Prerequisite: Linear algebra, Probability, and interest in programming

PR overview ‐ Feature extraction ‐ Statistical Pattern Recognition ‐ Supervised Learning ‐ Parametric methods ‐ Non-parametric methods; ML estimation ‐ Bayes estimation ‐ k NN approaches. Dimensionality reduction, data normalization. Regression, and time series analysis. Linear discriminant functions. Fisher's linear discriminant and linear perceptron. Kernel methods and Support vector machine. Decision trees for classification. Unsupervised learning and clustering. K ‐ means and hierarchical clustering. Decision Trees for classification.

The course is an introductory level computer vision course, suitable for graduate students. It will cover the basic topics of computer vision, and introduce some fundamental approaches for computer vision research: Image Filtering, Edge Detection, Interest Point Detectors, Motion and Optical Flow, Object Detection and Tracking, Region/Boundary Segmentation, Shape Analysis, and Statistical Shape Models, Deep Learning for Computer Vision, Imaging Geometry, Camera Modeling, and Calibration. Recent Advances in Computer vision.

Fractional Calculus: Review of basic definitions of integer‐order (IO) derivatives and integrals and their geometric and physical interpretations, Definition of Riemann‐Liouville (RL) integration, Definitions of RL, Caputo and Grunwald‐Letnikov (GL) fractional derivatives (FDs), Various geometrical and physical interpretations of these FDs, Computation of these FDs for some basic functions like constant, ramp, exponential, sine, cosine, etc., Laplace and Fourier transforms of FDs.

Introduction, discrete systems, basic signal theory, Open‐loop LTI SISO systems, time domain, frequency domain Least Squares Estimation, Covariance in Stationary, Ergodic Processes, White Noise, Detection of Periodicity and Transmission Delays, ARMA Processes.

Introduction and Background of state-of-art sensing and measurement techniques. Contactless potentiometer (resistance-capacitance scheme) – Methodology, Interface Circuits, Overview of Flight Instrumentation. Analog Electronic Blocks, CMRR Analysis (Non-ideal opamps) of an Instrumentation Amplifier, Linearization circuits for single-element wheatstone bridges (application to strain gauge), Direct Digital Converter for Strain gauges, Signal conditioning for Remote-connected sensor elements.

Attitude Kinematics: Particle Kinematics and Vector Frames, Angular Velocities, Vector Differentiation and the Transport Theorem, Rigid Body Kinematics, Direct Cosine Matrix (DCM), Euler Angles, Quaternions, Differential Kinematic Equations, Attitude Determination using TRIAD Method and QUEST Methods.

Vector and matrix Norms, Signal and System Norms, Singular Value Decomposition, Coprime factorization, LMIs, System representation, Sensitivity and Complementary sensitivity functions, pole and zero directions, performance imitations, well posedness, internal stability of feedback system, Nyquist plot, small gain theorem, Uncertainty representation (structured/parametric and unstructured), robust stability and robust performance, structured singular values, Kharitonov’s theorem, linear fractional transformation, stabilizing controllers, H- infinity controllers, μ synthesis, applications of

Coordinate systems, Attitude dynamics and control, Rotational kinematics, Direction cosine matrix, Euler angles, Euler’s Eigen axis rotation, Quaternions, Rigid body dynamics of launch vehicle, Angular momentum, Inertia matrix, Principal axes, Derivation of dynamic equations, Effect of aerodynamics, structural dynamics and flexibility, propellant sloshing, actuator dynamics, gimballed engine dynamics, External forces and moments, Linear model for Aero‐structure‐control‐slosh interaction studies.

Prerequisites: Vector Spaces (Linear Algebra)

An introduction to differentiable manifolds, tangent ff vectors, vector fields, co vector fields, immersions and submersions, Lie groups, actions of groups, Lie algebras, adjoint co‐adjoint maps, symmetries. Vector fields, integral curves, push‐forward and pull‐back, differential forms and Riemannian geometry.

Euler Poincare reduction for the rigid body and heavy top, satellite dynamics and control with coordinate free models, inverted pendulum on a cart.