coordination Office for HPCC, Arlington, VA. http://www.hpcc.gov/
47. Guan X.-H., and Luh P.B. A New Parallel Algorithm for Optimal Control Problems of Interconnected Systems. International Journal of Control 56 6 (1992) 1275-1297
48. Hackbush W. Parabolic Multigrid Methods. In: Glowinski R., and Lions J.-L. (Eds). Computing Methods in Applied Sciences and Engineering 6 (1984), North Holland, Amsterdam 189-197
49. Hanson F.B. Analysis of a Singular Functional Differential Equation that Arises from Stochastic Modeling of Population Growth. Journal of Mathematical Analysis and Applications 96 (1983) 73-100
50. Hanson F.B. Bioeconomic Model of the Lake Michigan Alewife Fishery. Canadian Journal of Fisheries and Aquatic Sciences 44 Suppl. 2 (1987) 298-305
51. Hanson F.B. Vector Multiprocessor Implementation for Stochastic Dynamic Programming. IEEE Distributed Processing Technical Committee Newsletter 10 (1988) 44-48
52. 26 pages. Hanson F.B. Computational Dynamic Programming for Stochastic Optimal Control on a Vector Multiprocessor. Argonne National Laboratory Technical Memorandum ANL/MCS-TM-113 (June 1988)
53. Hanson F.B. Parallel Computation for Stochastic Dynamic Programming: Row versus column code orientation. Proc. 1988 IEEE Conf. on Parallel Processing 3: Algorithms and Applications (1988) 117-119
54. Hanson F.B. Parallel and vector computation for optimal control applications. In: Bernard D.E., and Man G.K. (Eds). Proceedings of 3rd Annual Conference on Aerospace Computational Control, JPL Publication 85-45 1 (December 15, 1989), Jet Propulsion Laboratory, Pasadena 184-197
55. Hanson F.B. Stochastic Dynamic Programming: Advanced Computing Constructs. Proceedings of 28th IEEE Conference on Decision and Control 1 (1989) 901-903
56. Hanson F.B. A Real Introduction to Supercomputing: A User Training Course. Proceedings of Supercomputing '90 (1990) 376-385
57. Hanson F.B. Computational Dynamic Programming on a Vector Multiprocessor. IEEE Transactions on Automatic Control 36 4 (1991) 507-511
58. Hanson F.B., Jarvis D.J., and Xu H.H. Applications of FORALL-Formed Computations in Large Scale Stochastic Dynamic Programming. Proceedings of Scalable High Performance Computing Conference: SHPCC-92. IEEE Computer Society (1992) 182-185
59. Hanson F.B., and Naimipour K. Convergence of Numerical Method for Multistate Stochastic Dynamic Programming. Proceedings of International Federation of Automatic Control 12th World Congress 9 (1993) 501-504
60. Hanson F.B., Pratico C.J., Vetter M.S., and Xu H.H. Multidimensional Visualization Applied to Renewable Resource Management. Proceedings of Sixth SIAM Conference on Parallel Processing for Scientific Computing 2 (1993) 1033-1036
61. Hanson F.B., and Ryan D. Optimal harvesting in a Stochastic Environment with Density Dependent Jumps. In: Lamberson R. (Ed). Mathematical Models of Renewable Resources 3 (1984), Association of Resource Modelers, Arcata, Cal. 117-123
62. Hanson F.B., and Ryan D. Optimal Harvesting with Density Dependent Random Effects. Natural Resource Modeling 2 (1987) 439-455
63. Hanson F.B., and Tuckwell H.C. Logistic Growth with Random Density Independent Disasters. Theoretical Population Biology 19 (1981) 1-18
64. Hanson F.B., and Westman J.J. Computational Stochastic Dynamic Programming Problems: Groundwater Quality Remediation. Proceedings of 33rd IEEE Conference on Decision and Control 1 (1994) 6 pages
65. Horton G., and Vandewalle S. A Space-Time Multigrid Method for Parabolic PDEs. SIAM J. Scientific Computing (1995) 17 pages
66. Jacobson D.H., and Mayne D.Q. Differential Dynamic Programming (1970), American Elsevier, New York, NY
67. Jazwinski A.H. Stochastic Processes and Filtering Theory (1970), Academic Press, New York, NY
68. Johnson M.B. The Application Communication Library (1992), MIT Media Laboratory, Cambridge, MA
69. Johnsson S.L., and Mathur K.K. The Finite Element Method on a Data Parallel Computing. International Journal of High Speed Computing 1 (1989) 29-44
70. Jones L.D., Willis R., and Yeh W.W.-G. Optimal Control of Nonlinear Groundwater Hydraulics Using Differential Dynamic Programming. Water Resources Research 23 (1987) 2097-2106
71. Kerrigan J.F. Migrating to Fortran 90 (1993), O'Reilly & Associates, Sebastopol, CA
