Robust Control

Course objectives

General objectives The course presents advanced synthesis methods for the robust stabilization of linear multivariable and nonlinear systems in the presence of model uncertainties. Specific objectives Knowledge and understanding: Students will learn control design methods that handle the presence of structured or unstructured uncertainties on the model of the controlled system. The presented robust stabilization techniques will be based on the use of linear matrix inequalities (LMI) or methods based on high-gain controllers. Apply knowledge and understanding: Students will be able to analyze robust stabilization problems for linear and nonlinear dynamical systems and to use advanced design techniques in the synthesis of control laws for their resolution. Critical and judgment skills: Students will be able to characterize structured and/or unstructured uncertainties of the considered system, and to analyze the complexity of control law implementations, of their performance and critical issues. Communication skills: The course enables students to present some advanced and robust methods of solution for the classical problem of stabilization through feedback of dynamic systems. Learning ability: The course aims to create autonomous learning attitudes for the analysis and solution of control problems for linear multi-variable and nonlinear systems subject to model uncertainties.

Channel 1
STEFANO BATTILOTTI Lecturers' profile

Program - Frequency - Exams

Course program
Time-varying nonlinear systems. Theorems on exponential and uniform asymptotic stability. Linear Time-varying systems and stronger stability conditions. Total stability under non-vanishing perturbations. Uniform ultimate boundedness. Invariance-like Theorems: LaSalle Theorem, Barbalat Lemma, LaSalle-Yoshizawa Theorem and Anderson and Moore Theorem. Recalls on Passivity. Uniform Complete Observability (UCO) and invariance of UCO under output injection. Model-Reference Adaptive Control (MRAC) of Scalar Linear Systems: Direct and Indirect Methods. Asymptotic Stability of Adaptive Systems. Persistency-of-excitation conditions. The Issue of Robustness. Robust Modifications of Passivity-based Update Laws. Update Laws with Leakage. Update Laws with Leakage and Dead-zone modification. Update Laws with Parameter Projection. Adaptive Observers. Observers for systems in adaptive observer form. Examples of Practical Applications
Prerequisites
Fundamentals of Linear and Nonlinear Systems
Books
Notes of the course
Frequency
free attendance
Exam mode
The final grade consists of an oral exam: the Student must take an oral exam on all the topics discussed during the lectures.
Bibliography
S. Sastry, M. Bodson, Adaptive Control Stability, Convergence and Robustness, Prentice Hall, Upper Saddle River, NJ, 1989. P. Ioannu, J.Sun, Robust Adaptive Control, Prentice Hall, Upper Saddle River, NJ, 1996. H.K. Khalil, Nonlinear Systems, Prentice Hall, Saddle River, NJ, 3rd ed., 2002. R. Marino, P. Tomei, Global adaptive observers for nonlinear systems via filtered transformations, IEEE Transactions on Automatic Control, vol. 37, no. 8, pp. 1239-1245, 1992, A. Serrani, Lecture Notes on Adaptive Control, Bertinoro, 2018. All the textbooks can be found on-line or in public archives.
Lesson mode
The course takes place in the classroom, alternating theory and application-oriented lessons with examples in different fields
  • Lesson code1041453
  • Academic year2025/2026
  • CourseControl Engineering
  • CurriculumSingle curriculum
  • Year1st year
  • Semester2nd semester
  • SSDING-INF/04
  • CFU6