Course outline

The course is structured into 14 topics, each of them corresponding to one lecture. The topics are as follows:

• Optimization
  1. Theory: formulations, conditions, types of problems, optimization modellers, …
  2. Algorithms: computing derivatives (symbolic, finite difference, autdiff), gradient, Newton, …, solvers
• Discrete-time optimal control
  3. Direct approach (via optimization): on finite horizon, MPC
  4. Indirect approach (via Hamilton equations): finite and infinite horizon, LQR, Riccati equations, …
  5. Dynamic programming: Bellman’s principle, …
  6. More on MPC: combining direct and indirect approaches and dynamic programming
• Continuous-time optimal control
  7. Indirect approach (via calculus of variations): boundary value problem, Riccati equations, LQR
  8. Indirect approach (via Pontryagin’s principle of maximum): time-optimal constrained control
  9. Numerical methods for both direct and indirect approaches: shooting, multiple shooting, collocation
  10. Some extensions of LQ-optimal control: stochastic LQR, LQG, LTR, \(\mathcal{H}_2\)
• Robust control
  11. Modeling of uncertainty, robustness analysis: small gain theorem, structured singular values
  12. Robust control design: \(\mathcal{H}_\infty\)-optimal control, \(\mu\)-synthesis
  13. Analysis of achievable performance
• Other topics
  14. Model order reduction, controller order reduction