Fuzzy control, overview

Olivier Teytaudolivier.teytaud@gmail.com

Essentially mathematics free methodology

Not widely used in Europe or Us

Very frequent in Asia

A pragmatic solution for control & human expertise

Control: maximizing reward

At each time step, the agentreceives a description of the world (state)

makes a decision,

gets a reward

Control: example

Observation = temperature

Temperature control:If temperature < 16C, switch on heater

If temperature > 20C, switch off heater

If temperature > 26C, switch on air cond.

If temperature < 24C, switch off air cond.

Rewardreward = comfort reward cost penalty

comfort reward = 1 if 20 < temp < 24 (0 otherwise)

Penalty = 0.2 per appliance switched on

Tools for control

Dynamic programming (Bellman)

Model Predictive Controlbuild a model and a predictor

optimize the decisions so that the predicted reward is maximal over the next H time steps

Direct Policy Search: define a parametric control function

optimize the parameters on simulations

Reinforcement learning (many different things, close to DP or close to DPS or combining both)

Direct Policy Search

Expert temperature control:If temperature < 16C, switch on heater

If temperature > 20C, switch off heater

If temperature > 26C, switch on air cond.

If temperature < 24C, switch off air cond.

DPS: replace constants with parametersIf temperature < x1C, switch on heater

If temperature > x2C, switch off heater

If temperature > x3C, switch on air cond.

If temperature < x4C, switch off air cond.

Direct Policy Search

DPS: replace constants with parametersIf temperature < x1C, switch on heater

If temperature > x2C, switch off heater

If temperature > x3C, switch on air cond.

If temperature < x4C, switch off air cond.

Then define a simulator depending on x=(x1,x2,x3,x4):simulator(x) = average cost over 1000 simulations

x* = argmax simulator(x) 26C then switch on AC

becomes

switch on AC with power 100% if T > 27C

0% if T < 25C

50(T-25)% if 25