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Special Courses

Applied Robust Control

• Controlled systems, feedback, frequency response. Bode diagram, Nyquist diagram. PID-regulator. The concept of robustness. Frequency criteria of robustness in amplitude and phase.
• H - infinity optimization in time domain. Two Riccati theorem. Relations to game theory. Interpretation of H-infinity in frequency domain. Uncertainty. Small gain theorem.
• Digital control of mechanical systems. Sampling, its impact on stability and quality. Robust sampling algorithms.
• The concept of control and controllability in nonlinear systems. Controllability of non-holonomic systems. Wheeled vehicle control.

Data processing in airborne gravimetry

• Earth gravity model. Geoid, normal gravity, free air anomaly, topographic corrections, and transformations. Spherical harmonics, EGM-96. Stochastic models. Gravimeters. Principles of operation, error models. Stabilized platform and strapless systems. The gravimetric equation. Scalar and vector cases. Error budget. Gravity anomaly on a trajectory. Regularization, reduction to MLE, extended Kalman filter. Adaptive approach with wavelet analysis.
• Maps. Accuracy and resolution. Leveling, smoothing across lines. Map transformations. Fourier, Vening Meinesz. Remove and restore technique. Practice of data processing and software development. Data quality control. Field operation and post flight processing.

Signal processing

• Over determined linear systems. o Matrix decomposition: QR, SVD. Least squares estimation (LS), total least squares techniques (TLS), restricted total least squares (RTLS). L1- optimization, reduction to linear and quadratic programming.
• Filters. The concept a signal and a noise. Definition FIR and IIR filters. Frequency and impulse response. Elementary filters - differentiation, integration, simple average link. Classic smoothing filters-Hanning, Hamming, Butterworth. Z-transformation.
• Fourier series, continuous and discrete Fourier transform. Gibbs effect. Ideal filter with specified frequency response and its truncation. Data sampling. Theorem of Shannon-Kotelnikov.
• Stationary random processes and their spectral representation. Spectral factorization of spectral density. Identification of random processes. Classic spectral estimation methods. Periodograms. Parametric methods of spectral estimation. AR, ARMA identification. Optimal estimation of random processes. Kalman filter.

Theory of Inertial Navigation

• Method of the inertial navigation. Coordinates, coordinates frames and transforms. Shape of the Earth, navigation ellipsoids, gravity and gravitation. Instrument trihedron. Autonomous inertial navigation. The general structures of the position, velocity, attitude differential equations.
• Inertial sensors: accelerometers and gyros. Typical model of the instrumental errors of the inertial sensors: biases, scale factors, misalignments.
• Modeling equations of a inertial navigation systems (INS): inertia basic trihedron, Greenwich basic trihedron, geographical basic trihedron (different laws of the azimuth orientation). Modeling attitude equations of the strapdown inertial navigation systems (SINS). Numeric methods.
• INS, SINS error models. Ideal (basic), instrumental, modeling trihedrons, vectors of small turn. Dynamic and kinematic components of the whole position and velocity errors, attitude errors. Different forms of the INS error equations and its properties: Schuler oscillations and altitude instability.

Theory of the Global Positioning Navigation Systems (GNSS): GPS and GLONASS

• GPS and GLONASS systems description: space, ground, user segments, satellites orbits, constellation, GNSS receivers. GNSS signals and observables: C/A and P(Y) codes, L1 L2 signals, code, Doppler observables, carrier phases. Standard, differential, relative modes of the GNSS operation. PDOP conception.
• Motion of the GNSS satellites. Kepler's laws. Orbital elements, coordinates frames and transforms. Satellite position and relative velocity determination from GPS broadcast ephemeris parameters. Satellite position and relative velocity determination from GLONASS broadcast ephemeris parameters.
• Models of the GNSS observables: code, Doppler, carrier phases. GNSS systems errors: ephemeris errors, satellite clock errors, receiver clock errors, ionospheric and tropospheric delays, multipath effects, relativistic corrections, integer ambiguity of the carrier phases. Single, double, triple differences.
• User position, velocity, acceleration from GNSS code, Doppler, carrier phase observables in standard, differential, relative mode of GNSS. Dual system, dual frequency solutions.
• RINEX format, precise ephemeris IGS data, CODE data for ionospheric delays modeling.

