System Identification and Modeling

All programmes > System Identification and Modeling

System Identification and Modeling (B-KUL-H03E1B)

4 ECTS

English

First term

Cannot be taken as part of an examination contract

De Moor Bart (coordinator) | De Moor Bart | N.

POC Wiskundige ingenieurstechnieken

Aims

Estimating mathematical models, starting from measured data, is an important step in many engineering methods. This course contains a number of important methods and foundations for linear system identification and modeling. We discuss topics such as choosing a good model structure, appropriate parametrizations, criteria for model selection and statistical properties of the obtained estimates. The course deals with least squares estimation, prediction error techniques, state space models and realization theory. The emphasis is on methods that offer a good generalization. The methods are illustrated with many practical examples and applications.

Previous knowledge

Skills: the student should be able to analyze, synthesize and interpret

Knowledge:

Necessary: calculus, applied linear algebra, probability theory and statistics, system theory
Useful, but not necessary: control theory

Detailed list of prerequisites:

1. Calculus: Analyse 1 (H01A0B), Analyse 2 (H01A2B)

Logic reasoning and mathematical proofs
Functions of real numbers, e.g., trigonometric, exponential, logarithmic
Functions of vectors
Differentiation and integration of univariate and multivariate functions
Partial derivatives
Complex numbers: addition, multiplication, powers of complex numbers
Vector spaces, gradient
Analytic geometry: Cartesian coordinates and polar coordinates
Differential equations: set up and solve linear differential equations and sets of differential equations
Taylor series
Optimization problems: formulate, solve and interpret, with equality and inequality constraints, method of Lagrange
Difference equations: solve linear difference equations and sets of difference equations

2. Applied linear algebra: Toegepaste Algebra (H01A4B); David Lay, “Linear Algebra and its Applications"

Familiarity with concepts from linear algebra in higher dimensions: vector spaces, linear dependence, orthogonality
Matrix computations: addition, multiplication with scalar, product of matrices, inverse of a matrix
Determinant
Partitioned matrices
Vector spaces: subspaces, linear transformations, basis, dimension, orthogonal complement of subspaces, orthogonal projection
Rank, column space, row space, null space of a matrix
Eigenvalue decomposition: characteristic polynomial, Cayley-Hamilton theorem, similar matrices
Singular value decomposition, QR factorization
Recognize and solve least squares problems
Pseudo-inverse of a matrix and relation to least squares
Algebraic models for engineering problems: Setting up a set of linear equations, processing of experimental results, analyzing autonomous systems and vibrations as an eigenvalue problem, computing the response of linear time-invariant discrete-time systems, dimensional reduction by means of the singular value decomposition
Use MATLAB to do matrix computations

3. Probability Theory and Statistics: Kansrekenen en statistiek (H01A6A)

Basic principles of probability theory: random variables, probability distributions
Variance, standard deviation, covariance, correlation
Estimation of parameters
Confidence intervals
Regression analysis

4. System Theory: Systeemtheorie en regeltechniek (H01M8A)

Basics about modeling mechanical, electrical, thermal and hydraulic systems
Block diagrams
Convolution, Laplace transform and Z transform (and their inverse)
Fourier series
Linear time invariant systems
Impulse response and transfer function
Poles and zeros of a system
Stability
State-space representation
Analysis of continuous-time and discrete-time systems in the time domain and in the frequency domain
Modeling and linearization
Discretization of continuous-time systems