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### SC 601 - Modelling and Identification of Dynamical Systems

Classification of inputs and models, analytical and experimental methods of modelling: transform methods, impulse and frequency response, Fourier transform. Response to random inputs, state-space models, Z transform, correlation technique. pseudo-random signal testing parameter tracking, regression and least-square methods.

Discrete time series models: FIR and ARX models, development of ARX models by least square estimation, Unmeasured disturbance Modeling: AR-MAX, OE, Box-Jenkin'smodels, Time-series analysis, AR and ARX models, least-squares setting.

- E.O. Doeblin, System Modelling and Response, John Wiley Sons, 1980
- Desai and Lalwani, Identification Techniques, Tata McGraw Hill, 1977
- L. Ljung, System Identification: Theory for the User, Prentice Hall, 1992

### SC 602 - Control of Nonlinear Dynamical Systems

An introduction to vector fields, flows and integral curves of differential equations, affine-in-the control nonlinear systems, equilibria, notions of stability, La Salle's invariance principle, feedback linearization, zero dynamics, controller design examples, distributions, integrable and involutive distributions

Text/References :- H. K. Khalil, Nonlinear Systems -, Prentice Hall, 2002
- V. Arnold, Ordinary Differential Equations -, Springer, 1992.
- A. Isidori, Nonlinear Control Systems -, Springer, 1989.
- H. Neijmier and A. Van der Schaft ,Nonlinear Control Systems -, Springer,1992.

### SC 605 - Optimization-based Control of Stochastic Systems

Pre-requisites : SC 625 - Systems Theory , OR EE 635 - Applied Linear Algebra in Electrical Engineering, OR EE640 - Multivariable Control Systems (convex optimization is a plus but not a requirement ( the necessary theory will be reviewed ))

Review of finite-dimensional linear systems, review of LQ theory, basics of convex optimization, stochastic processes in discrete time, Markov processes. Optimization-based control, key concepts; brief excursion into Markov control processes. Finite-horizon problems: LQ with constraints-probabilistic, variance, ' integrated chance constraints ', etc. Infinite horizon considerations: stability, quantitative bounds on performance loss.

There is no required textbook; course notes will be supplied. In addition, the following is a non-exhaustive list of references:

- R. W. Brockett, Finite-dimensional linear Systems, John Wiley& Sons Inc, 1970
- J. M. Maciejowski, Predictive Control with Constraints, Prentice Hall, 2001
- S. P. Boyd and L. Vanderberghe, Convex Optimization, Cambridge University Press, 2004
- B. Hajek, Probability with Engineering Applications
- B. Hajek, An Exploration of Random Processes for Engineers, Lecture notes at University of Illinois, Jan 2011

### SC 607 - Optimization

Introduction to interval analysis. Interval numbers and interval arithmetic. Functions of intervals. Interval linear equations and linear inequalities. Taylor series. Interval Newton method for nonlinear equations of one variable and systems of nonlinear equations. Covering algorithm for parameter dependant systems of nonlinear equations. Global optimization using interval analysis.

Applications of interval analysis tools to control systems, robotics, neural networks and other areas of science and engineering.

- E. Hansen, Global Optimization Using Interval Analysis, Second edition, Marcel Dekker, New York, 2005.
- R. E. Moore, Methods and Application of Interval Analysis, SIAM, Philadelphia, 1979

### SC 612 - Introduction to Linear Filtering and Beyond

Pre-requisites : SC-625 (Systems Theory) or EE-635 (Applied Linear Algebra) in Electrical Engineering, and reasonable background in probability & randomprocesses, and sufficient mathematical maturity.

Probability spaces, conditional expectations as projections, etc.

