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Structure of Innovative MSc educational program «Navigation and Control in space»

This is the MSc program for the space and aviation industry. The students in mind are from scientific research and instrument making companies, the specialized design teams, developing integrated navigation and motion control systems.

Study Program consists of four parts:

1. Basic Courses
2. Special Courses
3. Workshop studies
4. Master's thesis

The basic lecture courses are read at MSU math department for more than ten years and provide a foundation for master's education. The content of these courses is constantly updated and modified in line with modern scientific trends and requirements of practice.

Special courses are aimed at teaching effective techniques of navigation, control and estimation, application of these methods to the challenges of inertial, satellite and personal navigation, airborne gravimetry, biomechanics, robotics. These courses are based on long experience of cooperation of the Department of Applied Mechanics and Control, and the Laboratory of Control and Navigation, Mechanics and Mathematics Department MSU with leading Russian companies involved in integrated navigation and control systems.

1. Basic courses: Methods of analysis and synthesis

• Foundations of celestial and analytical mechanics
• Stability and stabilization of aerospace systems
• Basics of inertial and satellite navigation
• Applied theory of estimation and control
• Fractional analysis of approximate models
• Elements of theory of random processes

2. Special courses

Navigation algorithms:

• Mechanics of navigation systems
• Theory of inertial navigation systems (INS)
• Theory of global positioning systems (GPS and GLONASS)
• Optimal estimation theory with applications to navigation
• Navigation applications - calibration of INS, initial alignment of INS at static site and in motion, integration of INS and GPS (loose, tight)
• Mathematical methods of the airborne gravimetry

Control algorithms:

• Functional analysis and optimal control
• Numerical methods of estimation and control
• Maximin testing of quality of stabilization
• Computer analysis of controlled mechanical systems
• Stabilization of satellites around the center of gravity
• Control of mobile robots
• Time-dependent dynamic systems in navigation and control
• Fuzzy artificial neural networks, wavelets, geometric game)
• Correlation theory of random processes and stochastic identification
• Perturbation theory in navigation and control of motion
• Robust control and Matlab programming

Personal navigation and semi-automatic control:

• Elements of personal navigation
• Reactions of human body to physical factors in aviation and spacecrafts
• Mathematical models of the excitable cellular membranes

3. Workshops

• Optimal control of a perturbed system
• Global positioning systems: GLONASS, GPS
• Testing quality of control for aerospace systems
• Control of inverted pendulum
• Control of levitating disk
• Calibration of strapdown IMU

Out workshops includes a number of a inertial and satellite navigation equipment, precise gyroscopes and accelerometers, computer equipment and software, a number of a commercial mechatronic equipment.

The navigation equipment is used in the workshop "Satellite navigation systems". High precision gyroscopes and accelerometers are used in the workshop, "Functional analysis and optimal control". Virtual reality equipment is used in the workshop "Testing Quality of aerospace control".

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