A gradient-type algorithm for the numerical solution of two-player zero-sum differential game problems

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1. J. Doležal P. Černý, The application of optimal control methods to the determination of multifunctional catalysts, 23rd CHISA Conference, Mariánské Lázně 1976. See also: Automatizace 21 (1978), 1, 3-8. In Czech. (1976) 
2. J. Doležal P. Černý, Numerical solution of differential games, In "Proceedings of Cybernetics Conference", Czechoslovak Cybernetical Society, Prague 1976, 39-51. In Czech. (1976) 
3. J. Doležal, A Numerical Approach to the Solution of Differential Games, Research Resort No. 709, Institute of Information Theory and Automation, Prague 1976. (1976) 
4. J. Doležal, Optimal parameter estimation in two-player zero-sum differential games, In "Transactions of the 8th Prague Conference on Information Theory, Statistical Decision Functions, Random Processes", Academia, Prague 1978, 143-156. (1978) MR0536774
5. J. Doležal, Parameter optimization for two-player zero-sum differential games, Transactions ASME, Ser. G. J. Dynamic Systems, Measurement, and Control. Submitted for publication. 
6. J. Doležal M. Thoma, On the numerical solution of N-player nonzero-sum differential games, Problems of Control and Information Theory. Submitted for publication. 
7. R. Isaacs, Differential Games, Wiley, New York 1965. (1965) Zbl0125.38001MR0210469
8. L. S. Pontrjagin, On differential games theory, Uspechi Mat. Nauk XXI (1966), 4, 219-274. In Russian. (1966) MR0204187
9. L. D. Berkovitz, Necessary conditions for optimal strategies in a class of differential games and control problems, SIAM J. Control 5 (1967), 1, 1-24. (1967) Zbl0156.10102MR0209027
10. B. N. Pšeničnyj, Structure of differential games, Dokl. Acad. Nauk SSSR 184 (1969), 2, 285 - 287. In Russian. (1969) MR0242511
11. A. V. Balakrishnan L. W. Neustadt (eds.)., Mathematical Theory of Control, Academic Press, New York 1967. (1967) MR0252054
12. Y. C. Ho G. Leitmann (eds.), Proceedings of the First International Conference on the Theory and Applications of Differential Games, Amherst, Mass. 1969. (1969) 
13. A. Blaquiere F. Gerard G. Leitmann, Quantitative and Qualitative Games, Academic Press, New York 1969. (1969) MR0261973
14. N. N. Krasovskij, Pursuit-Evasion Game Problems, Nauka, Moscow 1970. In Russian. (1970) 
15. A. Friedman, Differential Games, Wiley-Interscience, New York 1971. (1971) Zbl0231.90068MR0421700
16. P. Varaiya J. Lin, Existence of saddle points in differential Games, SIAM J. Control 7 (1969), 1, 141-157. (1969) 
17. R. J. Elliott N. J. Kalton L. Marcus, Saddle points for linear differential games, SIAM J. Control 11 (1973), 1, 100-112. (1973) MR0325164
18. T. Parthasarathy T. E. S. Raghavan, Existence of saddle points and Nash equilibrium points for differential games, SIAM J. Control 11 (1975), 5, 977-980. (1975) MR0406555
19. D. J. Wilson, Mixed strategy solutions for quadratic games, J. Optimization Theory Appl. 13 (1974), 3, 319-333. (1974) Zbl0258.90051MR0345657
20. H. W. Kuhn G. P. Szegö (eds.), Differential Games and Related Topics, North-Holland, Amsterdam 1971. (1971) MR0274063
21. A. Blaquière (ed.), Topics in Differential Games, North-Holland, Amsterdam 1973. (1973) MR0351470
22. J. D. Grote (ed.), Theory and Applications of Differential Games, Reidel, Dordrecht 1975. (1975) 
23. P. Hagedorn H. W. Knobloch G. J. Olsder (eds.), Differential Games and Applications, Springer-Verlag, Berlin 1977. (1977) MR0475944
24. E. Cockayne, Plane pursuit with curvature constraints, SIAM J. Appl. Math. 15 (1967), 6, 1511-1517. (1967) Zbl0158.38902MR0224378
25. A. W. Merz, The game of two identical cars, J. Optimization Theory Appl. 9 (1972), 5, 324-343. (1972) Zbl0223.90035MR0297411
26. J. P. Marec, Nguyen Van Nhan, Two-dimensional pursuit-evasion game with penalty on turning rates, J. Optimization Theory Appl. 23 (1977), 2, 305 - 345. (1977) Zbl0344.90047MR0469304
27. N. N. Krasovskij A. I. Subbotin, Positional Differential Games, Nauka, Moscow 1974. In Russian. (1974) MR0437107
28. Y. C. Ho A. E. Bryson, Jr. S. Baron, Differential games and optimal pursuit-evasion strategies, IEEE Trans. Automatic Control AC-10 (1965), 4, 385-389. (1965) MR0184747
29. Y. C. Ho, Differential games, dynamic optimization, and generalized control theory. Survey paper, J. Optimization Theory Appl. 6 (1970), 3, 179-209. (1970) MR0278752
