Control Systems and Machine Learning

-Basics of linear algebra: vectors, matrices, subspaces. -The Singular Value Decomposition of a matrix. -Frequency domain models of Linear Systems: Laplace Transform, Transfer Functions, Block diagrams. -Time domain models of Linear Systems: State space representation. -BIBO stability. -Control specifications for transient and steady-state responses. Polynomial and sinusoidal disturbances rejection. -PID controllers. -Analysis and control design using the eigenvalues assignment: controllability, observability, the separation principle. -Controller design using MATLAB. -QR factorization. First applications to data analysis and data compression: low-rank approximation of matrices and Eckart–Young–Mirsky theorem. -Data fitting: learning linear and nonlinear functions from data through regression. Regularized least squares and basics of applications to learning. -Prediction error methods (PEM) for models in input-output form (Box-Jenkins, ARMAX, ARX models). -Least-squares solution to PEM for ARX models. -Subspace identification: the Ho-Kalman method for deterministic realization of impulse responses. - The MOESP algorithm for noisy systems. - Model order reduction via truncated realization.