An introduction to Applied Category Theory at a more advanced level than Part I (this "Part II" is self-contained however). Category theory is increasingly used across a broad range of disciplines, from AI to physics, from linguistics to epidemiology. This course teaches the core mathematical concepts and highlights applications in applied sciences, with a special emphasis on engineering.

Analysis and synthesis for linear time-invariant control systems with one input and one output signal (SISO). State-space models, time response, stability conditions. Transfer functions and frequency response. Stability analysis under feedback: Root Locus, Bode plots, Nyquist condition. Feedback control synthesis: time- and frequency-domain specifications, PID lead/lag compensation, loop shaping.

This course builds upon the modeling and control of LTI SISO systems introduced in Control Systems I. It extends these foundations with state feedback and estimation, multi-input multi-output (MIMO) systems, nonlinear control, optimization, optimal control and model predictive control (MPC) for constrained linear systems.

Planning safe and efficient motions for robots in complex environments, often shared with humans and other robots, is a difficult problem combining discrete and continuous mathematics, as well as probabilistic, game-theoretic, and ethical/regulatory aspects. This course will cover the algorithmic foundations of motion planning, with an eye to real-world implementation issues.