MAE 546
Optimal Control
This course covers the main principles of optimal control theory applied to deterministic continuous-time problems and provide guidance on numerical methods for their solution. Fundamental results are reached starting with parameter optimization, the calculus of variations, and finally Pontryagin¿s principle(s), dynamic programming and the Hamilton-Jacobi-Bellman equation. Geometric and analytic properties of the formulations and solutions are highlighted. Numerical methods for direct and indirect optimal control problems are covered with applications. Emphasis is placed on intuition between the various aspects of the course.
Please see the Princeton Registrar for additional information.
MAE 342
Space System Design
This course provides a compact introduction to aerospace system engineering and management, as well as design and analysis of key aerospace subsystems. Concurrent to lectures and guest speakers, students complete a semester-long group project to design a space system. The semester design topic, objectives and requirements vary upon each offering. Along with learning the technical aspects of aerospace system design, students also get the chance to work on their professional writing and presentation skills with preliminary and critical design reviews.
Please see the Princeton Registrar for additional information.
MAE 341
Space Flight
Prof. Beeson provides three to four guest lectures for this course on the topic of spacecraft attitude control and dynamics. Starting from basic definitions of attitude coordinates (direction cosine matrix, Euler angles, and quaternions) we develop kinematic differential equations and discuss the properties of each representation. We then move onto rigid body dynamics, covering Euler’s rotational equations of motion, rigid body rotation, rotational stability, dual spin spacecraft, and gravity gradient torque.
Please see the Princeton Registrar for additional information.
MAE 433
Automatic Control Systems
This is a first course on control theory, covering both topics in classical (frequency-based) control and modern (state-space) control. The focus is on linear time invariant systems. Frequency-based techniques such as the root locus method, Bode plots, and Nyquist diagrams and stability are covered. Controllability, linear quadratic regulators, and observability are some of the highlights from the state-space portion of the course. Lectures are accompanied by terrific hands-on lab sections that were developed by Prof. Michael Littman, Prof. Clancy Rowley, and Jon Prevost over several years. Students implement control laws to control DC motors and inverted pendulums via Matlab Simulink and are introduced to digital control implementations as well.
Please see the Princeton Registrar for additional information.
MAE 575 / ECE 535
Data Assimilation
This course provides a broad introduction to data assimilation, which consists of the mathematical problem of solving for a conditional probability distribution for a signal process given partial noisy observations. We begin the course by focusing on the discrete-time signal and observation case before transitioning in the second half to the continuous-time signal and observation scenario. In between we review a number of versatile solution approaches, including variational methods, ensemble/particle methods, and Markov Chain Monte Carlo (MCMC). Highlights include both the Kalman and Kalman-Bucy filters, as well as Extended, Ensemble, and Unscented varieties. In the continuous-time case, a soft derivation of the Kushner-Stratonovich and Zakai equations are completed after a gentle introduction of stochastic calculus. A review of measure theoretic probability, with a strong focus on the Gaussian case, is provided at the start of the course. Students submit a short paper and give a presentation at the end of the semester on a topic related to the course material; often connected to their research.
Please see the Princeton Registrar for additional information.
MAE 342
Space System Design
This course provides a compact introduction to aerospace system engineering and management, as well as design and analysis of key aerospace subsystems. Concurrent to lectures and guest speakers, students complete a semester-long group project to design a space system. The semester design topic, objectives and requirements vary upon each offering. Along with learning the technical aspects of aerospace system design, students also get the chance to work on their professional writing and presentation skills with preliminary and critical design reviews.
Please see the Princeton Registrar for additional information.
MAE 341
Space Flight
Prof. Beeson provides three to four guest lectures for this course on the topic of spacecraft attitude control and dynamics. Starting from basic definitions of attitude coordinates (direction cosine matrix, Euler angles, and quaternions) we develop kinematic differential equations and discuss the properties of each representation. We then move onto rigid body dynamics, covering Euler’s rotational equations of motion, rigid body rotation, rotational stability, dual spin spacecraft, and gravity gradient torque.
Please see the Princeton Registrar for additional information.
MAE 546
Optimal Control
This course provides a rigorous introduction to optimal control for deterministic systems and provides a preview of extensions to the stochastic case. To prime the course we begin with reviewing parameter optimization problems and in particular the Karush-Kuhn-Tucker conditions for nonlinear programming. We then develop necessary and sufficient conditions from the Calculus of Variations, including the Euler-Lagrange equation, Legendre’s conditions, and those named after Weierstrass and Weierstrass-Erdmann. Corner stones of the course include proofs of Pontryagin’s Maximum Principle and the Hamilton-Jacobi-Bellman (HJB) equation, both with applications to finite and infinite-horizon Linear Quadratic Regulator (LQR) problems. The tailend of the course provides a succinct development of Ito’s calculus and then presentation of Pontryagin’s principle and HJB in the stochastic case. Students submit a short paper and give a presentation at the end of the semester on a topic related to the course material; often connected to their research.
Please see the Princeton Registrar for additional information.