Lecture 5 Neural Control

History Early stages Recession 1943 McCulloch-Pitts: neuron, origins 1948 Wiener: cybernatics 1949 Hebb: learning rule 1958 Rosenblatt: perceptron 1960 Widrow-Hoff: least mean square algorithm Recession 1969 Minsky-Papert: limitations perceptron model

History Revival 1982 Hopfield: recurrent network model 1982 Kohonen: self-organizing maps 1986 Rumelhart et. al.: backpropagation very large-scale integrated circuitry (VLSI) and parallel computers aided the developments in ANNs 1992 Hunt et al. applications of neural networks in Control Engineering

What is a Neural Network? Neural Networks What is a Neural Network? Biologically motivated approach to machine learning Similarity with biological network Fundamental processing elements of a neural network is a neuron 1.Receives inputs from other source 2.Combines them in someway 3.Performs a generally nonlinear operation on the result 4.Outputs the final result

Similarity with Biological Network Fundamental processing element of a neural network is a neuron A human brain has 100 billion neurons An ant brain has 250,000 neurons

Synapses, the basis of learning and memory

BIOLOGICAL ACTIVATIONS AND SIGNALS Introduction to units ： Dendrite: input Axon: output Synapse: transfer signal Membrane: potential difference between inside and outside of neuron Fig3. Key functional units of a biological neuron

ANN properties to control being non-linear by nature, they are eminently suited to the control of non-linear plants, they are directly applicable to multi-variable control, they are inherently fault tolerant due to their parallel structure, faced with new situations, they have the ability to generalize and extrapolate.

Artificial Neural Network- defination An ANN is essentially a cluster of suitably interconnected non-linear elements of very simple form that possess the ability of learning and adaptation. These networks are characterized by their topology, the way in which they communicate with their environment, the manner in which they are trained and their ability to process information.

Artificial Neural Network-- classifie static when they do not contain any memory elements and their input-output relationship is some non-linear instantaneous func-tion, dynamic when they involve memory elements and whose behavior is the solution of some differential equation

5.1 The Elemental Artificial Neuron elemental artificial neurons ------- vaguely approximate physical neurons ANNs ---- artificial neurons interconnected via branches synaptic weights are the gains or multipliers

5.1 The Elemental Artificial Neuron A model of an artificial neuron --- node

5.1 The Elemental Artificial Neuron A static neuron has a summer or linear combiner, whose output σ is the weighted sum of its inputs, i.e.: where w and x are the synaptic weight and input vectors of the neuron respectively, while b is the bias or offset. A positive synaptic weight implies activation, whereas a negative weight implies de-activation of the input. The absolute value of the synaptic weight defines the strength of the connection.

5.1 The Elemental Artificial Neuron The most common distorting (or compression) element f(.)

5.1 The Elemental Artificial Neuron

5.1 The Elemental Artificial Neuron The input to the compression element σ may take on either of the following forms

5.2 Topologies of Multi-layer Neural Networks

5.2 Topologies of Multi-layer Neural Networks the principal classes of ANNs the manner in which the various neurons in the network are connected, i.e., the network topology or network architecture, • Hopfield recurrent network where the nodes of one layer interact with nodes of the same, lower and higher layers, • feed-forward networks in which information flows from the lowest to the highest layers, • feedback networks in which information from any node can return to this node through some closed path, including that from the output layer to the input layer and • symmetric auto-associative networks whose connections and synaptic weights are symmetric.

5.2 Topologies of Multi-layer Neural Networks multi-layer feed-forward ANN single-layered Hopfield network,

5.3 Neural Control the basic characteristics neural control • is directly applicable to non-linear systems because of their ability to map any arbitrary transfer function, • has a parallel structure thereby permitting high computational speeds. The parallel structure implies that neural controllers have a much higher reliability and fault tolerance than conventional controllers, • can be trained from prior operational data and can generalize when subjected to causes that they were not trained with, and • have the inherent ability to process multiple inputs and generate multiple outputs simultaneously, making them ideal for multivariable intelligent control.

5.4 Properties of Neural Controllers neural networks properties for control: • possess a collective processing ability, • are inherently adaptable, • are easily implemented, • achieve their behavior following training, • can be used for plants that are non-linear and multivariable, • can process large numbers of inputs and outputs making them suitable for multi-variable control, • are relatively immune to noise, • are very fast in computing the desired control action due to their parallel nature and do not require an explicit model of the controlled process.

5.5 Neural Controller Architectures mid-1960s, Widrow and Smith demonstrated the first application of a neural network in Control used a single ADALINE to control an inverted pendulum the late 1980s, ANNs for identification and control of systems since the mid-1980s , Many architectures for the control of plants with ANNs have been proposed

5.5 Neural Controller Architectures the case, a SISO discrete system identification

Neural Controller Architectures

Inverse model architecture the objective is to establish the inverse relationship P-1 between the output(s) and the input(s) of the physical plant Network training is based on some measure of the open system error between the desired and the actual out-puts e=d-y of the closed system. so that the overall relationship between the input and the output of the closed controlled system is unity,

Specialized training architecture is now based on some measure of the closed system error ec=d-y The result is increased robustness coupled with the advantages of conventional feedback

Indirect learning architecture two dynamic ANNs one ANN is trained to model the physical plant following identification the second ANN performs the controlling task using a feed-forward network. Both ANNs are trained on-line from normal operating records.

Indirect learning architecture the identification phase the overall error is used to train the controller ANN

Indirect learning architecture The advantage of this architecture is that it presents easier training of the controller ANN on-line since the error can be propagated backwards through the simulator ANN at every sampling instant.