# Non investing buck boost converter analysis of covariance

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In [18] the states of a doubly fed induction generator connected to a complex power system are estimated using noisy phasor measurement unit measurements, this is performed using the unscented Kalman filter with a bad data detection scheme; a comparison with the EKF is also discussed. The buck converter circuit used has a capacitor at the connection point with the solar panel, as can be seen in Figure 2 , to be able to take V PV as a state.

Three states are taken into account in the model, which are: the voltage given by the solar panel V PV , the voltage at the output load resistor V O and the current flowing through the inductor i l. Two models are obtained depending on the state of the IGBT control input u; afterwards, these are combined into a single state space model, which will be used for the identification.

The corresponding state space is defined as:. This way, the state space is defined as:. From the state spaces 13 and 14 , a new state space model can be obtained:. The model 15 can also be written as:. In order to obtain a discrete-time model, the Euler discretization method is used:.

The second and third equations in 18 correspond to the internal dynamics of the system. The second equation describes the dynamics of the voltage at the load resistor of the buck converter; due to the nature of the converter, this voltage will always be lower than V PV. The third equation represents the dynamics of the current through the inductor.

The weight vectors are updated online using the extended Kalman filter EKF , the estimation error is defined by:. It is worth to note that the states need to be measurable. The control is based on the identification described in the previous subsection, its objective is that the voltage at the output of the solar panel reaches the trajectory, x 1 ref given by the MPPT, and then the tracking error is defined as:.

In order to test the performance of the proposed neural controller, a simulation is developed implementing the DC-DC Buck converter and the solar panel by means of the Simscape Power Systems 2 blocks, which includes the models of the electrical components, allowing to investigate to some degree the real-time performance of the proposed design and this way have a better idea of the necessary considerations for real-time implementation.

At the beginning of the simulation the plant is left in open-loop, having as input a linear swept-frequency cosine signal, this time is used to identify the states. The objective of the controller is to allow the solar panel to function at the highest efficiency possible, which means producing the maximum amount of power according to its characteristics and environmental conditions at each moment.

In Figure 6 , the theoretical maximum power level given by 1 for the particular solar panel chosen and applying the previously described irradiance values, is shown in the red dotted line. The blue line represents the power obtained at the output of the solar panel, controlled by the proposed controller as it follows the referenced given by the MPPT algorithm.

At the beginning, without solar irradiance, the theoretical maximum power and the actual power obtained are both obviously zero. When irradiance is applied, it can be seen that the actual power quickly converges to the theoretical maximum power with acceptable tracking error.

The biggest error is seen at the final irradiance change, this error can be attributed to the dissipation of power from the various components of the converter and the error in the reference given by the MPPT algorithm.

In Figure 7 , the identification errors are shown. During the first instant the error is quite large because the states of the neural network start in random locations, but the error diminishes almost instantly. After the training or identification time of 0. When irradiance is first applied at 1. It can be seen that the first state, which is the voltage at the output of the solar panel, is the one with the largest estimation error; nevertheless the errors remain within adequate bounds for the entire simulation.

Some changes in the amplitude of the estimation error are noticeable every time the irradiance value changes. In order to compare the proposed neural algorithm with a different controller of the same class, an additional simulation is performed using a discrete sliding mode controller DSM based on [19].

Since one of the main advantages of using on-line identification and control is to be able to withstand parametric changes in the model caused by variations in the environment, in this simulation, parametric changes in the DC-DC Buck converter components capacitors and inductors are applied.

To compare the proposed controller with the DSM controller, tracking error statistics of both are analyzed. Table 2 , shows the mean and the standard deviation SD of the error with negative changes in capacitance and inductance values to different percentages, shown in the left column.

The best values for each statistical measure are emphasized in bold. The least amount of standard deviation in the error is achieved with the neural controller when there are no parametric. It is evident that the error mean is lower when using the DSM controller but the SD grows as the parametric changes increase, meanwhile the neural controller mean and SD remain mostly constant.

The error in the mean of the neural controller can be attributed to the always existing identification errors, but this way it is shown that the same controller can be used for a completely different converter and very similar results as with the original will be obtained. This paper presents a novel application of the neural network on-line identification using the EKF as in [10] to achieve a photovoltaic panel MPP reference tracking under varying working conditions. The MPPT method used was the perturb and observe algorithm, which is the most common even though it may result in oscillations of the power output reference if a proper strategy is not adopted.

