optimal_control_gradient_descent {seeds}

estimating the optimal control using the dynamic elastic net

Description

estimating the optimal control using the dynamic elastic net

Usage

optimal_control_gradient_descent(
  alphaStep,
  armijoBeta,
  x0,
  parameters,
  alpha1,
  alpha2,
  measData,
  constStr,
  SD,
  modelFunc,
  measFunc,
  modelInput,
  optW,
  origAUC,
  maxIteration,
  plotEsti,
  conjGrad,
  eps,
  nnStates,
  verbose
)

Arguments

alphaStep

starting value of the stepsize for the gradient descent, will be calculate to minimize the cost function by backtracking algorithm

armijoBeta

scaling of the alphaStep to find a approximately optimal value for the stepsize

x0

initial state of the ode system

parameters

parameters of the ODE-system

alpha1

L1 cost term scalar

alpha2

L2 cost term scalar

measData

measured values of the experiment

constStr

a string that represents constrains, can be used to calculate a hidden input for a component that gradient is zero

SD

standard deviation of the experiment; leave empty if unknown; matrix should contain the timesteps in the first column

modelFunc

function that describes the ODE-system of the model

measFunc

function that maps the states to the outputs

modelInput

an dataset that describes the external input of the system

optW

vector that indicated at which knots of the network the algorithm should estimate the hidden inputs

origAUC

AUCs of the first optimization; only used by the algorithm

maxIteration

a upper bound for the maximal number of iterations

plotEsti

boolean that controls of the current estimates should be plotted

conjGrad

boolean that indicates the usage of conjugate gradient method over the normal steepest descent

eps

citeria for stopping the algorithm

nnStates

a bit vector indicating the states that should be non negative

verbose

Boolean indicating if an output in the console should be created to display the gradient descent steps

Value

A list containing the estimated hidden inputs, the AUCs, the estimated states and resulting measurements and the cost function