Læringsutbytte

A candidate who has passed the course will have a learning outcome in the form of acquired knowledge, skills, and general competence, as described below[1].

Knowledge

The candidate will:

1. Understand how realization theory based on impulse response and Hankel matrices is used to define state space model realizations for Multiple Input and Multiple Output (MIMO) systems.
2. Understand how regression methods as the Ordinary Least squares (OLS) method and the Principal Component Regression (PCR) method may be used to estimate parameters from over-determined systems of equations
3. Understand how state space models for autonomeous systems, deterministic systems, stochastic systems and combined deterministic and stochastic systems may be identified from known input and output discrete time series, using direct linear algebra and subspace based methods for system identification.
4. Understand how observer and optimal estimation methods, e.g. the Kalman filter, may be used to construct an optimal state estimator as well as an optimal prediction of the system output, and how the optimal output prediction is a function of the adequate system parameters.
5. Understand how optimisation based Prediction Error Methods (PEM) may be used to identify state space models for MIMO systems, from known input and output data

Skills

The candidate will :

1. Be able to analyze and realize state space models for MIMO systems from known impulse response matrices
2. Be able to estimate parameters using the OLS and PCR methods
3. Be able to identify state space models for general combined deterministic and stochastic MIMO systems from known input and output data
4. Be able to design optimal estimation methods, e.g. details about the Kalman filter, for MIMO systems.
5. Be able to use optimization based PEM to identify dynamic models for MIMO systems based on known input and output data

General competence

The candidate will:

1. Understand how system identification methods may be used to build models for dynamic MIMO systems
2. Understand how optimal estimators may be constructed in order to predict outputs, estimate states and parameters
3. Understand and provide the necessary foundation for further studies
4. Get experience in presenting scientific theory and applications

[1] Codes given in parentheses correspond to the codes given in the programme description.

Innhold

Description of stochastic processes. Discrete time process and measurement noise. Observability and detectability. Kalman filter for state and parameter estimation in linear and nonlinear systems. Kalman filter on prediction and innovation form. Deterministic and stochastic models, combined deterministic-stochastic models. Dynamic and static models. Modeling for control, prediction, simulation, operator support, diagnosis, failure detection, etc. Prefiltering of data, identification of trends etc. Experiment design for dynamic systems and persistent excitation. Least-squares system identification with statistical analysis. Singular value decomposition (SVD), principal component analysis and regression (PCA, PCR). Partial least squares (PLS). Identification of stochastic and dynamic systems from known input-output data. Details in subspace system identification methods such as DSR, and details in prediction error methods. Recursive system identification methods. Utilization of a priori knowledge. Handling of known nonlinearities and use of linearizing functions. Introduction to statistical process control (SPC) and data reconciliation.

Arbeids- og læringsformer

Lectures and assignments are used.

Lectures are used to highlight the main topics of the course, facilitating knowledge.

During the semester the students will work with several assignments. These assignments will be based on problem based learning giving the students better understanding of specific subtopics in the course and general competence in writing scientific reports with citing and referencing sources.

Vurderingsformer

The final test will count 70% of the course grade.

A set of mandatory assignments count 30% of the final grade.

It is necessary to pass the final examination in order to achieve a passing grade.

Det tas forbehold om mindre justeringer i planen.