30. D. Tabac, Numerical solutions of differential game problems, Int. J. Systems Sci. 6 (1975), 6, 591-599. (1975) 
31. A. W. Starr, Computation of Nash equilibria for nonlinear nonzero-sum differential games, See [12], IV 13-18. 
32. V. H. Quintana E. J. Davison, Two numerical techniques to solve differential game problems, Int. J. Control 16 (1972), 3, 465-474. (1972) MR0314475
33. V. Gourishankar A. Salama, A technique for solving a class of differential games, Int. J. Control 15 (1972), 3, 529-539. (1972) 
34. J. Doležal, Differential Dynamic Programming Approach to the Numerical Solution of Differential Games, Research Report No. 372, Institute of Information Theory and Automation, Prague 1971. In Czech. (1971) 
35. R. G. Graham C. T. Leondes, Solution of differential games by quasilinearization, Int. J. Systems Sci. 5 (1974), 6, 523-544. (1974) MR0465233
36. J. Hartung, Penalty-methods for optimal control problem and differential games, In "Optimization and Optimal Control Conference", Lecture Notes in Mathematics No. 477, Springer-Verlag, Berlin 1975. In German. (1975) 
37. L. W. Taylor, Jr., Application of the epsilon technique to a realistic optimal pursuit-evasion problem, J. Optimization Theory Appl. 15 (1975), 6, 685 - 702. (1975) Zbl0281.90103MR1551473
38. N. Leffler C. T. Leondes, An algorithm for the solution of differential games with bounds on the state and control variables - I, II, Comput. Elect. Engng. 2 (1975), 1, 67-81, 83 -94. (1975) 
39. B. N. Grevcov I. O. Meľc, Computation of improving variations for minimax problems without discontinuities in control, Avtomat. i Telemech. (1978), 3, 5-13. (In Russian.) (1978) MR0528448
40. G. M. Anderson, A near-optimal closed-loop solution method for nonsingular zero-sum differential games, J. Optimization Theory Appl. 13 (1974), 4, 303 - 318. (1974) Zbl0258.90058MR0384184
41. G. M. Anderson, A transition matrix method for generating near-optimal closed-loop solutions to non-linear zero-sum differential games, Int. J. Systems Sci. 7 (1976), 5, 529-543. (1976) Zbl0333.90058MR0475921
42. B. Järmark, Near-Optimal Closed-Loop Strategy for Aerial Combat Games, Research Report TRITA-REG-7602, The Royal Institute of Technology, Stockholm 1976. (1976) 
43. S. M. Roberts J. S. Shipman, Two-Point Boundary-Value Problems: Shooting Methods, American Elsevier, New York 1972. (1972) MR0323119
44. F. P. Vasiljev, Lectures on Solution Methods for Extremum Problems, Moscow Univ. Publishers, Moscow 1974. In Russian. (1974) 
45. M. A. Connor M. Vlach, A new augmented penalty function technique for optimal control problems, J. Optimization Theory Appl. 21 (1977), 1, 39 - 49. (1977) MR0442801
46. A. E. Bryson Y. C. Ho, Applied Optimal Control, Blaisdell, Waltham, Mass. 1969. (1969) 
47. P. Černý, Digital Simulation Program SIMFOR for the Solution of Two-Point Boundary-Value Problems, Research Report No. 639, Institute of Information Theory and Automation, Prague 1975. In Czech. (1975) 

1. Jaroslav Doležal, Parameter optimization in nonzero-sum differential games
2. Jaroslav Doležal, On the solution of optimal control problems involving parameters and general boundary conditions