SC 401 - Linear systems and electromagnetic waves

• Electromagnetic waves and propagation
• Waveguides and resonantors
• Antennas and Transmission lines
• rf and microwave engineering
• Geometric optics
• Optical Resonance

• Navin Khaneja, "Electomagnetic waves and optics, a linear system approach", 2018.
• E.M. Prucell and D. Morin, "Electricity and Magnetism", Cambridge University Press, 2013.
• R.K. Shevagaonkar, "Electromagnetic waves", TaTa McGraw Hill, 2006.
• D. Griffiths, "Introducation to Electrodynamics", Prentice Hall, 1999.

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

• 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

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.

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 ))

• 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
  
  

• 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

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.

Prerequisites : Systems Theory (SC 625) or EE 635

• 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)
The course will consist of three modules, with the underlying thread being examining dynamics and connected engineering applications from a geometric viewpoint, in particular, the framework of Lie groups.

Dynamics on Lie groups: A quick introduction to matrix Lie groups and the associated machinery of groups actions, Lie algebras, invariant vector fields, infinitesimal generators, metrics and the Euler-Lagrange(EL) equations on a Lie group.

Discrete Mechanics : The discrete variational principle and the discrete EL and Hamiltonian equations for a mechanical system; the fiber derivatives and the discrete equations for matrix Lie groups

Applications :

1. Attitude dynamics and control of a satellite and
2. Formation control of mechanical systems over Lie groups

• 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 - Automation and Feedback Control

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

• 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; H₂ 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)

Content:

• Review of multivariable calculus
• Smooth manifolds
• Vector fields, Lie bracket
• Frobenius’s theorem, Chow-Rashevsky theorem
• Lie groups and Lie algebras
• Left- and right-invariant vector fields on Lie groups
• Control theory on Lie groups, Feedback linearization
• Optimal control on Lie groups
• Pontryagin maximum principle on Lie groups

• Lectures in Geometry, Semester II and III, M. Postnikov, MIR Publishers, 1985
• Introduction to Smooth Manifolds, 2nd Ed., J. Lee, Springer, 2013
• B. Jakubczyk, Controllability and the Lie Bracket; ICTP Lecture Notes, Vol 8., 2002
• W. Respondek, Linearizability, Observability, Decoupling, ICTP Lecture Notes, Vol 8., 2002
• Nonlinear Control Systems - H. Neijmier and A. Van der Schaft, Springer,1992

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

SC 629 - Introduction to Probability and Random Processes

• Discrete and continuous random variables and random vectors, conditioning, Baye’s formula
• Gaussian random vectors, conditioning
• Minimum mean squared error (MMSE) estimation
• Elementary treatment of concentration of probability measures in high dimensions
• Kalman estimation and filtering
• Discrete-time Markov chains

• Probability with Engineering Applications, Bruce Hajek, Cambridge University Press, 2015
• Probability and Statistics by Example Vol I and Vol II, Y. Suhov and M. Kelbert, Cambridge University Press, 2014
• Finite Markov Chains, O. Haggstrom, Cambridge University Press, 1999
• Markov Chains, J. Norris, Cambridge University Press, 1997
• Markov Chains, 2nd Ed, P. Bremaud, Springer, 2022

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.

• 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.

• 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 637 - Sparsity methods in systems and Control

Prerequisites : Prerequisites : SC 625 or equivalent

• Vector spaces and redundant dictionaries
• Curve fitting via regularization
• Convex optimization for sparse optimization
• Greedy algorithms
• Dynamical Systems and Optimal Control
• Maximum Hands-off Control

• Sparse and Redundant Representations, M. Elad, Spring, 2010.
• Convex Optimization Algorithms, D. Bertsekas, Athena Scientific, 2015
• Optimal Control, M. Athans and P. Falb, Dover Publication, 1966

SC 638 - Quantum Control

Prerequisites : Prerequisites : A course in linear system theory, Familiarity with basics of mechanics, electricity and magnetism