- Gaussian and conditionally Gaussian processes
- The Kalman _lter:
- derivation, application areas
- the Kalman filter under communication constraints
- asymplectic algebraic view of the Kalman filter
- The Levinson and the Wiener filters, and connections to orthogonal polynomials on the unit circle
- Quick tour of nonlinear filters

No required text, course notes will be supplied. The following is a non-exhaustive list of references:

- B. Hajek, Probability with Engineering Applications
- A.V. Balakrishnan, Kalman Filtering Theory
- B.D.O. Anderson & J.B. Moore, Optimal Filtering
- A.H. Jazwinski, Stochastic Processes and Filtering Theory
- D. Luenberger, Optimization by Vector Space Methods
- D. Bertsekas, Dynamic Programming and Optimal Control, vol I

### SC 616 - Large Scale Systems

Prerequisites : SC 601 Modeling of Dynamic Systems

Introduction to Large Scale Systems. Principal Component based model reduction methods. Model reduction through aggregation. Frequency domain based model reduction techniques - Pade, Routh and Continued fraction approximations. Model reduction using step and inpulse error minimization techniques. Balanced truncation and Hankel norm minimization.

Pole placement techniques. State feedback and output feedback of single and multi-input systems. Multirate output feedback techniques - Periodic Output Feedback (POF) and Fast Output Sampling Feedback (FOS).

Robust Control Techniques. Uncertain systems. Kharitonov theorem. State Feedback design techniques for parametric uncertain systems.

- M. G. Singh, M.S. Mamoud, Large Scale Systems Modelling, International Series on Systems and Control, Pergamemon Press, 1981
- M.Jamshidi, Large Scale Systems: Modelling and Control, North Holland, New York, 1983
- Kemin Zhou, John C. Doyle, Keith Glover, Robust and Optimal Control, Prentice Hall, Upper Saddle River, New Jerset, 1996
- M. Gopal, Modern Control Systems Theory, 2nd Edition, John Wiley, 1993
- S. P. Bhattacharyya, H. Chappelat, L. H. Keel, Robust Control - The Parametric Approach, Prentice Hall, NJ, 1995
- Selected Papers from Technical Journals

### SC 617 - Adaptive Control Theory

Prerequisites : Systems Theory (SC 625) or EE 635

Stability of time-varying systems - Barbalat's Lemma, Overview of Lyapunov Stability Theory, Classical Adaptive Control Theory - Certainty Equivalence, Filter Construction and Non-Certainty Equivalence Adaptive Control, Advanced topics include parameter projection and robustness modifications in adaptive control.

There is no required text for the course and adequate notes will be provided. However, additional material and problems might be derived from the following sources:

- P. Ioannou and J. Sun, Robust Adaptive Control, Upper Saddle River, NJ: Prentice Hall, 1996.
- S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Upper Saddle River, NJ, Prentice Hall, 1989
- H. K. Khalil, Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall, 2002.

### SC 618 - Analytic and Geometric Dynamics

Prerequisites : An understanding of vector spaces (equivalent to SC 625)

- Elementary Newtonian Dynamic Dynamics of systems of particles - Newton's laws and rotational analogues, work-energy and impulse-momentum relationships, Kinematics of particles and rigid bodies, Impact problems, Changing mass problems.
- Kinematics Reference frames - orthonormal, dextral frames, sequence of rotations, Rates of change of vectors in various frames, Coriolis acceleration and effects.
- Analytical Dynamics - Lagrangian/Hamiltonian formulations, Constraints, generalized coordinates, Virtual work principle, generalized forces, Extension of dynaimics (D-Alembert principles), Lagrange's Equations, Conserved quantities and Cyclic coordinates, Generalized momenta, Hamilton/Jacobi integral, Hamilton's equations, Routhian and Routh's equations, Non-Holonomic Constrains, Lagrange Multipliers.
- Introduction to smooth manifolds and Lie groups, kinematics on the Lie groups SO(3) and SE(3), a geometric view of the rigid body motion both in a Hamiltonian and Lagrangian geometric framework, the rigid body stability and heavy top stability

- Introduction to Robotics: Mechanics and Control - J. J. Craig, Addison Wesley, 2nd Edition, 1989
- Analytical Mechanics - Joseph S. Torok, Wiley-Interscience, 1999
- Principles of Dynamics - Donald T. Greenwood, Prentice-Hall, 2nd Edition, 1987
- Methods of Analytical Dynamics - Leonard Meirovitch, McGraw-Hill, 1970
- Geometric Mechanics and Symmetry - D .D. Holm, T. Schmah and C. Stoica, Oxford University Press, 2009
- Introduction to Mechanics and Symmetry - J. Marsden and T. Ratiu, Springer-Verlag, 1994

