## 20810204 - Dynamics and Control of Complex Systems

Provide to the students methodologies and techniques for the analysis and modeling of linear time-invariant systems by focusing on the state-space representation. Provide the knowledge for the design of feedback control systems. Derive the state-space model of Multi-Input Multi-Output systems. Provide the knowledge of the structural properties of MIMO dynamical models and the asymptotic observer for the eigenvalue assignment problem and the regulation problem. Provide the students with basic concepts for the analysis of nonlinear system.

Curriculum

teacher profile | teaching materials

Programme

Linear Systems
1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. DIFFERENTIAL EQUATIONS
2.1. Linear Differential Equations with Constant Coefficients
2.2. Exponential Matrix
2.3. Free Evolution
2.4. Forced Evolution
3. RELATIONSHIP BETWEEN REPRESENTATIONS
3.1. From State-Spate to Transfer Function
3.2. From Transfer Function to State-Spate
4. MODAL DECOMPOSITION
4.1. Eigenvalues and Eigenvectors
4.2. Coordinate Transformation
4.3. Diagonalization and Jordanization
5. STRUCTURAL PROPERTIES
5.1. Controllability and Observability
5.2. Controllability and Observability Kalman Forms
5.3. Kalman Canonical Decomposition
7. EIGENVALUE ASSIGNMENT PROBLEM
7.1. Eigenvalue assignment using state feedback
7.1.1. Assignment Theorem (SISO/MIMO)
7.1.2. Assignment Unicity Theorem (SISO)
7.2. Stabilization Problem
7.3. State Asymptotic Observer
7.4. Separation Principle
7.5. Eigenvalue placement using output feedback
8. LINEAR OUTPUT REGULATION PROBLEM
8.1. Full-Information Problem
8.2. Error-Feedback Problem
Nonlinear Systems
9. INTRODUCTION TO NONLINEAR SYSTEMS
9.1. Fundamental Properties
9.2. Lipschitz Condition
9.3. Existence and Unicity of Solution
9.4. Comparison Lemma
10. LYAPUNOV STABILITY
10.1. Autonomous Systems
10.2. Stability Definition
10.3. Stability Theorem (Direct Criterion)
10.4. Chetaev Instability Theorem
10.5. Lyapunov Control Functions (Krasovskii)
10.6. Invariance Principle (LaSalla Theorem)
10.7. Stability Theorem for Linear Systems (Indirect Criterion)

Core Documentation

Linear Systems
1. An Introduction to Linear Control Systems, Thomas E. Fortmann, Konrad L. Hitz
2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)
3. Sistemi di controllo (Vol. 2), Alberto Isidori

Nonlinear Systems
1. Nonlinear Systems (3rd Edition), Hassan K. Khalil

Reference Bibliography

None

Type of delivery of the course

frontal lessons

Type of evaluation

Distinct Written and Oral Exam

teacher profile | teaching materials

Programme

Linear Systems
1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. DIFFERENTIAL EQUATIONS
2.1. Linear Differential Equations with Constant Coefficients
2.2. Exponential Matrix
2.3. Free Evolution
2.4. Forced Evolution
3. RELATIONSHIP BETWEEN REPRESENTATIONS
3.1. From State-Spate to Transfer Function
3.2. From Transfer Function to State-Spate
4. MODAL DECOMPOSITION
4.1. Eigenvalues and Eigenvectors
4.2. Coordinate Transformation
4.3. Diagonalization and Jordanization
5. STRUCTURAL PROPERTIES
5.1. Controllability and Observability
5.2. Controllability and Observability Kalman Forms
5.3. Kalman Canonical Decomposition
7. EIGENVALUE ASSIGNMENT PROBLEM
7.1. Eigenvalue assignment using state feedback
7.1.1. Assignment Theorem (SISO/MIMO)
7.1.2. Assignment Unicity Theorem (SISO)
7.2. Stabilization Problem
7.3. State Asymptotic Observer
7.4. Separation Principle
7.5. Eigenvalue placement using output feedback
8. LINEAR OUTPUT REGULATION PROBLEM
8.1. Full-Information Problem
8.2. Error-Feedback Problem
Nonlinear Systems
9. INTRODUCTION TO NONLINEAR SYSTEMS
9.1. Fundamental Properties
9.2. Lipschitz Condition
9.3. Existence and Unicity of Solution
9.4. Comparison Lemma
10. LYAPUNOV STABILITY
10.1. Autonomous Systems
10.2. Stability Definition
10.3. Stability Theorem (Direct Criterion)
10.4. Chetaev Instability Theorem
10.5. Lyapunov Control Functions (Krasovskii)
10.6. Invariance Principle (LaSalla Theorem)
10.7. Stability Theorem for Linear Systems (Indirect Criterion)

Core Documentation

Linear Systems
1. An Introduction to Linear Control Systems, Thomas E. Fortmann, Konrad L. Hitz
2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)
3. Sistemi di controllo (Vol. 2), Alberto Isidori

Nonlinear Systems
1. Nonlinear Systems (3rd Edition), Hassan K. Khalil

Reference Bibliography

None

Type of delivery of the course

frontal lessons

Type of evaluation

Distinct Written and Oral Exam