Control is a multi-disciplinary area, involving theoretical, numerical and hardware tools, finalized at modifying the behavior of real-world systems. Due to its nature, control is nowadays fundamental in most fields of science and technology, ranging from the "classical" aerospace, automotive, robotics and energy fields, to less "traditional" fields, e.g., related to biomedical, data analytics, communication and network applications. Starting from the observation that the majority of real-world dynamic systems are nonlinear, the first objective of the course is to provide the basic methodologies for analyzing the properties of a nonlinear system and for designing effective control algorithms, aimed at obtaining the desired behavior for the system variables of interest. The second objective of the course is to show how these methodologies can be applied to aerospace systems, allowing the accomplishment of the most challenging missions.

The knowledge acquired during the course will regard the following subjects:
properties of nonlinear systems;
properties of feedback systems;
modern control design methods for nonlinear systems;
coordinate reference systems, rotations and translations;
spacecraft/aircraft attitude kinematics and dynamics;
spacecraft orbital dynamics;
spacecraft/aircraft control design.

The skills acquired during the course will be the following:
understanding and analyzing the behavior of a dynamic system;
developing advanced control algorithms for nonlinear systems;
understanding and analyzing the behavior of a spacecraft/aircraft;
developing advanced control algorithms for spacecraft/aircraft systems;
developing simulation and control software in Matlab/Simulink.

The student will learn how to use in a comprehensive way the acquired knowledge and skills in order to deal with new problems, without being limited to a small set of applications/case studies.

Strong background in differential and integral calculus of vector valued functions and in linear algebra. Basic concepts of physics, mechanics, complex numbers, real rational functions. Basic notions on dynamic systems and automatic control.

Nonlinear system analysis:
basic notions on dynamic systems;
state equations;
basic stability concepts;
Lyapunov stability.

Control design for nonlinear systems. Overview on different approaches:
linearization and gain scheduling;
feedback linearization;
embedded model control;
sliding-mode control;
nonlinear model predictive control.

Observer design for nonlinear systems:
extended Kalman filter.

Aerospace topics:
coordinate reference systems;
rotations and translations;
rigid body attitude kinematics and dynamics;
orbital dynamics.

Aerospace applications/case studies will be about
spacecraft orbit/trajectory control;
spacecraft attitude control;
aircraft flight control.

Lectures will be concerned with theoretical topics, numerical examples and solved problems. LAB exercises will also be carried out, based on the Matlab/Simulink software. The LAB sessions will be focused on the development of academic and applicative examples.

[1] C. Novara, Nonlinear Control and Aerospace Applications: lecture notes. Politecnico di Torino, 2017.
[2] J-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991.
[3] S. Sastry, Nonlinear Systems: Analysis, Stability, and Control, Springer, 1999.
[4] M. H. Kaplan, Modern Spacecraft Dynamics and Control, I. John Wiley and Sons, 1976.
[5] B. Wie, Space Vehicle Dynamics and Control. Aiaa, 1998.
[6] F. Markley and J. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control. Cambridge University Press, 2014.
[7] D. G. Hull, Fundamentals of Airplane Flight Mechanics, Springer, 2007.
[8] A. Tewari, Atmospheric and Space Flight Dynamics: Modeling and Simulation with Matlab and Simulink, Birkhauser, 2007.

Written examination (carried out in lab with the help of the PC and the Matlab/Simulink software) with multiple choice questions and design problems. The number of questions will range between 7 and 11, depending on the average difficulty. A (small) negative score will be assigned to wrong answers. The duration of the exam will be 2 hours. The following material will be available during the exam: lecture slides (without students' notes), Matlab libraries. No other material will be allowed (in particular, no solved exercises). No oral examinations will be held.