### SC 619 - Control of Langrangian and Hamiltonian Systems

Prerequisites : Vector Spaces (Linear Algebra)

- Rigid body motions, Hamilton's principle, Euler - Lagrange equations, holonomic and nonholonomic constraints
- Differentiable manifolds, tangent bundles, distributions, fiber bundles, differential forms
- Symplectic manifolds, Poisson manifolds, momentum maps, the mechanical connection
- Dirac structures, distributed parameter systems, Stokes' theorem, Energy-Casimid techniques

- Introduction to Mechanics and Symmetry - J.E. Marsden and T.Ratiu, Springer - Verlag, 1994
- Nonholonomic Mechanics and Control - A.M.Bloch, Springer, 2003

### SC 620 - Process Automation

Basic concepts and techniques, tuning procedures, special feedback techniques, direct synthesis and adaptive control, decoupling and feed-forward methods, various multiple loop feedback control strategies widely used in industries, such as cascade, ratio, split-range, selective, feedforward compensation, sensors and actuators, basics of industrial automation systems: PLCs and Distributed control systems (DCS), their features and applications

Text/References :- M. Morari and T.J. McAvoy, Chemical Process Control - CPC/Elsevier, Amsterdam, 1986
- F. G. Shinskey, Process Control Systems, McGraw Hill, 1979
- Process control instrumentation technology (8th edition) by Curtis Johnson,TMH

### SC 621 - Quantitative Feedback Theory I

Prerequisites : A First Course in Control System Design

Introduction to feedback properties. One and two degrees of freedom structures. Properties of loop transmission function. Formulation of closed-loop specifications in time and frequency domain.
Basic procedure for single input-output linear-time-invariant systems: Extensions to time varying plants.

Design procedures for Multi input-output systems.

- I.M. Horowitz, Quantitative Feedback Theory (QFT), Volume 1, Colorado Press, Boulder, Colorado, 1993.
- C. H. Houpis, S. I. Rasmussen, Quantitative Feedback Theory : fundamentals and applications, Marcel Dekker, 1999.
- O. Yaniv, Quantitative Feedback Design of Linear and Nonlinear Control Systems, Kluwer Academic, Boston, 1999.

### SC 623 - Optimal and Robust Control

Prerequisites : Classical Control theory and elementary notions of state-space Theory.

The linear-Quadratic problem-formulation and solution; LQG problem; Frequency domain interpretations; loop transfer recovery; robustness issues; H_{2} optimization; small gain theorem; H_{∞} optimality-motivation, the standard set up. Co-prime factorization, the model-matching problem, state space solutions.

- Kwakernaak and Sivan Linear Optimal Control, John Wiley, 1972.
- Anderson and Moore Linear Optimal Control Prentice-Hall 1990.
- B. A. Francis A Course in H
_{∞}Control Theory-Springer Verlag 1987

### SC 624 - Differential Geometric Methods in Control

Prerequisites : Vector Spaces (Linear Algebra)

**Outline:**

- Hamilton's principle, Euler-Lagrange equations, holonomic and non-holonomic constraints, Lagrange D'Alembert equations, examples -rolling coin, knife edge, rolling sphere
- Rotations, rigid body motions and the Lie groups SO(3) and SE(3), the Lie algebras so(3) and se(3), the exponential map, twists and screw representations.
- Differentiable manifolds, tangent vectors, vector fields, covector fields, integrable distributions, Frobenius' theorem, differential forms
- Fibre bundles, connections

- A Mathematical Introduction to Robot Manipulation and Control - R. Murray, Z. Li and S. Sastry, CRC Press, 1992
- Nonholonomic Mechanics and Control - A. M. Bloch, Springer, 2003 Nonlinear Control Systems - H. Neijmier and A. Van der Schaft, Springer,1992.
- Ordinary Differential Equations - V. Arnold, Springer, 92.