• Wavefunctions, Schrodinger equation, formalism of quantum mechanics
• Hydrogen atom, angular momentum, spin
• Perturbation theory, two level systems
• Fundamentals of spin dynamics and NMR, product operator formalism
• Coupled spins dynamics, Multidimensional NMR spectroscopy
• Models of relaxation and decoherence in NMR, master equations
• Pulse sequences in NMR , broadband excitation and control, decoupling and recoupling

• D.J. Griffiths, “Introduction to Quantum Mechanics”, Pearson Prentice Hall, 2004
• J. Cavanagh, W. Fairbrother, A. Palmer, N. Skelton, “Protein NMR Spectroscopy”, Academic Press, 2007
• M. Goldman, “Quantum description of high resolution NMR in liquids”, Oxford Univ. Press, 1988

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 701 - Physics and Control

Prerequisites : A course in linear system theory, A course in linear algebra, A course in multivariable calculus.

• Basic differential geometry, vector fields, Lie groups, Lie algebras, Lie Brackets
• Theorem of Frobenius and Chow, nonlinear controllability
• Control systems on Lie groups, maximum principle and optimal control
• Fundamentals of spin dynamics and NMR
• Coupled spins dynamics, time optimal control in NMR
• Models of relaxation and decoherence in NMR, master equations and optional steering
• Ensemble control, broadband excitation and control, decoupling and recoupling

• V. Jurdjevic, “Geometric control theory”, Cambridge Univ. Press, 1997
• J. Cavanagh, W. Fairbrother, A. Palmer, N. Skelton, “Protein NMR Spectroscopy”, Academic Press, 2007
• M. Goldman, “Quantum description of high resolution NMR in liquids”, Oxford Univ. Press, 1988

SC 702 - Control of Distributed Parameter Systems

Prerequisites : Prerequisites : Linear Systems Theory at the level of SC 301, EE 302 or equivalent
Applications of tracking problem., tracking problem in finite dimensions, review of topics from real analysis and functional analysis, properties of operator semigroups, generation theorems, Riesz spectral operators, perturbation results, systems modeled by partial differential equations(PDEs) as abstract linear systems, controllability and observability, stabilizability and detectability., tracking problem for PDEs, application to the heat and wave equations.

• R.F. Curtain, H.J. Zwart, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer-Verlag, New York, 1995
• H.W. Knobloch, A. Isidori, D. Flockerzi, Topics in Control Theory, Birkh¨auserVerlag, Basel, 1993
• A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences 44, Springer, New York, 1983
• M. Tucsnak, G. Weiss, Observation and Control for Operator Semigroups, Birkh¨auser-Verlag, Basel, 2009

SC 639 - Mathematical Structures for Control

Prerequisites : First course in calculus

• K. Hoffman and R. Kunze, “Linear Algebra”, Prentice Hall, 2015
• I. N. Herstein, “Topics in Algebra”, Wiley, 2006
• W. Rudin, “Principles of Mathematical Analysis”, TaTa McGraw Hill, 1976
• J. Munkres, “Analysis on Manifolds”, CRC Press, 2018
• David G. Luenberger, “Optimization by vector space method”, New York: John Wiley, 1969

SC 640 - Applied Predictive Analytics

Prerequisites : Course 1- No pre-requisite courses. Only background of standard college level mathematics is assumed.

• Applied Predictive Analytics: Principles and Techniques for the Professional Data Analyst, Dean Abott, Wiley, 2014. ISBN: 978-1-118-72796-6 97 8-1-118-72796-978-1-118-72796
• Mastering Predictive Analytics with R, J. D. Miller and R. M. Forte, Second revised edition, Packt Publishing, 2017. ISBN-13: 978-1787121393
• Fundamentals of Machine Learning for Predictive Data Analytics - Algorithms, Worked Examples, and Case Studies. John D. Kelleher, Brian Mac Namee and Aoife D'Arcy, MIT Press July 2015. ISBN: 978-0262-02944-5

SC 641 - Solid State Systems and Control

• Bonding in Solids
• Phonons in Solids
• Electrons in periodic potential
• Electronic Devices
• Superconductivity
• Electrons in Magnetic fields
• Imaging solids

Prerequisites :