The on-line method for identification applied provides robustness against parametric changes in the components, although it is important to note that the states must be measurable, which in this case would mean having voltage and current sensors for the DC-DC Buck converter, which is not considered to be an important impediment.

The simulations were developed using the Simscape Power Systems blocks, which provide component libraries and analysis tools for modeling and simulating electrical power systems, and include the different component dynamics and the model of the photovoltaic array, establishing the basis for a real-time implementation. In the first simulation presented, irradiance values changed instantly at different points in time and with the presented controller the solar panel was able to produce the maximum amount of power according to its particular characteristics.

Considering that in a real application irradiance values would not change instantly, but rather as a smooth function, the controller is expected to function in a similar manner, and there would not be abrupt changes in the states. This would be an improvement that can be applied to the simulation to see how well it responds to ramp changes and smooth irradiance variations. In the following simulations, the same irradiance changes were applied and the performance of the proposed controller was validated compared to a DSM controller while applying different amounts of parametric change to the DC-DC Buck converter in each simulation.

In these simulations it was shown that the proposed controller has high precision and small convergence time even when working with a converter that has changed significantly due to environmental factors, or even with a different converter. It is left as future work to implement changes in temperature as the irradiance varies, which would represent more closely the working conditions of a solar panel.

This work represents the basis for the real-time implementation of the proposed controller, which would greatly improve the performance of solar panels under several conditions, especially those used in the private sector represented by citizens who invest in these systems.

A different study would need to be realized to be able to determine the extent of utility of these results for the industrial sector. The results obtained in this work are important for photovoltaic system users to be able to obtain the highest efficiency from their solar panels and this way generate the highest revenue possible, regardless of the climate changes.

Neural Network for Modeling Solar Panel. International Journal of Energy. Syafaruddin KE, Hiyama T. IET Power Electronics. Chatterjee A, Keyhani A. Esram T, Chapman PL. Zhang L, Bai YF. Engineering Applications of Artificial Intelligence. Discrete-time High Order Neural Control.

Warsaw: Springer; London: Springer; IEEE Sensors journal. Pajchrowski T, Janiszewski D. Received: 18 de septiembre del Approved: 26 de enero del Mesh protection in WDM networks. Transmission Lines. Plane Waves: Cutoffs and reflections in ionosphere. Anisotropic media: Faraday Rotation. Thin films. Introduction to optical filter design. Waveguides: Rectangular and cylindrical waveguides.

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Yagi, Horn, Parabola, micro strip and patch antennas. Case Studies of RF circuits in mobile phones and satellite communications. Non-recoprocal elements such as ferrite components, Isolators and circulators. Frequency-independent antennas, log-periodic antennas, spiral antennas. RF-Id systems. Designing an LED transceiver circuit 2.

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Image formation and camera model2. Coded computational imaging: Motion deblurring using coded exposure flutter shutter , focus deblurring using coded aperture3. Multi-image techniques: Panorama, flash no-flash photography, high dynamic range capture, focal stack, aperture-focus stack4. Light field imaging: Light field acquisition using camera array, lenslet array, programmable coded aperture, heterodyne light field camera. Light field rendering. Compressive sensing and dictionary learning: L0-L1 norm equivalence, dictionary learning and sparsity-based reconstruction6.

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Architectures for some transforms arising in signal processing including Discrete Fourier Transform and Discrete Hadamard transform; Direct realization and optimization for area. Systolic Architecture Design: Introduction, systolic array design methodology; Applications to signal processing problems. Need and Benefits of Smart Grid.

Divers for Smart grid, functions, opportunities and challenges. Difference between conventional and Smart Grid. Part B: Nature of Mathematics and Natural Sciences: Main components of mathematics, viz, logic, reasoning, quantification, conjectures, theorems, lemmas and their application to real world engineering problems through modeling.

Introduction to circulatory physiology I2. Introduction to circulatory physiology II3. Heart pacemakers and implanted defibrillators I4. Heart pacemakers and implanted defibrillators II5. Introduction to lung physiology and pathophysiology I7. Introduction to lung physiology and pathophysiology II8.

