Basic mathematical concepts: Finite dimensional optimization, Infinite dimensional optimization, Con- ditions for optimality, Performance measures for optimal control problems. Dynamic programming: The optimal control law, The principle of optimality, Dynamic programming concept, Recurrence relation, computational procedure, The Hamilton-Jacobi-Bellman equations.

Role of Interface Electronics, Example: Linear Position Sensing, Signal conditioners + ADC, Contactless potentiometer (resistance-capacitance scheme) – Methodology, Interface Circuits, Need of Current/Pneumatic Transmission, Analog Electronic Blocks, OPAMP – internal struc- ture, Open-loop gain, Input R, Output R, DC noise sources and their drifts, CMRR, PSRR, Band- width and stability, Slew rate, Noise – general introduction and noise in opamps and their anal- ysis, Noise-equivalent Bandwidth, Output voltage swing, Compensation Techniques.

Introduction: Parametric models of dynamical systems, Adaptive control problem Real time pa- rameter estimation: Least squares and regression models, Estimating parameters in Dynamical Systems, Experimental conditions, Prior information, MLE, RLS, Instrument variable method. Deterministic Self tuning regulators (STR): Pole placement design, Indirect self-tuning regula- tors, Continuous time self-tuners, Direct self-tuning regulators, disturbances with known charac- teristics.

Basics: Control system representations, System stabilities, Coprime factorization and stabilizing controllers, Signals and system norms Modelling of uncertain systems: Unstructured Uncertain- ties, Parametric uncertainty, Linear fractional transformation, Structured uncertainties.

Robust design specifications: Small gain theorem and robust stabilization, Performance con- siderations, Structured singular values.

Design: Mixed sensitivity optimization, 2-Degree of freedom design, Sub-optimal solutions, Formulae for discrete time cases.

Introduction to Power Semiconductor devices, Device Basic Structure and Characteristics , High current effects in diodes, Breakdown considerations for various devices, Junction Termination techniques for increasing breakdown voltage, edge termination in devices, beveling, open base transistor breakdown Structure & Performance of Schottky and PIN Power Diodes , Parasitic Circuit Elements in Power Diode Rectifiers, Circuit Requirements for Power Transistor Switches, Structure& Performance of Power Transistors: a. MOSFETs; b.

Noise pickup modes and reduction techniques for analog circuits.Use of co-axial cables. Con- ducted and radiated noise emission and control in power circuits. EMI induced failure mecha- nisms in power circuits. Power supply and ground line distribution in digital circuits. Cross talk and reflection issues in digital circuits.PCB design for signal integrity.Shielding of electronic equipment.ESD issues. EMC standards and test equipment.

Fundamentals of Semiconductors: Carrier concentration of semiconductor, Transport Equations, P-N Junction Diode, Schottky Junction Diode and MOSFET. Fundamentals of Compound Sem- iconductors: Introduction of Compound Semiconductors, Properties of Compound semiconduc- tors, Synthesis of Compound Semiconductors.

Introduction: Review of transmission lines; surge impedance loading; voltage profile along ra- dial and symmetrical lines, Ferranti effect, load flow analysis. Power systems dynamics, stability analysis, role of reactive power compensators; series, shunt and unified compensation; effect on power flow and voltage profile.

Active Front End Rectifiers: Power factor correction, single-phase and three-phase, vector control schemes. Operation and control of Grid-connected converters such as UPF FEC, STATCOM, UPS, harmonic compensator etc.

Power converters for microgrid and grid connection of renewable energy sources: design, control of converters, grid synchronization and filtering requirements, MPPT.

Lifetime estimation of power converters: Capacitor currents for various topologies, switch currents, thermal models and impact on lifetime.

Linear Algebra:

(a) Vector Spaces: Definition of Vector space, Sub spaces, linearly independence and depend- ence,linear Span, Basis, Dimension

(b) System of linear equations: Range space and Null space of a matrix, Rank of a matrix, Ex- istence and uniqueness of solution of the system of linear equations, Dimension of the Solution Space associated with the system of linear equations

(c) Eigen values and Eigen vectors: Definition of Eigen values and Eigen vectors of a square matrix and their properties including similarity matrices