• A course in electricity and magnetism
• A course in waves and mechanics

• C. Kittel , “Introduction to Solid State Physics ”, John Wiley & Sons , 2005
• N.W. Ashcroft and D. Mermin “Solid State Physics”, Harcourt College Publishers, 1976
• Steve H. Simon, “Solid Sate Basics”, Oxford Univ. Press, 2013

SC 642 - Observation Theory

Prerequisites :

• Revision of continuous and discrete time linear observers
• Continuous-time nonlinear observation theory: the Hermann-Krener theory, local decompositions and uniform observability
• Continuous-time nonlinear observation theory after Gauthier-Kupka: differential observability and canonical forms
• Recent advances on the observability of coupled cell networks
• Stochastic observation theory: linear filtering, the Kalman filter
• Moving horizon estimation: computational aspects
• Nonlinear filtering: computational aspects

• J-P. Gauthier and I. Kupka, Deterministic Observation Theory, Cambridge University Press, 2001
• D. G. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons, 1969
• S-I. Amari, Information Geometry and Its Applications, Springer-Verlag, 2016
• Instructor’s lecture notes

SC 643 - Stochastic and Networked Control

Prerequisites :

• Classical stochastic control and Markov decision processes. Bellman equation, dynamic programming and LP formulation
• Partially observed Markov decision processes. Reduction to the fully observed case. Linear quadratic Gaussian problem, Certainty equivalence and separation principle. Information structure.
• Witsenhausen problem. Discussion on current state of the art.
• Information theory. Introduction to entropy and mutual information. Coding theorems of information theory - channel coding and source coding and rate distortion theory.
• Control with communication constraints. Stabilization over noisy channels. Anytime capacity.
• Information structure and teams. Static and partially nested linear-quadratic Gaussian teams.
• Optimization approach to stochastic control and information theory.

• Dynamic Programming and Optimal Control Vol I, Dimitri Bertsekas, Athena Scientific, 2017
• Information Theory: Coding Theorems for Discrete Memoryless Systems, Imre Csiszar and Janos Korner, Cambridge University Press, 2011
• Elements of Information Theory, Thomas Cover and Joy Thomas, Wiley, 2012
• Stochastic Networked Control Systems, Serdar Yuksel and Tamer Basar, Birkhauser, 2013

SC 644 - Control of the Heat Equation

Prerequisites : Linear Systems Theory at the level of SC301, SC625 or equivalent

This course will focus on the dynamics and control of linear heat equation in one-dimension. The topics covered are as follows: Applications of heat equation, functional analysis preliminaries, unbounded operators on Hilbert spaces, semigroup theory, spectral properties, wellposedness and regularity of solutions, numerical approximations, null controllability via direct and duality methods, stabilization using backstepping technique, motion planning via flatness approach, optimal control problem and output regulation.

• R.F. Curtain, H.J. Zwart, "An Introduction to Infinite-Dimensional Linear Systems Theory," Springer-Verlag, New York, 1995.
• S. Salsa, "Partial Differential Equations in Action: From Modelling to Theory," Springer, Third edition, 2016.
• A. Smyshlyaev, M. Krstic, "Adaptive Control of Parabolic PDEs," Princeton University Press, Princeton, 2010.
• F. Troltzsch, "Optimal Control of Partial Differential Equations: Theory, Methods and Applications," American Mathematical Society, Providence, Rhode Island, 2010.
• M. Tucsnak, G. Weiss, "Observation and Control for Operator Semigroups," Birkhauser- Verlag, Basel, 2009.

SC 645 - Intelligent Feedback Control

Part-I: Fundamentals of feedback systems:
Basic concepts and techniques, tuning procedures, Model based PID tuning, Set point weighting, Integral wind-up, Benchmarking tuning techniques

Part-II: Industrial control techniques:
Cascade, Ratio, Split-range, Selective, Feedforward compensation, Gain scheduling and applying ISA standards

Part-III: Multi-variable control:
RGA, Condition number, Decoupling, Various multiple loop feedback control techniques, MIMO concepts

Part-IV: Latest PID techniques (optional):
Machine Learning methods for PID tuning, Event-driven, Data-driven PID Control techniques

