Neural network for control engineering

Neural Network for Control Engineering
Dr.-Ing. Sudchai Boonto
Department of Control System and Instrumentation Engineering King Mongkuts Unniversity of Technology Thonburi • A common application of neural networks is the solution of classification problems (e.g. pattern recognition) • In control applications, neural networks are mainly used to • Nonlinear version of the linear FIR, ARX, ARMAX, OE, BJ • Inverse model, model based control etc.
Neural Network for Control Engineering
Neural Network for Control Engineering
• dendrites represent a highly branching tree of fibres that carry
electrical signals to the cell body. 103 to 104 dendrites per neuron.
• soma or cell body realizes the logical functions of the neuron.
• axon is a single long nerve fibre attached to the soma that serves
as the output channel of the neuron.
• synapse is a point of contact between an axon of one cell and a
Neural Network for Control Engineering
• the neuron is modelled as a multi-input nonlinear device with r inputs φ1, φ2, . . . , φr, one output v and weighted interconnections • an extra input with a value fixed to 1 is provided that can be used Neural Network for Control Engineering
The sum h of the r weighted inputs and the bias is passed through a static nonlinear function f (h) according to v = f (h) = f v = f (wT φ + w0) Neural Network for Control Engineering
The nonlinear function f is called the activation function of the neuron.
Three types of activation function are commonly used: Neural Network for Control Engineering
The step function as activation function is defined by v(h) = σ(h) =  v = σ(w1φ + w0) Neural Network for Control Engineering
Neural Network for Control Engineering
The output of a linear activation function is equal to its input Neural Network for Control Engineering
v(h) = f (h) = 1 + e−h Neural Network for Control Engineering
v(h) = f (h) = eh + e−h Neural Network for Control Engineering
We can turn to networks formed by connecting single neurons.
The network has r inputs φ1, . . . , φr, a bias and s outputs v1, . . . , vs.
Neural Network for Control Engineering
The output of the summing junction of the ith neuron is where wij is the gain from input j to the ith neuron. Defining theweight vector Neural Network for Control Engineering
The vector v of network outputs is then v =  .  = f(W φ + w0) A single-layer network of this form is called a perceptron network.
Neural Network for Control Engineering
Several perceptron layers can be connected in series to form a multilayer Neural Network for Control Engineering
v1 = v1 = f 1(W 1φ + w1 The network output – the output of the second layer is = f 2(W 2v1 + w2 y = f 2(W 2f 1(W 1φ + w10) + w20) Neural Network for Control Engineering
Neural Network for Control Engineering
• a commonly used network structure is a two-layer perceptron network with sigmoidal activation functions in the hidden layer, and linear activation functions in the output layer.
• An important property of such networks is their universal • Any given real continuous function g : Rr → R can be approximated to any desired accuracy by a two-layer sig-lin • however on indication about the number of hidden units required Neural Network for Control Engineering
1. Lecture note on Neural and Genetic Computing for Control 2. System Identification: Theory for the user Ljung, L.,1999, Prentice 3. Neural Networks for Modelling and Control of Dynamic Systems Norgaard, M. Ravn, O. Poulsen, N. K. and Hansen, L. K.
Neural Network for Control Engineering

Source: http://staff.kmutt.ac.th/~sudchai.boo/Teaching/inc691/lecture18.pdf