B014050 - ANALYSIS OF ECOLOGICAL SYSTEMS

Italian or, by request, english.

The course consists of the following three parts:
1 - ELEMENTS OF SYSTEM THEORY
2 - MODELS OF ENVIRONMENTAL SYSTEMS
3 - PROCESSING OF ENVIRONMENTAL DATA

S. Marsili-Libelli: "Environmental systems with MATLAB", CRC Press, 2015.

S. Rinaldi, L. Farina: "I sistemi lineari positivi: teoria e applicazioni", Città Studi Edizioni, 1995.

M. Basso, L. Chisci, P. Falugi: "Fondamenti di automatica", Città Studi Edizioni, 2007.

Notes from the lectures.

Notes provided by the teacher.

The course aims to provide methodologies for the construction, analysis and exploitation for several purposes (e.g., forecasting, simulation, management) of models of environmental systems, using both mathematical tools of system theory and CAD tools (e.g., Matlab-Simulink).

Basics of mathematics, physics, linear algebra and numerical analysis.

Class lectures and exercises. Assignment of exercise/problems to be solved analytically and/or numerically with Matlab-Simulink as homework.

The final exam consists of an interview on the course subjects. The interview aims to assess, by means of numerical exercises and theoretical questions, the acquired knowledge and capabilities on:construction, analysis and exploitation for several purposes (e.g., forecasting, simulation, management) of models of environmental systems, using both mathematical tools of system theory and CAD tools (e.g., Matlab-Simulink). In particular, in order to assess the student ability in exploiting CAD tools, some problems are assigned during the course to be tackled with Matlab-Simulink and their solution is discussed during the interview.

The course aims to provide methodologies for the construction, analysis and exploitation for several purposes (e.g., forecasting, simulation, management) of models of environmental systems, using both mathematical tools of system theory and CAD tools (e.g., Matlab-Simulink).

ELEMENTS OF SYSTEM THEORY
- continuous-time & discrete-time state equations
- time-response analysis for linear time-invariant systems
- modal and frequency analysis
- stability
- nonlinear systems and linearisation
- analysis of linear discrete-time systems

MODELS OF ECOSYSTEMS
- population dynamics
- models for water quality
- distributed-parameter (PDE) models and their spatial discretisation
-simulation of ecosystems via Matlab-Simulink

PROCESSING OF ENVIRONMENTAL DATA
- The data assimilation problem for monitoring of environmental systems.
- Data assimilation for linear models and sensors: the Kalman filter.
- Data assimilation for nonlinear model and/or sensors: the extended Kalman filter.
- Data assimilation for continuous-time models: the Kalman-Bucy filter.
- Hybrid data assimilator for continuous-time model and discrete-time measurements.
- Hints on the ensemble Kalman filter for data assimilation of large-scale systems, e.g. in meteorology and oceanography.
- Parameter calibration (estimation) via data assimilation.