### SC 625 - Systems Theory

Prerequisites : None

**Outline:**

- (Basics of linear theory / linear algebra) Vector spaces, dimension, basis, subspaces, dual spaces, annihilators, direct sum, linear transformations, matrix representations, similarity, rank and nullity, a primer on linear systems - state-space models, minimal realization, controllability, observability
- (Optional instructor-dependant addition) Basics of nonlinear theory: n-surfaces, tangent vectors, vector fields, solutions of differential equations, parametrized n-surfaces, charts, at-lases, differentiable manifolds, tangent bundle, flows, a primer on non-linear systems

- Finite Dimensional Vector Spaces - P. Halmos, Springer, 84
- Elementary Topics in Differential Geometry - I. Thorpe, Springer, 88
- Ordinary Differential Equations - V. Arnold, Springer, 92
- A Comprehensive Introduction to Differential Geometry - Vol 1, M. Spivak, W. A. Benjamin Inc, 1965

### SC 627 - Motion Planning and Coordination of Autonomous Vehicles

Prerequisites : Classical Control Theory

**Outline:**

MOTION OF PLANNING:

Introduction : Overview of robot motion problems, Configuration space of a robot, Example configuration spaces. (~2 weeks)

Classical motion planning paradigm : the roadmap, potential field method, cellular decomposition approach, Graph search and Discrete planning Algorithms. (~3 weeks)

Sensor based motion planning : Class of Bug algorithms, Incremental Voronoi Graph. (~2 weeks)

MOTION COORDINATION:

Introduction to multi-agent systems, multi-agent coordination strategies (specifically for autonomous vehicle): Leader-follower, potential field theory, algebraic graph theory, behavioral based method (~2 weeks)

Multi-agent Consensus algorithms: basics of matrix theory and graph theory, consensus algorithms for dynamical systems, applications of consensus algorithms - Rendezvous, flocking, formation flying (~3 weeks)

Other applications: Area coverage problem, boundary tracking problem and resource allocation techniques (~2 week)

- Principles of Robot Motion : Theory, Algorithms and Implementation, Howie Choset and Others MIT Press, 2005
- Planning Algorithms, Cambridge University Press, Steven M. LaValle, Cambridge University Press
- Cooperative Control of Distributed Multi-Agent Systems - Jeff Shamma, John Wiley and Sons Ltd., 2007
- Distributed Control of Robotic Networks - F.Bullo and J. Cortés and S. Martínez, Princeton University Press, 2009
- Distributed Consensus in Multi-vehicle Cooperative Control : Theory and Applications – Wei Ren and Randal W. Beard, Springer, 2007

### SC 628 - Guidance Strategies for Autonomous Vehicles

Prerequisites : None

Basics of missile guidance - Introduction to missiles, missile guidance laws(pursuit, line-of-sight, proportional navigation), capturability analysis formaneuvering and non-maneuvering targets (8 weeks)

Applications of guidance strategies to cooperative control - multi-vehicle pathplanning, collision avoidance, rendezvous/docking problems

N.A.Shneydor: Missile guidance and pursuit: Kinematics,Dynamics and Control, Harwood Publishing, 1998

### SC 629 - Introduction to Probability and Random Processes

- Discrete-type random variables - random variables and probability mass function, mean and variance, conditional probabilities - independence, Baye's formula - discrete distributions: Bernoulli, binomial, geometric, Poisson maximum likelihood estimation
- Continuous-type random variables - cumulative distribution functions, probability density function - independence, Baye's formula - continuous distributions: uniform, exponential, Gaussian, chi-square - functions of random variables .
- Joint distributions, transformation of probability functions under maps, joint Gaussian distribution.
- Minimum mean square error estimation
- Basic ideas of the probabilistic method-the first and second moment techniques

- (Text) Probability with Engineering Applications by B. Hajek , Cambridge University Press, 2005.
- (reference) Probability and computing: Randomized Algorithms and Probabilistic Analysis, by Mitzenmacher and E. Upfal, Cambridge University Press, 2005
- (Reference) Applied Probability, by P. Pfeiffer, Birkh303244user Boston, 1978
- (Reference) Introduction to Probability, by D Bertsekas and J. Tsitsiklis, Athena Scientific, 2008

### SC630 - Variable Structure and Sliding Mode Control

Introduction to variable structure system, phase plane analysis, Discontinuous system- solution in Filippov sense, Sliding Hyper plane design-pole placement and LQR method, Reachability condition, Digital sliding mode control, Reaching law for discrete-time sliding mode (DSM), DSM for matched and unmatched uncertainties, DSM using multirate technique, Finite time and terminal sliding mode, Sliding mode observer, Integral sliding mode, Integral sliding mode with nonlinear composite feedback control (CNF),Second order sliding mode control and observation, Application of sliding mode control- Flight control design, Smart structure, slosh container system and Nuclear reactor.

