New Approach to Improve the Accuracy in Delayed Information Pursuit-Evasion Games

This chapter presents a new approach to improve the homing performance of a pursuer with delayed information on the evader’s lateral acceleration. This approach reduces the uncertainty set of the pursuer, created due to the estimation delay, by considering not only the current (pure feedback) measurements but also the available measurement history during the period of the estimation delay. The reduced uncertainty set is computed by solving two auxiliary optimization problems. By using the center of the new uncertainty set’s convex hull as a new state variable, the original game is transformed to a nonlinear delayed dynamics game with perfect information for both players. The solution of this new game is obtained in pure strategies for the pursuer and mixed ones for the evader. The value of this game (the guaranteed miss distance) is substantially less than the one obtained in previous works by using only the current measurements.

[1]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[2]  J. Lagnese,et al.  An example of the effect of time delays in boundary feedback stabilization of wave equations , 1985, 1985 24th IEEE Conference on Decision and Control.

[3]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[4]  Y. Ho,et al.  Differential games and optimal pursuit-evasion strategies , 1965 .

[5]  Josef Shinar,et al.  Solution of a delayed Information Linear Pursuit-Evasion Game with Bounded Controls , 1999, IGTR.

[6]  Josef Shinar,et al.  On the Compensation of Imperfect Information in Dynamic Games , 2000, IGTR.

[7]  Jiongmin Yong.  Differential pursuit games , 1987 .

[8]  Michael P. Polis,et al.  An example on the effect of time delays in boundary feedback stabilization of wave equations , 1986 .

[9]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[10]  R. D. Driver.  Introduction to the Theory and Application of Differential Equations with Deviating Arguments (L. E. El’sgol’ts and S. B. Norkin) , 1975 .

[11]  A. Halanay,et al.  Differential Games with Delay , 1968 .

[12]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[13]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[14]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[15]  V. S. Patsko,et al.  Optimal strategies in a pursuit problem with incomplete information , 1995 .

[16]  Moustafa A. Soliman,et al.  Optimal feedback control for linear-quadratic systems having time delays† , 1972 .

[17]  A. Ioffe,et al.  Theory of extremal problems , 1979 .

[18]  J. Shinar,et al.  Optimal Evasion from a Pursuer with Delayed Information , 2001 .

[19]  John L. Casti,et al.  Introduction to the theory and application of differential equations with deviating arguments , 1973 .

[20]  N. N. Bautin,et al.  Qualitative study of a certain equation of the theory of phase automatic frequency control: PMM vol. 34, n≗5, 1970, pp. 850–860 , 1970 .

[21]  Alain Bensoussan,et al.  Representation and Control of Infinite Dimensional Systems, 2nd Edition , 2007, Systems and control.

[22]  Michael D. Ciletti,et al.  New results in the theory of differential games with information time lag , 1971 .

[23]  N.Yu. Lukoyanov,et al.  Problems of conflict control of high dimensionality functional systems , 1998 .

[24]  Josef Shinar,et al.  Nonorthodox Guidance Law Development Approach for Intercepting Maneuvering Targets , 2002 .

[25]  B. N. Sokolov,et al.  Differential games with information lag PMM vol. 34, n≗5, 1970, pp. 812-819 , 1970 .

[26]  J. Shinar.  Solution Techniques for Realistic Pursuit-Evasion Games , 1981 .

[27]  R. Datko,et al.  Two examples of ill-posedness with respect to time delays revisited , 1997, IEEE Trans. Autom. Control..

[28]  J. F. Barman,et al.  L 2 -stability and L 2 -instability of linear time-invariant distributed feedback systems perturbed by a small delay in the loop , 1973 .