Artificial Ventilators9. Anaesthesia devices I Anaesthesia devices II Introduction to cerebrospinal fluid CSF physiology and to hydrocephalus therapy Introduction to glucose metabolism and the pathophysiology of diabetes mellitus including Introduction to renal physiology Dialysis machines Modalities for noncontact cardiovascular monitoring capacitive ECG, magnetic impedance Dynamics of blood flow Invasive measurement of constituents of blood Optical sensors for the measurement of venous blood flow dynamics Measurement of oxygen saturation in arterial blood An analytical model for the attenuation light in optical sensors Calibration free measurement of venous blood flow dynamics Model based measurement of oxygen saturation in arterial blood Model based measurement of hemoglobin content in arterial blood Fundamentals of ocular system Ailments and treatments in ocular system The cataract surgery and opthalmic anaesthesia Sinusoidal steady state analysis, phasors, response to periodic inputs, power and energy.

Registers as fast memory. Latency and throughput Caching memory accesses. Cache algorithms. Multilevel caches. Interrupt processing. CPU communication with peripherals. Students will create embedded programs on an ARM processor to generate analog traces, control motors, interface to peripherals and use of the I2C bus.

Advanced experiments may explore performance issues. Optical Communication- Physical Layer a. Introduction to optical communication b. Advanced modulation formats -generation c. Coherent detection d. Impairments in coherent communciation systems e. Noise in the detectors, quantum limit, BER analysis 2. Signal processing for advanced modulation formats a. Clock recovery and timing error correction b.

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Case studies from engineering disciplines will be used to illustrate the applicability of these methods, with a discussion on sources of numerical errors. Sensorless control of Induction Machines — methods of speed identification. Position estimation by signal injection Rotor Controlled induction machines — theory of power flow and control of rotor side converters BLDC drives Theory of operation of machine and bridge — triggering based on hall sensors — Control loop — sensorless control methods.

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Sampling Bridge continuous and discrete : Sampling theorem and signal reconstruction, notion of aliasing with examples, Sampling in frequency domain 5 classes 10 3 - 1 - 0 - 0 - 6 - 10 EE Power Management Integrated Circuits Unit Introduction to Power Management and Voltage RegulatorsNeed of power management, power management applications, classification of power management, power delivery of a VLSI system, power conversion, discrete vs. PMOS regulator, current regulator. Unit Switching DC-DC Converters and Control TechniquesTypes Buck, boost, buck-boost , power FETs, choosing L and C, PWM modulation, leading, trailing and dual edge modulation, Losses in switching converters, output ripple, voltage Vs current mode control, CCM and DCM modes, small signal model of dc-dc converter, loop gain analysis of un-compensated dc-dc converter, type-I, type-II and type-III compensation, compensation of a voltage mode dc-dc converter, compensation of a current mode dc-dc converter, hysteretic control, switched capacitor dc-dc converters.

Linear driver, differential and singled ended driver, sensor-less drive, back EMF sensing techniques, overdrive and braking, short and open circuit detection. Resistive Transducers: Resistance potentiometer — noise — resolution — signal conditioning — strain gauges — associated electrical circuitry — temperature compensation — load cells — torque and pressure measurement using strain gauges —resistive temperature device RTD — three-lead arrangement — thermistors — linearization - hot-wire anemometers — time constant improvement — measurement of direction of flow — peizo resistive transducers.

Capacitive Transducers: Single — push-pull — angle transducer — humidity sensor — parasitic effects — solutions — signal conditioning circuits. Miscellaneous transducers: Peizo electric — signal conditioning — thermo couples — theory — mass-spring accelerometer — force-balance. Applications of transducers: Measurement of displacement linear and angular — velocity — acceleration — force — torque — pressure — flow — temperature.

Models of physical and biological systems-- simple pendulum, segway scooter, consensu protocols for sensor networks, gene regulatory networks2. Minimal realization, Smith-McMillan form5. Reachable and controllable subspaces, Controllability and observability Gramians, Kalman and Popov-Belevitch-Hautus PBH test for controllability and observability, Controllable and observable canonical forms7.

Lyapunov stability, Lyapunov equation, Eigenvalue conditions for Lyapunov stability, Separation principle, pole-placement and observer design9. Review of state-space representation of systems2. Calculus of variations-Examples of variational problems, Brachistochrone, Catenary etc. Optimal control problem formulations- Variational approach to the fixed-time, free-endpoint problem5. Pontryagin maximum principle- Proof of the maximum principle, Time-optimal control of double integrator, Bang-bang control6.

Linear quadratic regulator LQR problem- candidate optimal feedback law, Riccati differential equation, proof of sufficiency using HJB equation8. Numerical methods for optimal control problems- Evaluation of parameter-dependent functionals and their gradients, Indirect methods, Direct methods, 9. Applications- Time-optimal control of linear systems, Singular control, Optimal control to target curves 12 3 - 1 - 0 - 0 - 8 - 0 EE Modern Coding Theory 1.

