Sytem and Control Theory

Goal: Providing the Students with with the fundamental classical knowledge in control technology. Following that considering certain modern approaches.

Course description: Model Predictive Controller (MPC): optimization under constraints, Lagrange multipliers, reduced gradient, auxiliary function, nonlinear programming. The heuristic Receding Horizon Control. Simulation issues: MS EXCEL – Solver, legally free alternatives of MATLAB: Julia Version 1.0.3 (2018-12-18). General description of the LTI systems: stability, observability, controllability. The method of “Pole Placement”. State estimation by the Luenberger Observer. MPC for LTI models and quadratic cost functions: the LQR regulator. Tackling the LTI systems in the frequency domain: basics in Distribution Theory: the function class D and its use for classical modelling. Singular Value Decomposition (SVD), the H_\infty nomr, robust design, the “minimax” principle. Robust nonlinear controller: the Sliding Mode / Variable Structure Controller. Adaptive controllers: the “kappa” function class, Lyapunov’s “stability”, “uniform stability”, and “asymptotic stability” definitions, quadratic Lyapunov functions, the “Adaptive Inverse Dynamics Robot Controller”.