72. Koelbel C.H., Loveman D.B., Schreiber R.S., Steele Jr. G.L., and Zosel M.E. The High Performance Fortran Handbook (1994), MIT Press, Cambridge, MA
73. Kushner H.J. A Survey of Some Applications of Probability and Stochastic Control Theory to Finite Difference Methods for Degenerate Elliptic and Parabolic Equations. SIAM Review 18 (1976) 545-577
74. Kushner H.J. Probability Methods for Approximations in Stochastic Control and for Elliptic Equations (1977), Academic Press, New York, NY
75. Kushner H.J. Numerical Methods for Stochastic Control in Continuous Time. SIAM J. Control and Optimizations 28 (1990) 999-1048
76. Kushner H.J., and Dupuis P.G. Numerical Methods for Stochastic Control in Continuous Time (1992), Springer-Verlag, New York, NY
77. 6 pages. Kushner H.J., and Jarvis D.J. Large-Scale Computations for High Dimension Control Systems. Proceedings of 33rd IEEE Conference on Decision and Control 1 (1994)
78. Kushner H.J., and Yang J.-C. A Numerical Method for Controlled Routing in Large Trunk Line Networks via Stochastic Control Theory. ORSA Journal on Computing 6 3 (1994) 300-316
79. Liao L.-Z., and Shoemaker C.A. Convergence in Unconstrained Discrete-Time Differential Dynamic Programming. IEEE Transactions on Automatic Control 36 6 (1991) 692-706
80. Larson R.E. Dynamic Programming with Reduced Computational Requirements. IEEE Transactions on Automatic Control AC-14 (1965) 135-143
81. Larson R.E. A Survey of Dynamic Programming Computational Procedures. IEEE Transactions on Automatic Control AC-16 (1967) 767-774
82. Larson R.E. State Increment Dynamic Programming (1968), American Elsevier, New York, NY
83. Larson R.E., and Tse E. Parallel Processing Algorithms for the Optimal Control of Nonlinear Systems. IEEE Transactions on Automatic Control AC-22 (1973) 777-786
84. Levesque J.M., and Williamson J.W. A Guidebook to FORTRAN on Supercomputers (1988), Academic Press, NY
85. Ludwig D. Optimal Harvesting of a Randomly Fluctuating Resource. I: Application of Perturbation Methods. SIAM J. Applied Mathematics 37 (1979) 185-205
86. Ludwig D., and Varah J.M. Optimal Harvesting of a Randomly Fluctuating Resource. II: Numerical Methods and Results. SIAM J. Applied Mathematics 37 (1979) 185-205
87. Luus R. Optimal Control by Dynamic Programming Using Systematic Reduction in Grid Size. International Journal of Control 51 5 (1990) 995-1013
88. Luus R. Application of Dynamic Programming to Higher-Dimensional Non-Linear Optimal Control Problems. International Journal of Control 52 1 (1990) 239-250
89. McCormack S.F. Multigrid Methods (1987), Society for Industrial and Applied Mathematics, Philadelphia, PA
90. Mathur K.K., and Johnsson S.L. Data Structures and Algorithms for the Finite Element Method, on a Data Parallel Supercomputer. International Journal on Numerical Methods in Engineering (1989)
91. Mayne D.Q. A Second-Order Gradient Method for Determining Optimal Control of Non-Linear Discrete Time Systems. International Journal of Control 3 (1966) 85-95
92. Mayne D.Q. Differential Dynamic Programming-A Unified Approach to the Optimization of Dynamical Systems. In: Leondes C.T. (Ed). Control and Dynamical Systems: Advances in Theory and Applications 10 (1973), Academic Press, New York, NY 179-254
93. Mitchell A.R., and Wait R. The Finite Element Method in Partial Differential Equations (1977), Wiley, New York
94. Mufti I.H. Computational Methods in Optimal Control Problems Lecture Notes in Operations Research and Mathematical Systems 27 (1970), Springer-Verlag, Berlin, Germany
95. Murray D.M., and Yakowitz S.J. Differential Dynamic Programming and Newton's Method for Discrete Optimal Control Problems. Journal of Optimization and Applications 43 (1984) 395-414
96. Naimipour K., and Hanson F.B. Convergence of a Numerical Method for the Bellman Equation of Stochastic Optimal Control with Quadratic Costs and Constrained Control. Dynamics and Control 3 3 (1993) 237-259
97. In: Revecheé H.J., and Chair (Eds). A National Computing Initiative: The Agenda for Leadership (1987), Society for Industrial and Applied Mathematics, Philadelphia, PA
98. Mark H. Overmars, "A Graphical User Interface Toolkit for Silicon Graphics Workstations," Dept. Computer Science, Utrecht University, P.O. Box 80.089 TB, Utrecht, The Netherlands.
