Syllabus:

Linear Systems Theory (EE 550)

L-T-P-C : 3-0-0-6
Course Contents:

Maths Preliminaries: Vector Spaces, Change of Basis, Similarity Transforms, Introduction: Linearity, Differential equations, Transfer functions, State Space representations, Evolution of State trajectories Time Invariant and Time Variant Systems, Controller Canonical Form, Transformation to Controller Canonical form SI, MI, State Feedback Design SI, MI, Discrete time systems representation, reachability and state feedback design, Observability: Grammian, Lyapunov Equation, Output Energy, Observability matrix Observer canonical form (SO, MO), Unobservable subspace, Leunberger Observer (SO, MO), State Feedback with Leunberger Observers, Minimum order observers, Stabilizability and Detectability.

Texts/References:

1. T. Kailath, Linear System, Prentice-Hall, Inc., 1st Edition, 1980
2. C.T. Chen, Linear System Theory and Design, Oxford University Press, 4th Edition, 2013
3. L. A. Zadeh and C. A. Desoer, Linear System Theory: The State Space Approach, Springer-Verlag, 2008.
4. W. Rugh, Linear System Theory, Prentice Hall, 2nd Edition, 1995.
5. S. Lang, Introduction to Linear Algebra, Springer-Verlag, 2nd Edition, 1997.
6. W. M. Wonham, Linear Multivariable Control, A Geometric approach, Springer-Verlag, 1985.
7. J.P. Hespanha, Linear Systems Theory, Princeton University Press, 2nd Edition, 2018.

Estimation and Identification (EE 551)

L-T-P-C : 3-0-0-6
Course Contents:

Estimation and identification – overview and preliminaries, Introduction to linear least squares estimation, Estimator properties – error bounds and convergence, Maximum likelihood estimation, Maximum a posteriori estimation, Linear mean squared estimation, Unmeasured disturbances and Kalman filter, Extended Kalman filter and Unscented Kalman filter for nonlinear systems, Frequency Response Identification – ETFE, ARX and ARMAX models for linear system identification, Recursive approaches for linear systems – RLS, ELS, RML, Introduction to nonlinear system identification – NARX, NRMAX models, Conditions on experimental data, Convergence properties of the identified model

Texts/References:

1. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, 1993
2. R. L. Eubank, Kalman filter primer, Chapman & Hall, 2006.
3. L. Ljung, System identification: theory for the user,. 2E, Prentice Hall, 1999
4. R. Pintelon and J. Schoukens, System identification: a frequency domain approach, Wiley & Sons, 2012
5. S. A. Billings, Nonlinear system identification: narmax methods in the time frequency and spatio temporal domains, Wiley , 2013

Applied Control Lab (EE 552)

L-T-P-C : 0-0-3-3
Course Contents:

Familiarization with Simulink/MultiSim, setting of model configuration parameters, Development of Simulink/MultiSim based control circuit, Design of automatic gain control (AGC) circuit,Limitations of proportional (P) control, offset error, Design of PI control for offset error improvement, PI control circuit-based speed and disturbance control of coupled DC motor.

Texts/References:

1. Norman. S. Nise, Control systems engineering, Wiley India Edition, 2018

Linear Algebra (EE 556)

L-T-P-C : 3-0-0-6
Course Contents:

Vector spaces, linear independence, bases and dimension, linear maps and matrices, fundamental subspaces, rank-nullity theorem, eigenvalues, invariant subspaces, inner products, norms, orthonormal bases, spectral theorem, unitary and orthogonal transformations, operators on real and complex vector spaces, singular value decomposition, annihilating polynomials, characteristic polynomial, minimal polynomial, Jordan canonical form of matrices, sign-definite matrices, basic iterative methods for solutions of linear systems and their rates of convergence, iterative methods for eigenvalue problems, least squares using linear algebra.

