Differential Games for an Infinite 2-Systems of Differential Equations

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

Multicentric tracking of multiple agents by anterior cingulate cortex during pursuit and evasion

Successful pursuit and evasion require rapid and precise coordination of navigation with adaptive motor control. We hypothesize that the dorsal anterior cingulate cortex (dACC), which communicates bidirectionally with both the hippocampal complex and premotor/motor areas, would serve a mapping role in this process. We recorded responses of dACC ensembles in two macaques performing a joystick-controlled continuous pursuit/evasion task. We find that dACC carries two sets of signals, (1) world-centric variables that together form a representation of the position and velocity of all relevant agents (self, prey, and predator) in the virtual world, and (2) avatar-centric variables, i.e. self-prey distance and angle. Both sets of variables are multiplexed within an overlapping set of neurons. Our results suggest that dACC may contribute to pursuit and evasion by computing and continuously updating a multicentric representation of the unfolding task state, and support the hypothesis that it plays a high-level abstract role in the control of behavior.

A Simplified Pursuit-evasion Game with Reinforcement Learning

In this paper we visit the problem of pursuit and evasion and specifically, the collision avoidance during the problem. Two distinct tasks are visited: the first is a scenario when the agents can communicate with each other online, meanwhile in the second scenario they have to only rely on the state information and the knowledge about other agents' actions. We propose a method combining the already existing Minimax-Q and Nash-Q algorithms to provide a solution that can better take the enemy as well as friendly agents' actions into consideration. This combination is a simple weighting of the two algorithms with the Minimax-Q algorithm being based on a linear programming problem.

Multicentric tracking of multiple agents by anterior cingulate cortex during pursuit and evasion

SUMMARYSuccessful pursuit and evasion require rapid and precise coordination of navigation with adaptive motor control. We hypothesized that the dorsal anterior cingulate cortex (dACC), which communicates bidirectionally with both the hippocampal complex and premotor/motor areas, would serve a mapping role in this process. We recorded responses of dACC ensembles in two macaques performing a joystick-controlled continuous pursuit/evasion task. We found that dACC multiplexes two sets of signals, (1) world-centric variables that together form a representation of the position and velocity of all relevant agents (self, prey, and predator) in the virtual world, and (2) avatar-centric variables, i.e. self-prey distance and angle. Both sets of variables are multiplexed within an overlapping set of neurons. Our results suggest that dACC may contribute to pursuit and evasion by computing and continuously updating a multicentric representation of the unfolding task state, and support the hypothesis that it plays a high-level abstract role in the control of behavior.