99. Polak E. Computational Methods in Optimization (1971), Academic Press, New York, NY
100. Polak E. An Historical Survey of Computational Methods in Optimal Control. SIAM Review 15 (1973) 553-584
101. Polychronopoulos C.D. Parallel Programming and Compilers (1988), Kluwer Academic, Boston, MA
102. color plates p. 843. Pratico C.J., Hanson F.B., Xu H.H., Jarvis D.J., and Vetter M.S. Visualization for the Management of Renewable Resources in an Uncertain Environment. Proceedings of Supercomputing '92 (1992) 258-266
103. Rabbani R.G., and Warner J.W. Shortcomings of Existing Finite Element Formulations for Subsurface Water Pollution Modeling and Its Rectification: One-Dimensional Case. SIAM J. Applied Mathematics 54 3 (1994) 660-673
104. Ryan D., and Hanson F.B. Optimal Harvesting with Exponential Growth in an Environment with Random Disasters and Bonanzas. Mathematical Biosciences 74 (1985) 37-57
105. Ryan D., and Hanson F.B. Optimal Harvesting of a Logistic Population in an Environment with Stochastic Jumps. Journal of Mathematical Biology 24 (1986) 259-277
106. Schuss Z. Theory and Applications of Stochastic Differential Equations (1980), Wiley, New York, NY
107. Snyder D.L., and Miller M.I. Random Point Processes in Time and Space (1991), Springer-Verlag, New York, NY
108. Souganidis P.E. Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations. Journal of Differential Equations 59 (1985) 1-43
109. Stengel R.F. Stochastic Optimal Control (1986), Wiley, New York, NY
110. Strang G., and Fix G.J. An Analysis of the Finite Element Method (1973), Prentice-Hall, Englewood Cliffs, NJ
111. In: Messina P., and Sterling T. (Eds). System Software and Tools for High Performance Computing Environments (1988), Society for Industrial and Applied Mathematics, Philadelphia, PA
112. Thinking Machines Corporation. Connection Machine Model CM-5 Technical Summary, Cambridge, MA (November 1992)
113. 23 pages. Weerawarana S., and Wang P.S. A Portable Code Generator for Parallel Cray Fortran. Kent State University Preprint (June 1989)
114. Wonham W.M. Random Differential Equations in Control Theory. Probabilistic Methods in Applied Mathematics 2 (1970), Academic Press, New York 131-212
115. Xirouchakis P.C., and Wang P.Y. In: Leondes C.T. (Ed). Finite Element Computing on Parallel Architectures. Control and Dynamical Systems: Advances in Theory and Applications 58 (1993), Academic Press, New York, NY 233-260
116. Xu H.H., Hanson F., and Chung S.L. Optimal Data Parallel Methods for the Stochastic Dynamical Programming. In: So K. (Ed). Proceedings of 1991 International Conference on Parallel Processing 3: Algorithms & Applications (1991) 142-146
117. Xu H.H., Hanson F., and Chung S.L. Parallel Solutions of Dimensionality Problems for the Stochastic Dynamical Programming. Proceedings of 30th IEEE Conference on Decision and Control 2 (1991) 1717-1723
118. Xu H.H., Jarvis D.J., and Hanson F.B. Parallel Data Vault Methods for Larger Scale Stochastic Dynamic Programming. Proceedings of 1992 American Control Conference 1 (1992) 142-146
119. Yakowitz S. Dynamic Programming Applications in Water Resources. Water Resources Research 18 (1982) 673-696
120. Yakowitz S. Algorithms and Computational Techniques in Differential Dynamic Programming. In: Leondes C.T. (Ed). Control and Dynamical Systems: Advances in Theory and Applications 31 (1989), Academic Press, New York, NY 75-91
121. Yakowitz S., and Rutherford B. Computational Aspects of Discrete-Time Control. Applied Mathematics and Computation 15 (1984) 29-45