Texts/References:

1. K. Hoffman and R. Kunze, Linear Algebra, Pearson Education Inc., 2nd Edition, 2013.
2. G.H. Golub and C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, 4th Edition, 2013.
3. S. Axler, Linear Algebra Done Right, 3rd Edition, Springer, 2015.
4. G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, U.S., 5th Edition, 2016.
5. D.S. Watkins, Fundamental of Matrix Computations, Wiley, 3rd Edition, 2010.
6. N. Johnston, Introduction to Linear and Matrix Algebra, Springer, 1st Edition, 2021

Optimal Control (EE 553)

L-T-P-C : 3-0-0-6
Course Contents:

Mathematical preliminaries, Static optimization, Calculus of variations, Solution of general continuous time optimal control problem, Continuous time Linear Quadratic Regulator design - Riccati equation, Optimal tracking problem, Free final time problems, Minimum time problem, Constrained input control and Pontryagin’s maximum principle, Bang-Bang control, Principle of optimality, Dynamic Programming, Discrete LQR using Dynamic Programming, Continuous control and Hamilton-Bellman-Jacobi Equation.

Texts/References:

1. D. E. Kirk, Optimal Control Theory: An Introduction, Prentice-Hall, 2004.
2. B.D.O. Anderson and J.B. Moore, Optimal Control: Linear Quadratic Methods, Dover Publications, 2014.
3. F.L. Lewis, D. Vrabie and V.L. Syrmos, Optimal Control, 3rd edition, Wiley & Sons, 2012

Nonlinear Systems and Control (EE 554)

L-T-P-C : 3-0-0-6
Course Contents:

Introduction: state-space representation of dynamical systems, phase-portraits of second order systems, types of equilibrium points; Existence and uniqueness of solutions; Features of nonlinear dynamical systems; Stability analysis: Lyapunov stability of autonomous systems, Lyapunov theorem of stability, LaSalle invariance principle, input/output stability of non-autonomous systems, passivity theorem, small gain theorem, Kalman-Yakubovich-Popov lemma, Aizermann conjecture, circle/Popov criteria; Limit cycles: Bendixson criterion, Poincare-Bendixson criterion; Describing functions method, methods of integral quadratic constraints; Introduction to manifolds.

Texts/References:

1. H. K. Khalil, Nonlinear systems, Prentice Hall, 3rd Edition, 2002.
2. M. Vidyasagar, Nonlinear systems analysis, 2nd Edition, Society of Industrial and Applied Mathematics, 2002.
3. H. Marquez,Nonlinear Control Systems, Analysis and Design, Wiley, 2003.
4. A. Isidori,Nonlinear Control Systems, Springer, 3rd Edition, 1995.
5. F. Verhulst,Nonlinear Differential Equations and Dynamical Systems, Springer, 2nd Edition, 1996.

Automation Lab (EE 555)

L-T-P-C : 0-0-3-3
Course Contents:

Introduction to ROS, Familiarization with platforms for simulating robotic systems in open-loop and in closed-loop, Controller design for robotic systems, Experiments on swarm behavior of networked UGVs, AI-based simple robotic experiments.

Texts/References:

1. Peter Corke, Robotics, Vision and Control, Springer Cham, Second Edition, 2017.

Optimization (EE 557)

L-T-P-C : 3-0-0-6
Course Contents:

Concepts from geometry, calculus, and set theory required in optimization; Unconstrained Optimization: Conditions for local minimizers, gradient methods, Newton’s method, Least squares; Duality theory; Constrained Optimization: Lagrange multipliers, KKT condition; Convex optimization problems; Semi-definite programming; Applications to various fields of engineering; Numerical software for optimization; Introduction to advanced topics in optimization;

Texts/References:

1. E. K. P. Chong and S. H. Zak, An Introduction to Optimization, 4th Edition., Wiley India Pvt. Ltd., 2013.
2. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge: Cambridge University Press, 2004.
3. D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 5th Edition., Springer, 2021.