Machine learning basics: capacity, overfitting and underfitting, hyperparameters and validation sets, bias & variance; PAC model; Rademacher complexity; growth function; VC-dimension; fundamental concepts of artificial neural networks; single layer perceptron classifier; multi- layer feed forward networks; single layer feed-back networks; associative memories; introduc- tory concepts of reinforcement learning, Markhov decision process.

Optimization: need for unconstrained methods in solving constrained problems, necessary con- ditions of unconstrained optimization, structure methods, quadratic models, methods of line search, steepest descent method; quasi-Newton methods: DFP, BFGS, conjugate-direction meth- ods: methods for sums of squares and nonlinear equations; linear programming: simplex meth- ods, duality in linear programming, transportation problem; nonlinear programming: Lagrange multiplier, KKT conditions, convex programing

Linear Algebra: n- dimensional Euclidean spaces, linear transformation, Matrices, Eigen values and Eigen vectors, Generalised inverses, SVD.

Numerical Methods: Numerical Solution of nonlinear equations, Direct and iterative methods to solve system of linear equations, Numerical integration – Trapezoidal and Simpson’s rule, Interpolation, Splines and curve fitting, Numerical solution of ODE – Euler’s method and 4th order Runge- Kutta Method.

Dynamic model of DC-DC converters in DCM: averaged switched model, small signal model- ling of the low frequency model. High frequency dynamics of converter operating in DCM.

Forced commutated AC-AC converters – Matrix Converters: operation, topologies, commutation strategies, voltage modulation – Direct and Indirect schemes.Dynamic model, design of passive elements and control scheme.

Basic Concepts of dynamical systems and stability.Modelling of power system components for stability studies: generators, transmission lines, excitation and prime mover controllers, flexible AC transmission (FACTS) controllers.

Introduction: Nonlinear system behavior, Nonlinear control.

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.