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Návod
Webová stránka:
http://dce.fel.cvut.cz/studium/nelinearni-systemy-chaos
Anotace:
This advanced course will cover modern methods in nonlinear systems theory and applications. Basic feature of nonlinear systems theory is that state space approach is prevailing and frequency response methods are not generally applicable. The course will cover the topic: state model of nonlinear dynamical systems and its analysis, Lyapunov's stability, asymtotic stability and Lyapunov's methods, control synthesis via approximate linearization, high gain observers, gain scheduling. The main stress is on the so-called structural methods for the nonlinear control design, i.e. study of the system structural properties allowing easier applications of known control methods. That would consist of basics of differential geometry, Lie derivative, various types of exact feedback linearization, input-output linearization, zero dynamics, minimum phase systems, MIMO systems, decoupling. Last but not least, the course will provide verz basci information about chaotic systems including some motivating examples.
Osnovy přednášek:
| 1. | | State space model of nonlinear dynamical system, typical nonlinear phenomena, examples.State space model of nonlinear dynamical system, typical nonlinear phenomena, examples. |
| 2. | | Further practical examples of nonlinear dynamical systems. Chaotic systems. |
| 3. | | Mathematical basics. Existence and uniqueness of solutions, dependence on initial conditions and parameters.. |
| 4. | | Definitions and methods of stability analysis. Ljapunov's function method and approx. linearization method. |
| 5. | | Analysis of stability of perturbed asymptotically and exponentially stable systems. |
| 6. | | Control synthesis via approximate linearization and obust linear methods. High gain observers. |
| 7. | | Control synthesis via approximate linearization and gain scheduling. |
| 8. | | Structural methods in nonlinear control synthesis - basic notions, exact transformations of nonlinear systems. |
| 9. | | Structural methods and various types of exact linearization. Zero dynamics and minimum phase. |
| 10. | | Structural methods and some basics of differential geometry and advanced analysis. |
| 11. | | SISO systems. Relative degree. Input-output linearization. Zero dynamics, minimum phase systems. |
| 12. | | MIMO systems I. Vector relative degree. Input-output linearization. |
| 13. | | MIMO systems. Zero dynamics, minimum phase systems. |
| 14. | | MIMO systems. Decoupling. |
Osnovy cvičení:
| 1. | | Example of nonlinear models and their simulations. |
| 2. | | Laboratory examples of nonlinear systems. |
| 3. | | Setting of individual long term homeworks for analysis and design of nonlinear systems control. |
| 4. | | Sustems modelling |
| 5. | | Modeling and simulation model design |
| 6. | | Nonlinear systems simulations |
| 7. | | Analysis of stability |
| 8. | | Desing tasks and algorithms of control |
| 9. | | Realization of control algorithms |
| 10. | | Verification of control algorithms on simulation models |
| 11. | | Exact feedback linearization design |
| 12. | | Exact feedback linearization design - MIMO systems |
| 13. | | Realization of controllers based on Exact feedback linearization design |
| 14. | | Defense of results of long term homework |
Literatura:
| 1. | | H. K. Khalil, Nonlinear Systems. Third edition. Prentice Hall 2002. ISBN 0-13-067389-7. |
Požadavky:
Prerequisites for this course is good knowledge of basics of control systems (frequency response, feedback, stability, PID regulation,...), then good knovledge of advanced course of linear control introducing notions like controllability, observability, minimal realization. Examples of these course are Automatic control and dynamical systems theory teache at CTU. last but not least, good knowledge of linear algebar (eigenvectors, eigenvalues, canonical forms of matrices,...) and mathematical analysis (differential calculus of more variables) are required.
Stránky předmětu:
https://moodle.dce.fel.cvut.cz/
Poznámka:
| Rozsah výuky v kombinované formě studia: 21p+3c |
Klíčová slova:
nonlinear systems, chaos, exact feedback linearization
Předmět je zahrnut do těchto studijních plánů:
| Plán |
Obor |
Role |
Dop. semestr |
| Stránka vytvořena 26.3.2025 17:50:36, semestry: Z/2024-5, Z,L/2025-6, L/2024-5, připomínky k informační náplni zasílejte správci studijních plánů |
Návrh a realizace: I. Halaška (K336), J. Novák (K336) |