Low Density Parity Check LDPC Codes, Definition and construction, degree distributions, regular and irregular ensembles, Hard and soft message-passing decoders, peeling decoder, bit flipping and sum product algorithms, and approximations, Computation trees, density evolution and threshold for symmetric channels, EXIT charts and optimization of degree distribution 4.

Advanced topics A selection will be covered Repeat accumulate RA codes: Definition and construction, regular and irregular RA codes, decoding RA codes, Polar Codes: Definition and construction, Encoding and decoding of polar codes, Capacity-approaching property of polar codes, Protograph LDPC codes : Definition and construction, decoding and vector density evolution, Spatially coupled LDPC codes: Definition and construction, decoding and threshold saturation property, Linear programming decoding of block codes, Coding for distributed storage, Codes in standards and codec implementations, Other applications of coding theory 9 3 - 0 - 0 - 0 - 6 - 9 EE Error Control Coding 1.

Mathematical Preliminaries: Groups, rings, fields, vector spaces, linear algebra review, Finite fields: construction, structure of fields, polynomials over finite fields, minimal polynomials, factorization of polynomials 2. Linear block codes: Generator and parity check matrices, dual code, distance of a code. Decoding linear codes: MAP decoder, ML decoder, standard array and syndrome decoding, bounded distance decoder. Bounds on codes: Singleton, Hamming, Plotkin, Gilbert-Varshamov bounds and asymptotic bounds, Weight enumerators, MacWilliams relation for binary block codes, Code constructions: puncturing, extending, shortening, direct sum, product construction, interleaving, concatenation, Performance of block codes 3.

Convolutional codes, Various formulations of convolutional codes using shift registers, generator sequences, polynomials, and matrices, recursive and non recursive encoders, Code parameters: constraint length, memory, free distance, Structural properties of convolutional codes: state diagram, trellis diagram, non-catastrophic encoders, weight enumerators, Decoding convolutional codes: Viterbi and BCJR algorithms, hard decision and soft decision decoding, Performance of convolutional codes 5.

Electronic and optical properties of silicon, convergence of CMOS electronics and photonics 2. Single-mode and multimode waveguide design in SOI substrate; polarization and dispersion effects 3. Orthogonality condition, coupled mode theory and multimode interference MMI 4. Fiber-waveguide interface : grating coupler, spot-size converter and waveguide trimming 7. Design and working principles of modulators, switches, tunable filters, variable optical attenuator VOA 9.

III-V integration for light sources: state of the art technology and implementation Hybrid integration of photodetectors: state of the art technology and implementation Waveguide-integrated junction linear and avalanche photodetectors.

Advanced review of guided-wave light propagation in high index contrast waveguides. Nonlinear effects in silicon photonics. Four-wave mixing, wavelength conversion, two-photon absorption and free-carrier induced limitations; carrier sweepout for partial improvement. Nonlinear effects in micro-resonators; slow and fast light effects; enhancements and impairments. Frequency comb generation. Raman effect, Brillouin effect, coupling to electronic carrier and thermal effects.

Amplitude-phase coupling in wavelength conversion and in hybrid lasers. Introduction to quantum photonics and the role played by solid-state materials. Photon generation, qubit manipulation and detection technologies. Continued discussion of photon generation, qubit manipulation and detection technologies. Storage systems consisting of battery, supercapacitors, their modeling, analysis, design and applications in microgrid, integration of storage system with the DC grid using bidirectional DC-DC converters.

DC and AC grid integration using voltage source converters VSC , control strategies for VSC to operate it in standalone or grid connected mode, power flow, energy management systems and power quality issues in microgrid systems. Programming your own analysis in MAPP. Sensitivity analysis.

Stationary noise in linear ized systems. Noise contd. Simulation of oscillatory systems. Steady state methods, distortion. Link design, case studies Ultra long links: Communicating across the solar system - link design for the deep space probes sent out by NASA. Optical communication: Sources: Modulation, power, beam spreading, beam wander Receivers: Sensitivity, noise, bandwidth Channel: Bandwidth, Fibre or free space, Channel noise, Turbulence, Fog Optical link design basics Free Space link design, case studies.

