Laboratory for Autonomy in Data-Driven and Complex Systems: Teaching
Flight Vehicle Dynamics
- Write equations of translational motion of aircraft and spacecraft, i.e. their motion as a dimensionless particle of finite mass,
- Write nonlinear equations for six degree of freedom motion of aircraft,
- Analyze dynamic aircraft flight conditions using the nonlinear equations of motion,
- Use small perturbation theory to identify flight modes and understand static and dynamic stability,
- Identify appropriate attitude parameterization for rigid bodies,
- Analyze free and forced rotational dynamics of rigid bodies, with application to aircraft and spacecraft
Stability and Control of Flight Vehicles
- Analyze free and forced rotational dynamics of rigid bodies
- Write nonlinear equations for six degree of freedom motion of aircraft
- Analyze dynamic aircraft flight conditions using the nonlinear equations of motion
- Use small perturbation theory to identify flight modes and understand static and dynamic stability
- Use feedback control tools to design stability augmentation systems for aircraft
- Use feedback control design tools to achieve automatic response holds and attitude control, i.e. autopilot design
AAE 8194: Random Dynamical Systems
The objective of this course is the treatment of stochastic dynamic systems encountered in science and engineering. We begin with the fundamentals of deterministic dynamical systems, axiomatic theory of probability as developed by Kolmogorov, and measure theory.
Focus then shifts to the practice of uncertainty analysis in nonlinear dynamic systems, including the exploration of existing tools such as generating functions, numerical simulations, sequential Monte Carlo, stochastic linearization, moment closure, Fokker-Planck equations and Bayesian data fusion. Broad ranging applications in uncertainty forecasting and nonlinear parameter and state estimation will be studied.
Robust Multivariable Control with Applications
- Have a solid grasp of linear algebra tools central to the analysis and design of robust control systems,
- Understand and compute the H-2 and H-infinity norms and their role in characterizing system stability and performance,
- Understand the notion of a system's internal stability and apply various tests to evaluate it,
- Apply the principles of linear fractional transformations and structured singular value analysis, i.e. mu-synthesis
- Pose and solve H-2 and H-infinity control problems
ME 8518/AAE 8802
Advanced Mathematical Methods
The objective of this course is to introduce to the mechanical/aerospace engineering graduate students some important mathematical methods commonly used for conducting research. The methods are mainly derived from two core areas:
(i.) differential equations and
(ii.) applied linear algebra.
To a lesser extent, some components will also be derived from statistics and probability theory. The course will focus more on the practice of mathematical methods, i.e. their implementational aspects rather than their theoretical aspects.
From differential equations, we will consider series approximations, initial and boundary value problems, special functions and inverse methods.
From linear algebra, we will consider vector spaces, approximation theorems, matrix algebra and decompositions.
From probability theory, we will consider error analysis and estimation methods.
Upon completion of this course, the student should be favorably situated to derive/design and analyze mathematical models from physical situations