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System (Process) Identification

The exhaustive list of topics in System (Process) Identification Problems in which we provide Help with Homework Assignment and Help with Project is as follows:

  • System Identification
    • Models of Discrete-Time LTI Systems - Convolution equation.
    • Difference equations
    • Transfer functions
    • State-space models
    • Discretization
    • Sampling and Hold operations
    • Sampling theorem.
  • Non-parametric models - impulse response, step response and frequency response models.
  • Disturbance models - random processes, representation of stationary processes, white-noise process, auto-covariance function (ACF), ARMA models.
  • Parametric model structures - ARX, ARMAX, OE, Bj and PEM - structures.
    • Linear Regression - Least Squares estimates
    • Statistical properties of LS Estimates.
  • Weighted Least Squares, Recursive Least Squares, Maximum Likelihood Estimation.
  • Estimation of non-parametric models - impulse / step response coefficients, frequency response models.
  • Estimation of parametric models - notions of prediction and simulation, predictors for parametric models, prediction-error methods, Instrumental Variable method.
  • Model Structure Selection and Diagnostics - estimation of delay and order, residual checks, properties of parameter estimates, model validation.
  • Experimental Design - input design for identification, notion of persistent excitation, identifiability.
    • Subspace Identification - classical and innovations forms, free and structured parametrizations.
    • Least squares estimation, extended observability matrix, order determination through singular-value decomposition.
  • Case studies and topics for further study.