Fog and free space optical links Optical Fibre Communication basics. Link design of a fibre link. Single phase AC, voltage and current phasors, impedance, network theorems application to AC, frequency response of ac circuits, resonance, filters, active power, reactive power, apparent power, power factor. Balanced Three phase AC, three phase power, star and delta connection. Single phase transformer: Principle of operation, equivalent circuit, OC and SC test, voltage regulation, efficiency.

Three phase Induction motor: Construction, rotating magnetic field, principle of operation, slip, torque, equivalent circuit, efficiency. DC machines: Principle of operation, excitation, equivalent circuit, emf, speed and torque characteristics. Diodes and applications: Diode characteristics, voltage and current relationship, diode circuits-rectifiers, peak and envelop detectors, solar cell.

Operational amplifiers: Description of amplifiers as a black box and definition of gain, effect of feedback on gain, Operational amplifier circuits: Non-inverting, inverting, summing, differential, integrators, differentiators, buffers. Standards Relay networks,inter-vehicular networks, Dynamic spectrum access and cognitive radio networks, Wireless sensor networks, Wireless-specific security, privacy, and authentication, mobile computing. Heterogeneous networks, Mobile data offloading, storage area networks, peer-to-peer networking, issues related to social networks, location aware networking, network management, software defined networks.

LTE massive machine type communication. Mechanical and acoustic sensors: metallic, thin-film and semiconductor strain gauges, silicon pressure sensors, accelerometers, displacement transducers, piezo junction devices, piezoelectric field-effect transducers, surface acoustic wave devices, ultrasonic based sensors, flow sensors. Magnetic and Electric field sensors: Sensors based on variable magnetic coupling, search coil, magnetoresistors, Hall-effect devices, integrated Hall devices, flux-gate sensors, solid-state read and write heads, electrostatic sensors and applications.

Light-sensitive sensors: photovoltaic diodes, photoconductors, photodiodes, phototransistors, positron-sensitive photodetectors, opto-isolators, photodiode arrays, charge-coupled devices, fiber-optic sensor technologies and applications. Thermal sensors: Platinum resistors, thermistors, silicon transistor thermometers, integrated temperature transducers, thermocouples.

Sensor systems and applications: integrated sensors-actuators, microsystems, sensor buses, multiple-sensor systems, sensor networks and automotive, consumer, power, medical measurement systems. The students are assumed to have studied the basic concepts of information theory and capacity of point-to-point channels. The actual topics covered in class will be a selection from the following. Transmission Lines: i Equations of current and voltage, ii Standing waves and impedance transformation, iii Power transfer on a transmission line, iv Loss-less and low-loss transmission lines, v Discontinuity, Bounce diagram and Digital transmission lines.

Introduction to Computers, programming language a. C language history 2. Variables constants and declarations 3. Arithmetic, relational and logical operators. Precedence order 4. Control flow statements a. For loop b. While loop c. If, If-else d. Switch 5. Arrays a. One dimensional and two dimensional arrays 6.

Characters and strings 7. Functions a. Pass by value, pass by reference b. Recursive functions c. Scope of variables 8. Sorting algorithms a. Selection sort b. Insertion sort 9. Introduction to pointers a. Basic pointers b. Pointers to arrays and two dimensional arrays c. Pointer arithmetic d. Malloc, stack vs heap Structures a. Basic introduction b. Pointers to structures c. Basic linked lists File processing IO processing a. Opening, closing and reading files b.

Introduction to various Python toolkits: Numpy for handling arrays and matrices; SciPy for scientific computing; Matplotlib for data visualization; Pandas for data manipulation; SciKit Learn library for machine learning. Linear models for regression: Ordinary least squares; Ridge regression l2 regularization ; Lasso l1 regularization ; Elastic Net l2-l1 regularization. Neural network. It subsequently introduces students to the coupling-matrix design theory followed by many practical synthesis examples.

Without sacrificing mathematical rigor, the course emphasizes the practical step-by-step design process. Relevant matlab scripts will be provided to students so they can perform their own designs. Students will be able to design complex transfer-function filters that go beyond traditional textbook-style filters. In addition, planar and three dimensional practical filter examples will be presented.

The course will conclude by providing examples of the most successful reconfigurable filter architectures that exploit the aforementioned techniques. Students completing this course will be able to understand basic and advanced filter concepts as well as comprehend state-of-the-art tunable designs published in the technical literature. Centralised and Decentralised Power generation systems using Solar PV: technology and economics; solar-DC systems; bi-directional grid synchronisation 4.

