Introduction to BOXES Control

Abstract

The first version of the BOXES paradigm that Michie (http://en.wikipedia.org/wiki/Donald_Michie, Accessed September 12, 2011) introduced appeared using the acronym MENACE which stands for Machine Educable Noughts And Crosses Engine. Using a simple array of matchboxes, it was possible to play noughts and crosses using no other strategy than to add or remove colored beads in each matchbox based on the outcome of each game. In order to move away from board games and focus on real-time control, a paradigm shift is necessary. Instead of the player selecting a position on the board, the state variables of the real-time system are encoded into a system integer that corresponds with the board position. The algorithm uses this integer to look up a control value from a signature table and returns it for direct application to the system’s control mechanism. The methodology behind the BOXES algorithm as it is applicable to system control falls into five essential components: defining the game board; identifying the game pieces; establishing legal values for those pieces; creating an end game detection mechanism; and finally, enforcing strategies for optimality and eventual winning. The BOXES algorithm operates in two phases: reactive in which real-time closed loop control is achieved; and reflective in which modifications to the signature table values are made based on past performance statistics.