• K. Astrom and T. Hagglund, PID Controllers: Theory, Design and Tuning, ISA: The Instrumentation, Systems, and Automation Society, 1995
• R. Vilanova and A. Visioli, PID Control in the third millennium: Lessons learned and new approaches, Advances in Industrial Control, Springer, 2012
• Multivariable control systems: An engineering approach, by P. Albertos and A.Sala, Springer, Advanced texbooks in control and signal processing, 2004
• T. Kailath, Linear system, Prentice Hall, 1980

SC 646 - Distributed Optimization and Machine Learning

Prerequisites :
Systems theory at the level of SC625 / SC301 or equivalent is necessary

Content :
Review of convex optimization:

• Properties of convex functions
• Iterative algorithms for constrained and unconstrained optimization
• First and second-order methods
• Dynamical systems viewpoint

• Lyapunov theory
• Single and double-integrator systems

• Elements of graph theory
• Network topology
• Multi-agent systems

• Problem formulation
• Distributed consensus
• Algorithms for distributed optimization
• Dynamical Systems viewpoint
• Robustness

• Distributed economic dispatch
• Distributed control of UAVs

• Distributed clustering
• Distributed training of neural networks
• Federated learning

• Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer.
• J. Nocedal and S. Wright, Numerical Optimization, Springer, 2nd Edition.
• Boyd, S., Parikh, N., & Chu, E. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Now Publishers Inc.
• A. Nedic (2015). Convergence Rate of Distributed Averaging Dynamics and Optimization. Now Publishers Inc.
• Yang, Q., Liu, Y., Cheng, Y., Kang, Y., Chen, T., & Yu, H. (2019). Federated learning. Synthesis Lectures on Artificial Intelligence and Machine Learning

SC 647 - Topological Methods in Control and Data Science

Prerequisites :
Systems theory at the level of SC625 / SC301 or equivalent is necessary

Content :
Topological methods in control theory:

• Topological index and the fixed point index
• Krasnoselskii’s theory of indices of vector fields and their ramifications

• Simplicial homology
• Rips, Cech, Alpha complexes, and their applications in data science
• Persistence homology and its ramifications in learning theory

• Geometrical Methods of Nonlinear Analysis, A. Krasnoselskii and P. P. Zabreiko; Springer
• Control and Nonlinearity, J-M. Coron; American Mathematical Society
• Organized Collapse, D. Kozlov; American Mathematical Society
• Algebraic Topology, A. Hatcher; Cambridge University Press

SC 648 - Stochastic Processes in Engineering and Natural Systems

Prerequisites :
Systems theory at the level of SC625 / SC301 or equivalent is necessary

Content :
Review of probability theory:

• Probability spaces
• Random variables and processes

• Random Walk Model of Brownian Motion
• Einstein’s Brownian Motion
• Ornstein-Uhlenbeck Processes
• Langevin's Brownian Motion
• Stochastic Damped Harmonic Oscillator

• Solution in the sense of Ito
• Solution in the sense of Stratonovic
• Fokker-Planck for jump processes
• Fokker-Planck for jump-diffusion processes

• LTI Systems
• Controllability and Observability

• Filtering: Kalman filter as an LMSE estimator
• Applications in Mathematical Finance

• An Introduction to Stochastic Processes in Physics (Don S. Lemons)
• Handbook of Stochastic methods for Physics, Chemistry, and Natural Sciences (C.W. Gardiner)
• An Informal Introduction to Stochastic Calculus with Applications (O. Calin)
• Stochastic Differential Equations: An Introduction with Applications (B. Øksendal)
• Stochastic systems (G. Adomian)

SC 649 - Embedded Control & Robotics

Prerequisites :
Systems theory at the level of SC625 / SC301 or equivalent is necessary

Content :

• Mobile robot kinematics– direct and inverse kinematics, nonholonomic constraints, unicycle, differential drive, omnidirectional (~3 weeks)
• Embedded Technologies: Design challenges, Processors (General purpose – software and single purposehardware, application specific), Peripherals (Timer, counter, UART, PWM, ADC, real-time clocks etc.), memory and interfacing techniques, serial, parallel and wireless communication protocols. (~3 weeks)
• Sensors and actuators – range sensors, motors and their interfacing (~2 weeks)
• Control – Discrete-time model, Stability in embedded implementation, position control, nonlinear control methods (~3 weeks)
• Localization – Kalman filter, triangulation, trilateration, topological (~3 weeks)