Centralised and Decentralised Wind Power systems: technology and economics 5. Other Renewable Energy sources 6. Grid-storage for Renewable Energy 7. System level analysis of power consumed in EVs; Electric Vehicle architecture and sub-systems 8.

Batteries for EVs 9. EV Chargers and battery-Swappers Cost-challenges of EVs in India and the world Electric 2-wheelrs, 3-wheelers, 4-wheelers, buses, small goods-vehicles 9 3 - 0 - 0 - 0 - 6 - 9 EE High Voltage Technology Generation and measurement of high AC, DC and transient votlages. Introduction to Digital Systems and Boolean AlgebraBinary, octal and hexadecimal number systems; Truth table; Basic logic operation and logic gates.

Combinational Logic Multi level gate circuits, Decoders, encoders, multiplexers, demultiplexers and their applications; Parity circuits and comparators; Representation of signed numbers; Adders, Ripple carry. HDL description of sequential circuits. State Machine Design State machine as a sequential controller; Moore and Mealy state machines; Derivation of state graph and tables; Sequence detector; state table reduction using Implication table; state assignment, logic realization; equivalent state machines, Designing state machine using ASM charts.

Advanced TopicsAsynchronous Sequential Machines, Static and Dynamic hazards; race free design; testing digital circuits. Syllabus: LaboratoryExperiments on design of combinational circuits including adders and magnitude comparators; realization using multiplexers and other approaches; identification of critical path Design of sequential circuits including flip-flops, counters and registers Digital to analog converter design and study of characteristicsExperiments on motor control using flip-flops and gates Introduction to hardware description languages and simulation of simple circuits 16 3 - 1 - 6 - 0 - 6 - 16 EE Advanced Topics in Microelectronics and MEMS Contents will be decided by the respective instructor 9 3 - 0 - 0 - 0 - 6 - 9 EE Wireless System Design Module I.

Digital communications fundamentalsModule II. Understand specifications of wireless standard under considerationModule VII. Communications: wireless local-area networks, wireless wide-area networks and back-haul networks2. Sensing and Actuation, remote-processing3. Powering devices4. Cloud storage and processing; Data Analytics and Intelligent Management5. Applications in Electric Vehicle; Optimising Battery usage7.

Applications in water-distribution management8. Applications in Agriculture9. Nodal analysis with controlled sources and magnetically coupled systems. Resonant circuits. Small signal analysis of networks. Lumped vs distributed representations. Lossless vs lossy transmission lines. Special cases - quarter wavelength; short, open and matched loads. Op-amp based building blocks. Stability criteria, review of bode plot with gain and phase margin. Noise analysis in networks including controlled sources.

Input referred current and voltage sources. Noise correlation. Effects on noise. Basic Neural Network: Perceptron; Multi-layer Perceptron; Back propagation; Stochastic gradient descent; Universal approximation theorem; Applications in imaging such as for denoising.

Autoencoders: Autoencoder; Denoising auto-encoder; Sparse auto-encoder; Variational autoencoder; Applications in imaging such as segnet and image generation. Non-volatile memory devices: Magnetic memories, HDDs; Silicon based thin film transistor non-volatile memories; Flash memories, classification and operation; challenges; advancements in vertically stackable arrays.

Applications: Nonsmooth harmonic oscillator, stick-slip system and systems involving discontinuous stabilizing control law2. Semicontinuity, proper and improper convex functions, Lipschitz property of convex function, projection of a point onto a set, distance function, gradient of the distance function and the projection inequality, normal and tangent cones, properties of normal cones3.

Subdifferential of a convex function and its properties, connection to convex geometry, basic inequality, subgradient calculus and optimality conditions. Directional derivatives, relation between subgradients and directional derivatives, existence of subgradient, subdifferential and gradient direction of steepest descent, examples involving the subgradient of a norm, distance function, indicator function, max function and maximum eigen value of a symmetric matrix.

Solution notions for discontinuous systems, Caratheodory, Fillipov, sample-and-hold solutions. Lyapunov-like stability theorems for nonsmooth systems and optimality conditions for nonsmooth optimization. An introduction to machine learning: why and what. A comparison of artificial intelligence, machine learning, and widely adored deep neural networks. The most fundamental problem of electrical engineering: decision making under uncertainty elaborated with examples from communication and signal processing.

Supervised learning discrete labels : signal detection without the knowledge of path loss and noise distribution, image recognition, etc. Linear classifier, support vector machine and kernel method. Logistic regression. Supervised learning continuous labels a. Linear regression, support vector regression. A brief tour of neural networks. Why function representation?

