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; control design for aerospace systems. 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 aerospace 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: Jacobian linearization; feedback linearization; sliding-mode control; nonlinear model predictive control. Observer design for nonlinear systems: linear and 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.

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 application examples, most of which are taken from the aerospace field. Experimental lab sessions will be held as well, finalized at showing how the learnt control methodologies can be applied to real physical plants.

[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] A. Isidori, Nonlinear Control Systems, Springer, 1995. [5] M. H. Kaplan, Modern Spacecraft Dynamics and Control, I. John Wiley and Sons, 1976. [6] B. Wie, Space Vehicle Dynamics and Control. Aiaa, 1998. [7] F. Markley and J. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control. Cambridge University Press, 2014. [8] D. G. Hull, Fundamentals of Airplane Flight Mechanics, Springer, 2007. [9] A. Tewari, Atmospheric and Space Flight Dynamics: Modeling and Simulation with Matlab and Simulink, Birkhauser, 2007. [10] E. Canuto, C. Novara, L. Massotti, C. Perez Montenegro and D. Carlucci, Spacecraft dynamics and control. The embedded model control approach, Butterworth-Heinemann (Elsevier), 2018.

Lecture slides; Exercise with solutions ; Lab exercises with solutions; Video lectures (previous years); Simulation tools; Student collaboration tools;

Exam: Computer lab-based test;

The objectives of the exam are to assess the student's preparation/capability about the following topics: theoretical and numerical analysis of dynamic systems; theoretical and numerical analysis of aerospace systems; derivation of the equations of dynamic systems; design of different types of controllers; observer design; implementation and simulation in Matlab/Simulink of dynamic systems and, in particular, of aerospace systems. Written examination (carried out in lab with the help of the PC and the Matlab/Simulink software) with multiple choice questions, open questions and design problems. Allowed exam material: Slides of the course selected by the teacher; the Matlab/Simulink libraries used in the course. This material can be downloaded from the EXAM platform during the exam. Any other material is forbidden. Topics/material to study: All the topics treated in the slides, except those presented in the slides with a light blue background; all the topics treated during the Lab session; the related Matlab/Simulink files. The exam consists of multiple choice questions and, possibly, some open question. Answers are given directly on the Exam platform. The number of questions may range between 7 and 11, depending on the average difficulty. A (small) negative score is assigned to wrong answers. The duration may range between 2 and 2:15 hours, depending on the difficulty of the questions. The final grade takes also into account the results obtained by the student during the lab sessions. Allowed software: Matlab/Simulink, pdf reader. Any other software is forbidden. Navigation is forbidden. Taking photos and screenshots is forbidden. White paper sheets for handwritten calculations are allowed. A small number of separated sheets should be used. Paper notebooks of any kind are not allowed.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.