Robust pursuit of a hybrid evader

A pursuit-evasion differential game with bounded controls and prescribed duration is considered. The evader has two possible dynamics, while the pursuer dynamics is fixed. The evader can change the dynamics once during the game. The pursuer knows the possible dynamics of the evader, but not the actual one. The optimal pursuer strategy in this game is obtained. It is robust with respect to the control of the evader, the order of its dynamics and the time of the mode change. The capture conditions of the game are established and the pursuer capture zone is constructed. An illustrative example of the game is also presented.

[1]  Alexandre M. Bayen,et al.  A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games , 2005, IEEE Transactions on Automatic Control.

[2]  Han Ho Choi,et al.  An analysis and design method for uncertain variable structure systems with bounded controllers , 2004, IEEE Trans. Autom. Control..

[3]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[4]  Basil Kouvaritakis,et al.  Robust receding horizon predictive control for systems with uncertain dynamics and input saturation , 2000, Autom..

[5]  F. L. Cheronousko,et al.  Some Differential Games with Incomplete Information , 1974, Optimization Techniques.

[6]  T. Grundy,et al.  Progress in Astronautics and Aeronautics , 2001 .

[7]  Alexandre M. Bayen,et al.  Validating a Hamilton-Jacobi Approximation to Hybrid System Reachable Sets , 2001, HSCC.

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

[9]  Valery Y. Glizer,et al.  Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls , 2010 .

[10]  Rufus Isaacs,et al.  Differential Games , 1965 .

[11]  Josef Shinar,et al.  A pursuit-evasion game with hybrid pursuer dynamics , 2007, 2007 European Control Conference (ECC).

[12]  Josef Shinar,et al.  Pursuit of an Evader with Hybrid Dynamics , 2009, ADHS.

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

[14]  J. Shinar,et al.  Time-Varying Linear Pursuit-Evasion Game Models with Bounded Controls , 2002 .

[15]  Frédéric Kratz,et al.  An Optimal Control Approach for Hybrid Systems , 2003, Eur. J. Control.

[16]  Yan Gao,et al.  On the Reachability Problem for Uncertain Hybrid Systems , 2007, IEEE Transactions on Automatic Control.

[17]  Leon A. Petrosjan,et al.  Differential Games of Pursuit , 1993 .

[18]  Toshio Fukuda,et al.  Variable structure system theory based disturbance identification and its applications , 1997 .

[19]  G. Bartolini,et al.  Control of nonlinear variable structure systems , 1986 .

[20]  H. Sussmann.  A nonsmooth hybrid maximum principle , 1999 .

[21]  N. N. Krasovskii,et al.  The problem of control under conditions of incomplete information , 1984 .