• Embedded System Design : A unified hardware/software introduction by F. Vahid and T.D.Givargis, John Wiley & Sons, 2002
• Applied Control Theory for embedded systems by Tim Wescott, Newness publications, 2006
• Embedded Control for Mobile Robotic Applications, L. Vachhani and others, Wiley-IEEE Control Series, Under preparation for production

SC 650 - High Energy Physics and Systems

Prerequisites :
First course in mechanics and electromagnetism

Content :

• Historical introduction to elementary particles
• Relativity, electrons and photons
• Feynman calculus
• Quantum electrodynamics
• Weak interactions
• Quantum chromodynamics

• Navin Khaneja, “High Energy Physics, a level and transition approach”, 2020
• D. Griffiths, “Introduction to elementary particles”, John Wiley & Sons, 1987
• W. N. Cottingham and D.A. Greenwood, “Introduction to standard model of particle physics”, Cambridge university press, 2007
• M. Thomson, “Modern particle physics”, Cambridge university press, 2013

SC 651 - Estimation on Lie Groups

Prerequisites :
An understanding of vector spaces (or MA 108 or SC 639)

Content :

• Kalman filtering: Studying R. E. Kalman’s first two papers on linear filtering and prediction problems.
• Embedded Technologies: Design challenges, Processors (General purpose – software and single purposehardware, application specific), Peripherals (Timer, counter, UART, PWM, ADC, real-time clocks etc.), memory and interfacing techniques, serial, parallel and wireless communication protocols. (~3 weeks)
• Manifolds, Lie groups and bundles: Introduction to the machinery of manifolds and Lie groups, group actions, the adjoint and co-adjoint actions, the infinitesimal generator, fiber bundles
• Structure of estimators on Lie groups - Setting the framework for attitude estimation in satellites and spacecraft, Visual Simultaneous and Localization (VSLAM) in mobile robotics, working out the structure and design of observers in both cases.
• Extended Kalman Filters (EKF) on Lie groups - Understanding and developing the notion of linearization on a Lie group and the equivalent EKF.

• Stochastic Processes and Filtering Theory - A. H. Jazwinski, Elsevier 1970.
• Kalman Filtering Theory - A. V. Balakrishnan, Optimization Software Inc, 1970.
• Optimal Filtering - B. D. O. Anderson and J. B. Moore, Prentice Hall, 1979.
• Introduction to Mechanics and Symmetry - J. Marsden and T. Ratiu, SpringerVerlag, 1994.

• A New Approach to Linear Filtering and Prediction Problems - R. E. Kalman, Transactions of the ASME, J. Basic Eng. Mar 1960, 82(1): 35-45 (11 pages) https://doi.org/10.1115/1.3662552.
• Nonlinear Complementary Filters on the Special Orthogonal Group -R. Mahony, T. Hamel and J. Pflimlin, in IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1203-1218, June 2008, doi: 10.1109/TAC.2008.923738.
• A bundle framework for observer design on smooth manifolds with symmetry - Anant A. Joshi, D. H. S. Maithripala, Ravi N. Banavar, Journal of Geometric Mechanics, 2021, 13 (2) : 247-271. doi: 10.3934/jgm.2021015.
• The Invariant Extended Kalman Filter as a Stable Observer - A. Barrau and S. Bonnabel, IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 1797-1812, April 2017, doi: 10.1109/TAC.2016.2594085.

