Dynamic Physical Systems

- Conventional control theory requires a mathematical model to predict the behaviour of a process so that appropriate control decisions can be made.
- Many processes are too complicated to model accurately.
- Often, not enough information is available about the process' environment.
- When the system is too complicated or the environment is not well understood, an adaptive controller may work.
- An adaptive controller learns how to use the control actions available to meet the system's objective.
- The process is treated as a 'black box' and the program interacts with it by conditioned response.

- m_c
- mass of cart
- m_p
- mass of pole
- l
- distance of centre of mass of pole from the pivot
- g
- acceleration due to gravity
- F
- force applied to cart
- t
- time interval of simulation

A box contains

- an action setting (left or right)
- the weighted sum of lifetimes after a left decision (left life)
- the weighted number of times a left decision has been made (left usage)
- the weighted sum of lifetimes after a right decision (right life)
- the weighted number of times a right decision has been made (right usage)

boxes loop randomly set starting position put trial into t if t > 10,000 then exit for each box, b if number of entries into b != 0 check_box(b) trial put 0 into t find the current box if pole has fallen then return t add one to t if t > 10,000 then return t add one to number of entries into current box add t to time sum of current box make move according to setting of box check_box(b) multiply left life by decay multiply left usage by decay multiply right life by decay multiply left usage by decay if action setting is LEFT add no. of entries - time sum to left life add no. of entries to left usage if action setting is RIGHT add no. of entries - time sum to right life add no. of entries to right usage put 0 into the no. of entries put zero into time sum

if LeftValue > RightValue set action to LEFT else if LeftValue < RightValue set action to RIGHT else make random choice

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