Elements of the estimation theory with application to navigation

• Over determined linear system. Least squares method (LSM), pseudo inverse matrix, SVD decomposition. Singular values as measures of observability. LSM and spline smoothing.
• General linear estimation problem statement. Criterion of a minimum of a dispersion, criterion of orthogonality, criterion of conditional mean. The normal distribution. Concepts of a-priori and a-posteriori estimates.
• Stochastic linear discrete estimation problem. Discrete Kalman filter. Square root method for Kalman filter: S and U-D modifications. Smoothing problem: forward and backward Kalman filters. Fixed point smoothing algorithm. Continuous Kalman filter. Riccati equation. Theorems of the stability. Stochastic measure of observability and estimation problem reduction.
• INS, SINS inertial sensors calibration and compensation. Models of the instrument errors of the accelerometers, mechanical , optical gyros: scale factors, bias, misalignment. Accelerometers and gyros composite errors. Multi-position rotating test bench for calibration.
• INS, SINS alignment at the static site. Coarse and fine alignment. Double gyrocompassing. Alignment with given heading.
• Two approaches to the correction problem in inertial navigation:
  1. Direct INS errors estimation and its external compensation;
  2. Modification of the navigation modeling equations: feedback to navigation algorithms using external measurements.
• Loose GNSS-INS integration algorithms. Tight GNSS-INS integration algorithms ( code, Doppler, carrier phase GNSS observables). Ground vehicle integrated navigation: INS, GNSS, odometers, zero velocity update technology. INS (SINS) alignment in motion.

Attitude stabilization systems for satellite

• Frames of reference. Satellite orbit. Problem of attitude stabilization. Kinematics equations. Dynamics equations of the motion around center of masses for rigid body with rotating masses.
• Perturbation moments acting at the satellite - gravitational moment, magnetic moment, aerodynamic moment, moment from the forces of solar pressure.
• Passive stabilization systems: advantages and disadvantages. Idea for gravity-gradient stabilization. Magnetic, aerodynamic, spin stabilization.
• Active stabilization systems: advantages and disadvantages. Thrusters. Three-axes stabilization using reaction wheels (momentum wheels). Magnetorquers. Combined stabilization systems.
• Measurement units. Optic-electro sensors. Domestic vertical constructer. Solar sensor. Magnetometer. Gyro sensors. Angular velocities measurement. Micro-electro-mechanical (MEMS) units. MEMS gyroscope operation basics.
• Stabilization system for satellite with flexible elements.

Computer analysis of controlled mechanical systems

• MATLAB - software for scientific and engineering computations. MATLAB commands. MATLAB language and programming. Matrix algebra in MATLAB. Results visualization. Solution of linear and nonlinear equation systems. Minimization problem. Ordinary differential equation solution with MATLAB and SIMULINK. SIMULINK programs usage to control program making. Problems of hard system integration. Controlled systems analysis and synthesis of regulators in MATLAB.
• Robust control. Data filtering in MATLAB. Fourier analysis in MATLAB.
• MAPLE - system of symbolic calculation. Commands and functions. Differentiation and integration, simplification of results. Graphics and visualization. Ordinary and differential equation solution. Lagrange equation deduction.

Robust Stability and Control

• Controlled systems, program control, feedback, Laplace transform, frequency response. Robustness. P and PD-regulators with full state-space information. Frequency criteria of robustness in amplitude and phase.
• Output feedback with regular errors. PID-regulator - the simplest adaptation algorithms. Regulators with prescription of system pole placements. Uncertainty. Robust stability and stabilization. Kharitonov's theorem. Small gain theorem. H - infinity stabilization in time domain. Two Rikkati theorem.
• Robustness of nonlinear systems.
• Application to mechanical systems: active suspension of road vehicles.

Mathematical models of the excitable cellular membranes

• Cells and their general characteristics. The plasmatic membrane of a cell, its structure, types of plasmatic membranes. Methods of studying cell's structure and functioning .
• Mathematical models of natural processes. Model of a predators and their prey population. Model of a process in a reactor of yeast. Bolzman's equation for probability of system transitions from one stationary power level to another.
• The ionic channels of plasmatic membranes. The ions moving under the diffusion laws and under electric gradient. Nerst-equation for equilibrium potential, activation and inactivation of the ionic channels. Cells of nervous system of animals: neurons and sensors of the primary information.
• Vestibular system of animals, its structure and functions. Sensors of the vestibular information. The hair cells (morphology, combination of ionic channels in membranes). The primary neurons. Methods for studying of the vestibular systems. Experiments on rotating platforms. (Goldberg-Fernandez's experiment et al.).
• Characteristics of signals from vestibular sensors. Frequency modulation, regularity and irregularity. Noise immunity, sensitivity, speed, adaptation.

Maximin tests of motion stabilization quality

• The course explains a new approach to testing of control systems, which provides objective rating of human operation in extreme conditions. The test disturbances and the limits of stabilization quality are evaluated by solving a special differential game. The course discusses approaches to solving such games.
• Maximin tests of control quality are a high priority when faulty control yields great or unacceptable losses, like in semi-automatic control of spacecrafts.

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