SC 652 - Statistical Learning and Sequential Prediction

Prerequisites :
Probability and linear algebra

Content :

• Module 1: Sequential Learning with Full Information:
  Mathematical Basics (Probability theory, Convergence concepts, Fundamentals of Convex functions with applications), Prediction with Multiple Experts, The Weighted Majority algorithm, Exponential Weights/Hedge algorithm, Randomization, Applications


• Module 2: Online Convex Optimization:
  Introduction to Online Convex Optimization, Basic Algorithms: Follow the Regularized Leader, Online Gradient Descent, Convergence for structured convex learning, Online Mirror Descent


• Module 3: Multi-Armed Bandits:
  Introduction to Multi-armed bandits, Greedy Exploration– epsilon greedy policy, Optimistic explorationUpper Confidence Bound (UCB) algorithm, Performance of UCB, Lower bounds using Information Theory principles, Le-cam and Fano Inequality. Best Arm identification/Pure exploration problems and the Median elimination algorithm, Adversarial Bandits with EXP3 algorithm


• Module 4: Reinforcement Learning:
  Markov Decision Process (MDP) framework, Dynamic Programming and Bellman Equations, Planning problems: Value iteration and Policy iteration, Learning/Control Problems: Temporal Difference (TD) learning, Q learning

• Prediction Learning and Games, N. Cesa-Bianchi and G. Lugosi, Cambridge Univ. Press, 2006
• Introduction to Online Convex Optimization, E. Hazan, MIT Press, 2021
• Bandit Algorithms, T. Lattimore and C. Szepesvari, Cambridge Univ. Press, 2020
• Reinforcement Learning: An introduction, Sutton and Barto, MIT Press, 2018
• Control Systems and Reinforcement Learning, Sean Meyn, Cambridge University Press, 2022

SC 653 - Optimisation for Large Scale Machine Learning

Prerequisites :
No Formal Prereq. Basics of Probability, Linear Algebra and Optimisation, Instructor’s Consent

Content : Module I: Convergence rates of Convex objective, accelerated Methods, Constrained Optimisation, Large Scale Sparse Opt., Proximal Methods.

Module II: Stochastic Optimisation, SGD, Convergence rate of SGD for convex and non-convex objectives, Variance Reduction, SVRG.

Module III: Large Scale Learning: Federated Learning, Federated Averaging, Convergence of Fed-Avg, Variance reduced Fed-Avg, SCAFFOLD.

Module IV: Neural Networks, SGD convergence for NN, Practical Algorithms: ADAM, Overparameterized Regime, Benign Overfitting

• Numerical Optimisation, J. Nocedal, Stephen J. Wright, Springer, 1999.
• Optimisation for Modern Data Analysis, Stephen J. Wright and Benjamin Recent, Cambridge University Press, 2022.
• Lectures on Convex Optimisation, Y. Nesterov, Springer, 2018.
• On the Convergence of Fed-Avg on non-iid data, X. Li, K. Huang, W. Yang,S. Wang, Z. Zhang, ICLR 2020.
• SCAFFOLD, S. Karimireddy, S. Kale, M. Mohri, S. Reddi, S. Stich, A Suresh, ICML 2020.
• On the convergence of ADAM and beyond, S Reddi, S. Kale, S. Kumar, ICLR, 2018.

SC 654 - Social Learning and Herding

Prerequisites :
Elementary course in probability

Content :

1. Basic Bayesian learning and inference framework
2. Social learning with common memory
3. Cascades and herds
4. Learning with delays and limited memory
5. Guessing and coordination
6. Gaussian financial markets
7. Financial trades, herds and frenzies


1-5: will constitute 75% of the course

• Christophe Chamley, “Rational Herds: Economic Models of Social Learning”, Cambridge University Press, 2004
• Maschler, Solan and Zamir, “Game Theory”, Cambridge University Press, 2020
• Bala, Venkatesh, and Sanjeev Goyal. "Learning from neighbours." The review of economic studies 65.3 (1998): 595-621.
• Bala, Venkatesh, and Sanjeev Goyal. "A theory of learning with heterogeneous agents." International Economic Review (1995): 303-323.
• Fudenberg and Tirole, “The Theory of Learning in Games”, MIT Press, 1998.
• Hajek, “Random Processes for Engineers”, Cambridge University Press, 2015

SC 626 - Systems and Control Engineering Laboratory

Content :

1. First Half
• 2DOF helicopter - LQR controller design
• Inverted pendulum - Pole placement
• Industrial load emulator - parameter estimation
• Turtlebot (wheeled robot)
• Crazyfly (quadcopter)


2. Second Half
• Global optimization - simulated annealing
• Linear programming in python