Text/References :- Sliding Mode Control : Theory and Applications - C. Edwards and S. Spurgeon, Taylor & Francis, 1998.
- Discrete-time Sliding Mode Control : A Multirate Output Feedback Approach, B. Bandyopadhyay and S. Janardhanan, Vol. 323, in Lecture Notes in Control and Information Science, 147 p., Springer-Verlag, ISBN 3-540-28140-1, Oct. 2005.
- Sliding Mode Control using Novel Sliding Surfaces, B. Bandyopadhyay, Deepak Fulwani and K. S. Kim, Vol.392 Lecture Notes in Control and Information Science, Springer-Verlag, ISBN 978-3-642-03447-3, Oct. 2009.
- Sliding Mode Control in Electromechanical Systems, VadimIvanovichUtkin, Jürgen Gulder, Jingxin Shi, CRC PressINC, 2009 - 485 pages.

### SC 631 - Games and Information

Prerequisites : A course in optimization, such as SC 607, AE 310, EE 659,IE 501, IE 601 or consent of instructor

Basics of static games: Zero-sum and non-zero sum games, concept of Nash equilibrium and Stackelberg equilibrium. Multi-act games: extensive form of games and information sets. Aumann's common knowledge, rationality, bounded rationality. Dynamic games: Incomplete information, Bayesian Nash equilibrium. General formulation of dynamic games: sub-game perfectness, open-loop, closedloop and feedback Nash equilibria, informational properties of Nash equilibria, informational nonuniqueness. Information structures: static and dynamic information structures. Dynamic stochastic team problems: introduction, person-by-person optimality, Witsenhausen problem, signalling, connections to economics and information theory.

- T. Basar and G. Olsder, Dynamic Noncooperative Game Theory, SIAM, 1999
- E. Rasmusen. Games and Information: An Introduction to Game Theory. Wiley-Blackwell, 4th ed, 2006
- M. J. Osborne and A. Rubinstein. Course in Game Theory. MIT Press, 1994
- S. Yuksel and T. Basar, Stochastic Networked Control Systems - Stabilization and Optimization under Information Constraints. Birkhauser, 2013

### SC 633 - Geometric and Analytic Aspects of Optimal Control

Prerequisites : SC-625 (Systems Theory) or EE-635 (Applied Linear Algebrain Electrical Engineering)

- Geometric theory of the Pontryagin minimum principle, applications to nonlinear filtering, management science ,operations research
- Dynamic programming: analytical foundations, deterministic and stochastic versions, applications to mathematical finance
- Reachability of nonlinear dynamical systems viewed asoptimal control problems, motion planning of controlled stochastic processes
- Average cost optimal control

- Geometric Optimal Control, H. Schattler and U. Ledzewicz, Springer Verlag, 2013
- Calculus of Variations and Optimal Control, D. Liberzon, Princeton University Press, 2012
- Dynamic Programming and Viscosity Solutions toHamilton-Jacobi-Bellman equations, M. Bardi and I. Capuzo-Dolcetta, Birkhauser, Boston, 1998

### SC 634 - Introduction to Mobile robotics

- Mobile robot kinematics - direct and inverse kinematics, nonholonomic constraints, unicycle, differential drive, omnidirectional (~3 weeks)
- Mobile robot dynamics - Newton-Euler model, Lagrange equation, dyamic modelling of nonholonomic robots (~3 weeks)
- Sensors and actuators - range sensors, motors and their interfacing (~2 weeks)
- Localization - Kalman filter, triangulation, trilateration, topological (~3 weeks)
- Control - position control, kinematic tracking control, dynamic tracking control, lyapunov based methods, feedback linearization (~3 weeks)
- Applications (optional) - collision avoidance, line following, occupancy grid methods