Why NN? Why deep NN? Some architectures: convolutional neural networks image processing , recurrent neural networks communication and control. Training, backpropagation and SGD. Unsupervised learning: vector quantization and clustering, k-means algorithm, spectral clustering 7.

Sparse recovery: applications in signal processing. Low dimensional structure in high dimensional data: PCA 9. Graphical model: a statistical model for error correction codes, social networks, etc. Reinforcement learning: applications in robotics and wireless scheduling.

LC resonant circuits and RF impedance matching2. Design of Low noise amplifiers4. Design of active and passive mixers5. Design of LC Oscillators6. A nuanced look at Conditional Expectations 4 classes a. The Hilbert Space L2 - covariance as an inner productb. Conditioning on sigma-algebras. Filtrations—sequence of sigma-algebras evolving in time 1 class 3. Random Walks 4 classes a. Martingales classes a. Definitions, basic properties b.

Kolmogorov Submartingale Inequality d. Martingale Convergence Theorems and applications Polya urn, stochastic approximation, population extinction, polar codes etc. Exchangeability and Zero-One Laws classes a. Concentration of Measure and applications classes a. Logarithmic Sobolev Inequality d. Passives for Power Electronic Applications: Basics of MMF, flux, reluctance and B-H curves, inductor design, transformer design, magnetic materials, fringing, magnetic losses, capacitor types and selection, resistors for power electronic applications.

Heatsink Selection for Power Electronic Converters: Device power losses, dynamic and steady state circuit model for heatsink, cooling fan selection, thermal protections. Design of a few example applications. Recap of probability theory: Probability spaces, Random variables, Convergence of random variables, Conditionalexpectation, Filtrations2.

Recap of linear systems theory: Controllability, Observability, Kalman decomposition, Stability3. Stochastic processes: Classification of stochastic processes, Second order processes, Mean-Square calculus,Random walk and Brownian motion, Properties of Brownian motion, White noise4. Stochastic differential equations: Differential equations driven by white noise, Riemann-Stieltjes integral, Wienerintegral, Ito and Stratonovich integrals, Fokker-Planck equation, Langevin equation, Ornstein—Uhlenbeck process.

Estimation and Filtering: Linear least squares estimator, Kalman filter in continuous and discrete time, Separationprinciple, Certainty equivalence6. Stochastic optimal control -- Dynamic programming, Hamilton—Jacobi—Bellman HJB equation, Linear quadraticGaussian control, Linear exponential Gaussian control, Stochastic maximum principle 12 3 - 1 - 0 - 0 - 8 - 12 EE Devices and technologies for AI and neuromorphic computing Neurons as computational units: models for neurons Hodgkin-Huxley; Leaky-integrate and Fire , Learning in artificial neural networks: types of ANNs, learning algorithms, role of non-volatile memory devices as synapses and device requirements, physics of filamentary memristive devices, modeling of memristive devices, memristive crossbar arrays: design challenges and requirement of selectors, emerging devices for artificial neurons Mott insulators, threshold switching resistive switches.

Preliminaries: Graph theory, consensus protocol, convex analysis, convergence analysis, Lyapunov functions 2. With network constraints: Time varying networks, Directed networks, Event-triggered, Resilient optimization, Online optimization 4. Applications in Control: Estimation problem, Power system control, Model predictive control, Coordination of autonomous agents, Rate control of communication networks 12 3 - 1 - 0 - 0 - 8 - 12 EE RF Integrated Circuits 1.

Design of Power amplifiers7. Transmitter and receiver architectures 12 4 - 0 - 0 - 0 - 8 - 12 ID Quantum Integer Programming Part1-Integerprogramming classicalmethods : Integer Programming basics, cutting plane theory and relaxations, introduction to test sets, Grobner basis, Graver basis.

Higher order nonlinear effects in crystals and in optical fibres, with their applications to self phase modulation, cross phase modulation and 4-wave mixing. Numerical solutions to the nonlinar Schrodinger equation, application of the nonlinar optical loop mirror and nonlinear effects in semiconductor optical amplifiers. Part 2: Optical quantum information processing starting with the descriptions of Fock states, the weak coherent states and the cluster states, and the methods for their generation and detection.

