evaluate

Evaluate a neural state-space system for a given set of state and input values and return state derivative (or next state) and output values

Since R2022b

Syntax

[dxdt,y] = evaluate(nss,x)

[dxdt,y] = evaluate(nss,x,u)

[dxdt,y] = evaluate(nss,t,x)

[dxdt,y] = evaluate(nss,t,x,u)

[xNext,y] = evaluate(nss,x)

[xNext,y] = evaluate(nss,x,u)

[xNext,y] = evaluate(nss,t,x)

[xNext,y] = evaluate(nss,t,x,u)

Description

Continuous-time

[dxdt,y] = evaluate(nss,x) evaluates the state and output networks of the autonomous time-invariant neural state-space system nss at state x, and returns the time-derivative of the state dxdt and the output y.

[dxdt,y] = evaluate(nss,x,u) evaluates the state and output networks of the time-invariant neural state-space system nss with input u.

[dxdt,y] = evaluate(nss,t,x) evaluates the state and output networks of the autonomous time-varying neural state-space system nss at time t.

[dxdt,y] = evaluate(nss,t,x,u) evaluates the state and output networks of the time-varying neural state-space system nss at time t.

Discrete-time

[xNext,y] = evaluate(nss,x) evaluates the state and output networks of the autonomous time-invariant neural state-space system nss at state x, and returns the next state xNext and the output y.

[xNext,y] = evaluate(nss,x,u) evaluates the state and output networks of the time-invariant neural state-space system nss with input u.

[xNext,y] = evaluate(nss,t,x) evaluates the state and output networks of the autonomous time-varying neural state-space system nss at time t.

[xNext,y] = evaluate(nss,t,x,u) evaluates the state and output networks of the time-varying neural state-space system nss at time t.

Examples

Evaluate Continuous-Time Neural State-Space Object

Use idNeuralStateSpace to create a continuous-time neural state-space object with two states, one input, and outputs identical to states.

nss = idNeuralStateSpace(2,NumInputs=1)

nss =

Continuous-time Neural ODE in 2 variables
     dx/dt = f(x(t),u(t))
      y(t) = x(t) + e(t)
 
f(.) network:
  Deep network with 2 fully connected, hidden layers
  Activation function: tanh
 
Variables: x1, x2
 
Status:                                                         
Created by direct construction or transformation. Not estimated.

Model Properties

Define random state and input values.

x = rand(2,1)

x = 2×1

    0.6785
    0.0557

u = rand(1)

u = 
0.0341

Evaluate the (untrained) state and output networks of nss at the defined state and input.

[dxdt,y] = evaluate(nss,x,u)

dxdt = 2×1

   -0.1448
    0.1793

y = 2×1

    0.6785
    0.0557

Note that the output is identical to the current state, as expected.

Evaluate Discrete-Time Neural State-Space Object

Use idNeuralStateSpace to create a discrete-time neural state-space object with three states, two inputs, four outputs, and sample time 0.1.

nss = idNeuralStateSpace(3,NumInputs=2,NumOutputs=4,Ts=0.1)

nss =

Discrete-time Neural State-Space Model with 4 outputs, 3 states, and 2 inputs
     x(t+1) = f(x(t),u(t))
     y_1(t) = x(t) + e_1(t)
     y_2(t) = g(x(t),u(t)) + e_2(t)
       y(t) = [y_1(t); y_2(t)]
 
f(.) network:
  Deep network with 2 fully connected, hidden layers
  Activation function: tanh
g(.) network:
  Deep network with 2 fully connected, hidden layers
  Activation function: tanh
 
Inputs: u1, u2
Outputs: y1, y2, y3, y4
States: x1, x2, x3
Sample time: 0.1 seconds
 
Status:                                                         
Created by direct construction or transformation. Not estimated.

Model Properties

Define random state and input values.

x = rand(3,1)

x = 3×1

    0.9165
    0.4326
    0.4270

u = rand(2,1)

u = 2×1

    0.0293
    0.5104

Evaluate the (untrained) state and output networks of nss at the defined state and input.

[xNext,y] = evaluate(nss,x,u)

xNext = 3×1

    0.4405
    0.0511
    0.1522

y = 4×1

    0.9165
    0.4326
    0.4270
   -0.4388

Note that the first three outputs are the current states, as expected.

Input Arguments

nss — Neural state-space system

idNeuralStateSpace object

Neural state-space system, specified as an idNeuralStateSpace object.

Example: myNrlSS

t — Value of the time variable

scalar

Value of the time variable, specified as a scalar, for time-varying idNeuralStateSpace systems.

Example: 1.8

x — Value of the state

scalar | column vector

Value of the state, specified as a scalar or column vector.

If you added an encoder or decoder to nss, then x is the value of the latent state, specified as a scalar or column vector.

Example: [-1.2 -0.3]'

u — Value of the input

scalar | column vector

Value of the input, specified as a scalar or column vector.

Example: 2.9

Output Arguments

dxdt — Value of the time-derivative of the state

scalar | column vector

Value of the time-derivative of the state, returned as a scalar or column vector. This is obtained by evaluating the state network of the continuous-time idNeuralStateSpace system nss.

If you added an encoder or decoder to nss, then dxdt is the value of the time-derivative of the latent state, returned as a scalar or column vector.

Example: [-1.2 -4.9 3.8]'

xNext — Value of the state at the next sample time

scalar | column vector

Value of the state at the next sample time, returned as a scalar or column vector. This is obtained by evaluating the state network of the discrete-time idNeuralStateSpace system nss.

If you added an encoder or decoder to nss, then xNext is the value of the latent state at the next sample time, returned as a scalar or column vector.

Example: [0.69 0.31]'

y — Value of the output

scalar | column vector

Value of the output, returned as a scalar or column vector with as may elements as the total number of outputs. This is obtained by evaluating both output networks of the idNeuralStateSpace system nss. Note that the first n_x elements of y are always equal to the elements of x, where n_x is the number of states specified in nss.

Example: [2 -3.1]

Version History

Introduced in R2022b