Advanced Methods in Control
Master of Science in Control Engineering
A.A. 2021/22 - 6 CFU
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IMPORTANT NEWS.
Starting from AA 2022-23 the course will be taught by Prof. Antonio Franchi.
Aims. The course is aimed at providing basic tools for the analysis and design of nonlinear systems under sampling and delays.
Prerequisites. Basics of nonlinear control systems as given in the course "Nonlinear Systems and Control".
The course is composed of two modules:
Nonlinear control systems under sampling and delays (3 CFU, Dr. Mattia Mattioni);
Adaptive control for nonlinear systems (3 CFU, prof. Stefano Battilotti, homepage).
Nonlinear control systems under sampling and delays- Contents
Nonlinear control systems under sampling and delays- Contents
Introduction to nonlinear systems under sampling and delays
Sampled-data representations of nonlinear sampled-data dynamics
From single-rate to multi-rate sampled-data equivalent models; the problem of the sampled-data zero-dynamics and the relative degree; the differential-difference representation.
Passivity and passivity-based control: from continuous-time to sampling
Passivity and PBC in continuous time: the case of Hamiltonian systems.
Passivity and PBC in discrete-time and under sampling: the notion of u-average passivity; passivity-based control for stabilization at the origin: damping feedback; computational issues and approximate feedback solutions; applicative examples.
Nonlinear systems under sampling and delays
Time delay systems in continuous time: the state-space and the initial condition problem; tools for stability investigation and design; the prediction approach.
Time delay systems under sampling: representations as cascades; the prediction-based method for delay compensation.
Adaptive control for nonlinear systems - Contents
Adaptive control for nonlinear systems - Contents
Stability of time-varying systems
Basics on the stability of continuous time-varying systems: Uniform and exponential stability of equilibrium points, direct and converse Lyapunov theorems, invariance theorems. Barbalat Lemma. Construction of Lyapunov functions.
Identification algorithm and adaptive control
Basics on identification problems. Parameter identification: least squares, gradient and normalized gradient algorithms. Persistent excitation and parameter convergence. Model reference identifiers. Frequency domain conditions for paramater convergence. Elements of adaptive control.
Nonlinear control systems under sampling and delays
Instructors. Dr. Mattia Mattioni.
Lectures
Lectures
Period. 2nd Semester (February, 21st-May, 27th 2022)
Schedule.
Wednesdays, 10:00-13:00 (Room A2, DIAG and via zoom)
Note: For seat reservation, see the Sapienza procedure (the DIAG department in Via Ariosto 25 has building code RM102 of Sapienza).
Course Material
Course Material
Hassan Khalil, Nonlinear Systems. 3rd Edition. Ed Prentice Hall, 2002.
Mattia Mattioni, Stabilization of Nonlinear Systems under Sampling and Delays. PhD Thesis. May, 2018. Univ. Paris-Saclay and Univ. La Sapienza. (here) -- Chapters 1,2, 5 and 6.
Further Reading
Passivity and passivity-based control in continuous time
Willems, J. C. "The behavioral approach to open and interconnected systems." IEEE control systems magazine 27.6 (2007): 46-99 (pdf).
Sepulchre, R., Mrdjan J. and P. V. Kokotovic. "Constructive nonlinear control". Chapter 2. Springer Science & Business Media, 2012 (available in the library, @DIAG).
Ortega, R., et al. "Putting energy back in control." IEEE Control Systems Magazine 21.2 (2001): 18-33 (pdf).
Bymes, C. I., Isidori, A. and Willems, J.C.." Passivity, feedback equivalence, and the global stabilization of minimum-phase nonlinear systems", IEEE Transactions on Automatic Control,(1991): 1228-1240 (pdf).
Ortega, Romeo, et al. "Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems." Automatica 38.4 (2002): 585-596 (pdf).
Discrete-time representations of nonlinear dynamics under sampling
Monaco, S. and Normand-Cyrot, D.. "On nonlinear digital control." Nonlinear systems. Springer, Boston, MA, 1997. 127-155 (pdf).
Monaco, S. and Normand-Cyrot, D.. "Issues on nonlinear digital control." European Journal of Control 7.2-3 (2001): 160-177 (pdf).
Passivity and passivity-based control in discrete time and under sampling
Monaco, S. and Normand-Cyrot, D.. "Nonlinear average passivity and stabilizing controllers in discrete time." Systems & Control Letters 60.6 (2011): 431-439 (pdf).
Tiefensee, F., Monaco, S. and Normand-Cyrot, D.. "Average passivity for discrete-time and sampled-data linear systems." 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010 (pdf).
Byrnes, C.I., Lin, W. "Losslessness, equivalence, and the global stabilization of discrete-tiem nonlinear systems". IEEE Transactions on Automatic Control 30.1 (1994): 83-97 (pdf).
Moreschini, A, Mattioni, M., Monaco, S. and Normand-Cyrot, D.. "Discrete port-controlled hamiltonian dynamics and average passivation." 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019 (pdf).
Time-delay systems and prediction-based control for continuous-time and sampled-data systems
Exam
Exam
Exam modalities. Preparation of a project (involving simulations and a case study) and oral test.
Calendar of the exams.
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