The use of qubits in optical communications for implementation of quantum key distribution, quantum communication, quantum teleportation. The description of different technologies leading to their use in quantum memory and quantum repeaters 9 3 - 0 - 0 - 0 - 6 - 9 EEW VLSI Broadband Communication Circuits Digital signal transmission; Drivers and receivers for low frequencies; Serialization and Deserialization; Digital signal transmission over lossy and dispersive channels; Eye diagrams; Eye closure; crosstalk, and jitter; Equalization: Linear and non-linear equalizers; Integrated circuit implementation of broadband ampliers for transmission and reception, feedforward and decision feedback equalization; Synchronization: clock and data recovery circuits using phase locked loops and delay locked loops; 12 0 - 0 - 0 - 0 - 8 - 12 EEW Power Management Integrated Circuits Unit Introduction to Power Management and Voltage RegulatorsNeed of power management, power management applications, classification of power management, power delivery of a VLSI system, power conversion, discrete vs.

Platforms: Data buoys — Tsunami buoys, mooring design, satellite communication, AUVs basic design, propulsion, guidance, inertial navigation system, Glider: basic design, gliding principle, payloads, Autonomous profiling drifter AUPD — principle of operation, variable buoyancy engine — payloads — deep sea operation — satellite issues, Ship based - Wire walker — operating principle. Sonar: principle — side scan, single beam, multibeam. Calibration: Need for calibration — primary standards — secondary standards, calibration labs, accreditation, Temperature baths, Wind tunnels, Humidity standards.

Ship related Instrumentation: Ship propulsion basics, prod propulsion, diesel electric propulsion, thrusters, speed control, controlled pitch propulsion, Measurement of speed, GPS, current, wind speed, wind direction, Radar, Dynamic positioning of ship — diving bell — position keeping, accuracy 9 3 - 0 - 0 - 0 - 6 - 9 EE Basic Electrical Engineering 1. Sampling Bridge continuous and discrete : Sampling theorem and signal reconstruction, notion of aliasing with examples, Sampling in frequency domain 5 classes 10 3 - 1 - 0 - 0 - 6 - 0 EEW Introduction to Machine Learning 1.

Unsupervised learning: vector quantization and clustering, k-means algorithm, spectral clustering7. Low dimensional structure in high dimensional data: PCA9. Sampling: Impulse train sampling—relationship between impulse trained sampled continuous-time signal spectrum and the DTFT of its discrete-time counterpart—scaling of the frequency axis—relationship between true frequency and digital frequency—reconstruction through sinc interpolation—aliasing—effects of oversampling—discrete-time processing of continuous-time signals.

FIR Filter Design: Review of conditions needed for precise linear phase--design techniques for linear phase FIR filters: a windowing method, b frequency sampling, c weighted Chebyshev approximation. Quantization Effects: Review of binary representation of numbers--truncation and rounding--coefficient quantization--roundoff noise--interaction of roundoff noise and dynamic range--scaling for parallel and cascade forms--limit-cycle oscillations--state-space structures--error spectrum shaping via feedback.

Review of Probability, Statistics and Random Processes: Random process characterization—bias and variance—ergodicity. Autoregressive Spectral Estimation: Properties of AR processes: connection to linear prediction and the minimum-phase property—Levinson-Durbin recursion—lattice filter representation—implied ACF extension—connection to maximum entropy spectral estimation—MLE of AR parameters—statistics of the MLE—spectral flatness measure and the effects of noise on the AR spectral estimator—AR spectral estimation algorithms auto-correlation, covariance, modified covariance, and Burg —model order selection.

Basics of Gaussian beam optics and use in imaging confocal. Introduction to complex light: propagation invariant beams Bessel, Airy and Laguerre-Gaussian modes3. Dynamic diffractive optics: spatial light modulators and digital micro mirror devices for complex light generation4. Complex light for imaging, e. Basics of optical micromanipulation, complex light for micromanipulation6. Complex light for enhanced depth penetration: biomedical studies, multimode fibres and applications 6 2 - 0 - 0 - 0 - 6 - 0 EE Nonlinear Systems Analysis 1.

Mathematical preliminaries: Open and closed sets, compact set, dense set, Continuity of functions, Lipschitz condition, Vector space, norm of a vector, normed linear space, inner product space. Examples of nonlinear systems drawn from mechanical, electrical, biological and chemical systems.

Notion of equilibrium points and operating points, Jacobian linearization. Second-order nonlinear systems , vector field, trajectories, flow, vector field plot, phase-plane portrait and positively invariant sets. Classification of equilibrium points based on the eigenvalues of the linearized system.

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