Neural network and its PID control

I. Artificial neural element model

1. Synaptic value (connection right)

Each synapse is characterized by its weight, and the connection strength between each neuron is represented by the synaptic value. On synapses connected to neurons, the connected input signal enters the sum unit of the neuron by weighting the weights.

2. Summation Unit

The summation unit is used to calculate the synaptic weighting of each input signal and this operation forms a linear combiner.

3. Activation function

The activation function acts as a nonlinear mapping and is used to limit the neuron output amplitude. An activation function is also called a restriction function, or a transfer function. Normally a neuron outputs a normal range of [0, 1] intervals or [? 1, 1] intervals.

4. External bias

In addition, the neuron model also includes an external bias, or an external bias called threshold, where the action of the bias is based on its positive or negative, corresponding increase or decrease in the activation function of the network input.

5. A pair of equations describe neurons

6. Activation function

(1) Step function

(2) piecewise linear function

(3) sigmoid function

(4) Hyperbolic tangent function:

II. structure of the neural network 1, feedforward type network

This kind of network connects each layer of neurons, the first layer of output is the input of the next layer, there is no feedback connection in the network

(1) Node classification

The node has the input unit, the calculation unit and the output unit three class

(2) Hierarchical classification

Input layer: The source node forms the input layer, the input layer is not computed, and the input signal is passed directly to the calculation unit of the next layer.

Visible layer: The input and output nodes are directly connected with the outside world and can be directly affected by the external environment.

Hidden layer: The middle layer is not directly related to the outside world, so it is called the hidden layer

(3) The Feedforward network can often have multiple hidden layers, thus constituting a multilayer feedforward network, the figure is a n-p-q three-layer Feedforward network

The Feedforward network is a kind of static nonlinear mapping, and the complex nonlinear processing ability can be obtained by using the complex mapping of simple nonlinear processing. However, from a computational point of view, Feedforward networks are not a powerful computing system and do not have a rich dynamic behavior.

2. Feedback Type Network

In the feedback network, the input signal determines the initial state of the feedback system, and then after a series of state transfer, the system converges to the equilibrium state gradually, so that the equilibrium state is the result of the output of the feedback network after the calculation, it should be noted that there are usually multiple equilibrium states. Therefore, stability is one of the most important problems in feedback networks. If we can find the Lyapunov (Lyapunov) function of the network, we can ensure that the network can converge to the local minimum point from any initial state, that is, the optimal solution is obtained.

3. How to determine the network structure

(1) Number of inputs to the network = number of input to the application problem

(2) Number of output layer neurons = number of outputs applied problem

(3) The transfer function selection of the output layer is at least partially dependent on the output description of the application problem

Iii. Learning of Neural Networks 1, overview

The most important nature for neural networks is the ability of the network to learn from the environment and improve its behavior through learning. During the learning process, the synaptic weights and bias (threshold) levels of the neural network are constantly modified according to a specified measure, and ideally, the neural network will have more knowledge of its environment after each repetition of the learning process. In the context of neural networks, the definition of learning is as follows:
Learning is a process through which the free parameters of a neural network are regulated under the process of its embedded environmental mechanism. The type of learning is determined by how the parameters change. The definition of this learning process implies the fact that the neural network is stimulated by an environment, and as a result of this stimulation, the self-parameters of the neural network change and respond to the environment in new ways due to the internal changes in the neural network.

2. Learning Style

(1) Supervised learning

Supervised learning, also known as tutor Learning, requires the presence of a "mentor" who can provide the neural network with the desired response to the input training sample, based on some of the knowledge that it has mastered. The expected response generally represents the optimal output of the neural network. When the input action to the network, the expected response of the neural network and the actual response compared to produce an error signal, according to the error signal gradually and repeatedly adjust the network weights and thresholds, so that the actual output of the network is constantly close to the desired output, the ultimate goal is to make the neural network simulation tutor, in some statistical sense, This simulation is optimal. Using this learning approach, the instructor's knowledge of the environment can be trained to the maximum of the neural network, when the conditions are ripe, the tutor can be excluded, so that the neural network fully autonomous response to the environment.

(2) Unsupervised learning

Unsupervised learning does not exist outside mentors, the learning system adjusts its own parameters or structures exactly according to some statistical laws of the data provided by the environment, which is a self-organizing process to represent an intrinsic characteristic of an external input (such as clustering, or some statistical distribution feature). In unsupervised learning, the weights and thresholds of the network are adjusted only according to the input of the network, it has no target output. At first glance, this kind of learning does not seem feasible, do not know what the purpose of the network, but also to train the network? In fact, most of this type of algorithm is to accomplish some sort of clustering operation, learning to divide the input pattern into a limited number of different types. This function is especially suitable for applications such as vector quantization.

(3) Enhanced Learning

Reinforcement learning is also called re-excitation learning. In this learning mode, the learning system is based on an evaluation, and the evaluation will convert the original enhanced signal received from the external environment into a high-quality enhancement signal that inspires enhanced signals. It is important to note that the external environment gives an evaluation (award or punishment) to the output of the learning system, rather than the correct answer, and the learning system improves its performance by reinforcing the actions that are rewarded. Enhanced learning is similar to supervised learning, except that it does not provide the corresponding target output for each input as supervised learning, but merely gives a level (evaluation), which is a measure of the performance of the network on some input sequences. At present, enhanced learning is less common than supervised learning, and it is most suitable for control system Application field.

3. Learning Style

(1) Error correction learning-learning rules

Learning rules use the error between the expected output of the neuron and the actual output to learn, and by adjusting the synaptic weights, the error is reduced

(2) Hebb learning rules

(3) Competitive learning rules

(4) Boltzmann learning rules

Neural network and its PID control