- "Where am I" - sensors and methods for mobile robot positioning, by J. Borenstein, H.R.Everett and L. Feng,e-book 1996
- Introduction to autonomous mobile robots by R.Siegwart, I.R.Nourbaksh and D.Scaramuzza, Second edition, PHI publications, 2004
- Introduction to mobile robot control by Spyros G Tzafestas, First edition, Elsevier, 2014

### SC 635 - Advance Topics in Mobile Robotics

Prerequisites : If needed, it will be taught or handouts will be given

- Probabilistic methods of motion planning: velocity and position models (~3weeks)
- Recursive state estimation: interaction between the robot and environment, Markov model, parametric and nonparametric filters with case studies of range and feature based visual sensing (~ 4 weeks)
- swarm robotics (~3 weeks)
- robot art - artistic geometry, generating music, dancing robots (~2 weeks)
- modular robots, aerial robots and underwater robots - dynamics, control and guidance (~2 weeks)

- Probabilistic robotics by S.Thrun, W.Burgard and D.Fox 2006
- Space-time continuous models of swarm robotic systems: Supporting Global-to-Local Programming by H. Hamann, Springer. 2010
- Controls and art: Inquiries at the intersection of the subjective and the objective by A. LaViers and M. Egerstedt, Springer, 2014

### SC 636 - Theory of Output Regulation

Prerequisites : SC301 or Instructor Consent

Introduction to the linear regulator problem, linear regulator equations, robust output regulation, repetitive control, transfer function approach to output regulation, center manifold theorem, nonlinear regulator equations, immersion of dynamical systems, brief introduction to infinite-dimensional systems, output regulation for linear infinite-dimensional systems.

There are no required textbooks. The lecture notes, and handouts given during the class, will be sufficient. Some relevant books are listed below.

- H.W. Knobloch, A. Isidori, D. Flockerzi, Topics in Control Theory, Birkhäuser-Verlag, Basel, 1993
- A. Isidori, Nonlinear Control Systems, 3rd ed., Springer-Verlag, London, 1995
- C.I. Byrnes, F.D. Priscoli, A. Isidori, Output Regulation of Uncertain Nonlinear Systems, Birkhäuser, Boston, 1997
- J. Huang, Nonlinear Output Regulation: Theory and Applications, SIAM, Philadelphia, PA, 2004
- R.F. Curtain, H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer-Verlag, New York, 1995

### SC 700 - Embeded Control System

Embedded Systems : Design challenges, Processors (General purpose ?? software and single purpose- hardware, application specific), Peripherals (Timer, counter, UART, PWM, ADC, real-time clocks etc.), memory and interfacing techniques, serial, parallel and wireless communication protocols. ( 5 weeks)

Optimization Techniques : Introduction to pipelining and parallel processing, Retiming, Folding and Unfolding. (weeks)

Control Systems : Overview of sampling theory, design issues with computer based control, data types, quantization, overflow and resource issues, real-world issues in measuring frequency response. ( 6 weeks)

- Embedded System Design : A unified hardware/software introduction by F. Vahid and T.D.Givargis, John Wiley & Sons, 2002
- VLSI Digital Signal Processing Systems : Design and Implementation by Keshab K. Parhi, John Wiley & Sons, 2003
- Applied Control Theory for embedded systems by Tim Wescott, Newness publications, 2006

### SC 792 - Communication Skill II

The departmental component of this course will consist of a series of seminars delivered both by faculty members and teaching assistants, in addition to talks streamed from online repositories. The students would also view/listen to appropriate video/audio modules from the web. The assessment would be based on a report and presentation towards the end of the semester.

Text/References :- Based on resources from the web

### SC 202 - Signals and Feedback Systems

Prerequisites : Course 1- Mathematical structures for control, signal processing and dynamical systems.

Signals and systems and their interconnections, convolution, differential and difference equations, state variable models, Fourier, Laplace and z-transforms, regions of convergence, the transfer function, linear feedback systems, the stability problem, the Routh-Hurwitz and root locus method.

- Signals and Systems - S. Haykin and B. Van Veen, John Wiley, 2003.