Syllabus

Syllabus:
Introduction and Mathematical Preliminaries [3 L]: Modeling complex systems as nonlinear systems, motivating examples, detailed discussions on practical nonlinear systems and their salient features, necessary mathematical tools.
Analysis of second order Nonlinear systems [2L]: Phase Plane Analysis techniques, Poincare Bendixon theorem for limit cycle detection.
Stability of equilibrium points and Region of Attractions [10 L]: Lyapunov stability analysis for nonlinear systems, Local and Global Stability, concept of stability basin, Cheatev's Instability Theorem, Condition of linearization and stability analysis of the linearized model near an equilibrium point, invariant set theorems and its importance. Stability analysis of nonautonomous systems, use of comparison lemma to analyze stability,
Mid-Sem
Input-state and Input-output stability [5L]: Boundedness and ultimate boundedness, concept of input to state stability, Input Output Stability Analysis, Introduction to L-P space, L Stability analysis of state models, small gain theorem.
Passivity [4 L]: Memoryless functions and Sector Nonlinearities, PRTF & Lyapunov Feedback systems, Lure’s Problem, Circle & Popov Criteria
Controller Design for Nonlinear Systems [6L]: Normal form, Controller form, Concepts & linearization, Feedback linearization, Sliding Mode Control
End Sem

Link to Lecture Plan:
https://nitrklacin-my.sharepoint.com/:b:/g/personal/rudras_nitrkl_ac_in/EXRTBxPGleVLj0NykkGlDiYB0vsou7GrE8ZLbtre4k5faA?e=Vf2mNY

Link to important reference and supporting study materials:
https://flyingv.ucsd.edu/krstic/files/Khalil-3rd.pdf (Courtesy:
University of California San Diego)
https://people.ee.ethz.ch/~apnoco/Lectures2020/2020_NLSC_lecture_notes.pdf (Courtesy ETH Zurich)
https://web.mit.edu/nsl/www/videos/lectures.html (Courtesy:
Massachusetts Institute of Technology)

Elaborating salient features of the nonlinear differential equations

Explaining the stability analysis tools of the nonlinear systems.

Introducing different advanced analysis techniques for nonautonomous nonlinear systems.

To introduce the design techniques of nonlinear controllers for different complicated dynamical systems.

After attending this course, students should be able to:
1) Find out the fixed point of a given nonlinear dynamical system and explore the possibilities of carrying out linear analysis.
2) Analyse the stability of nonlinear systems using LaSalle's invariance theorem and determine the region of attraction for the same.
3) Determine a suitable analysis method for assessing the stability of the autonomous and nonautonomous nonlinear systems
4) Utilize the Lebsigue space concept to analyse the nonlinear systems' stability subject to different excitation signals.
5) Carry out the passivity analysis for a given system.
6) Design nonlinear control law to address the performance issues of complicated nonlinear systems.

The above COs indicate how this course will enhance or empower a particular ability in a student.
List of POs of the M.Tech control engineering:
PO1: An ability to independently carry out research /investigation and development work to solve practical problems
PO2: An ability to write and present a substantial technical report/document
PO3: Students should be able to demonstrate mastery over the area as per the program's specialisation. The mastery should be at a level higher than the requirements in the appropriate bachelor's program
PO4: Utilize industry-standard software, hardware, and programming tools to design, simulate, and implement control and automation systems.
PO5: Exhibit advanced competence in identifying and addressing control problems in Electric Vehicles, Renewable Energy, Automation, Defense, Aerospace, Networking, and Biological Systems.
PO6: Demonstrate professionalism and ethical responsibility and engage in lifelong learning to adapt to technological advancements and evolving industry demands
For the current list of Course Outcomes, the course articulation matrix is as follows.

3 1 3 2 2 1
3 1 3 1 3 1
3 1 3 1 3 1
3 1 3 1 1 1
3 1 3 1 1 1
3 1 3 2 3 1
The rows of the above matrix denote how different skills or habits mentioned in different POs are aligned with the particular ability mentioned for an individual CO. On the other hand, the columns of the above matrix indicate how one particular PO's skill or habit is aligned with different COs.

H. K. Khalil, Nonlinear Systems, Prentice Hall, 3rd ed., 2002

J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, 1991

Nijemjer and A. van der schaft, Nonlinear dynamical control systems, Springer, 1989

M. Vidyasagar, Nonlinear Systems Analysis, Society for Industrial and Applied Mathematics, 2002.

https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=37

https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9