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Basic knowledge of dynamic systems analysis and control.
The first part of the course aims to teach the student to analyse a complex dynamic system and to set up a regulator integrated system, taking into account also uncertainties. The control variables have to be optimized with respect to an objective function, with assigned constraints. Optimal control can be formulated for both continuous-time and discrete-time systems. Pontryagin maximum principle and Dynamic programming approaches are illustrated for linear and non linear systems and examples are presented and discussed. Moreover Kalman filter techniques allow to estimate the state of the system when uncertainty is not negligible. Finally the integrated control system designed has to be reliable and robust with respect to external events. In the second part of the course Data mining techniques are illustrated with the aim to extract the maximum essential information from the analysis of big amount of data and variables. Multiple regression model, neural networks, principal components analysis, factor analysis, Granger causality analysis are introduced together with examples of real data applications.
Optimal control of linear and non linear dynamic systems with uncertainties. Data mining techniques.
The lessons will deal with the following topics: • Dynamic systems control Classical and modern approach. • Regulator synthesis Controllability and observability. Canonical forms. Feedback control. Observers. Eigenvalue separation theorem. • Optimal control The basic optimal control problem. Problems with terminal constraints. Minimum time control (bang-bang). Linear systems with Quadratic cost (LQ). Dynamic programming. • State observer with uncertainty Kalman filter. • Data mining Analysis and classification of big amounts of data and multivariate systems. Multiple regression models, Neural Networks, Principal Component Analysis, Factor Analysis, Cluster Analysis, Granger causality analysis. • Computer lab exercises Examples of application to real data will be performed by the student in a computer lab with the support of MATLAB, SIMULINK and Application Toolbox.
Notes from the lessons on the Moodle Community web site. D.G Luenberger, Introduction to Dynamic Systems. Theory, Models. and Applications, John Wiley & Sons, ISBN 0-471-02594-1
Lessons and computer lab exercises.
Written examination in computer lab with the support of software tools and answers to theoretical questions.
Students may be invited to join scientific seminars given by experts in the field.